diff --git a/404.html b/404.html
index a034fe6..4619e08 100644
--- a/404.html
+++ b/404.html
@@ -6,28 +6,28 @@
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Page not found (404) • graphicalMCP</title>
-<!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="https://gilead-biostats.github.io/graphicalMCP/favicon-16x16.png">
-<link rel="icon" type="image/png" sizes="32x32" href="https://gilead-biostats.github.io/graphicalMCP/favicon-32x32.png">
-<link rel="apple-touch-icon" type="image/png" sizes="180x180" href="https://gilead-biostats.github.io/graphicalMCP/apple-touch-icon.png">
-<link rel="apple-touch-icon" type="image/png" sizes="120x120" href="https://gilead-biostats.github.io/graphicalMCP/apple-touch-icon-120x120.png">
-<link rel="apple-touch-icon" type="image/png" sizes="76x76" href="https://gilead-biostats.github.io/graphicalMCP/apple-touch-icon-76x76.png">
-<link rel="apple-touch-icon" type="image/png" sizes="60x60" href="https://gilead-biostats.github.io/graphicalMCP/apple-touch-icon-60x60.png">
-<script src="https://gilead-biostats.github.io/graphicalMCP/deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
-<link href="https://gilead-biostats.github.io/graphicalMCP/deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
-<script src="https://gilead-biostats.github.io/graphicalMCP/deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="https://gilead-biostats.github.io/graphicalMCP/deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet">
-<link href="https://gilead-biostats.github.io/graphicalMCP/deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="https://gilead-biostats.github.io/graphicalMCP/deps/headroom-0.11.0/headroom.min.js"></script><script src="https://gilead-biostats.github.io/graphicalMCP/deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="https://gilead-biostats.github.io/graphicalMCP/deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="https://gilead-biostats.github.io/graphicalMCP/deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="https://gilead-biostats.github.io/graphicalMCP/deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="https://gilead-biostats.github.io/graphicalMCP/deps/search-1.0.0/fuse.min.js"></script><script src="https://gilead-biostats.github.io/graphicalMCP/deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="https://gilead-biostats.github.io/graphicalMCP/pkgdown.js"></script><meta property="og:title" content="Page not found (404)">
-<meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png">
+<!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="https://openpharma.github.io/graphicalMCP/favicon-16x16.png">
+<link rel="icon" type="image/png" sizes="32x32" href="https://openpharma.github.io/graphicalMCP/favicon-32x32.png">
+<link rel="apple-touch-icon" type="image/png" sizes="180x180" href="https://openpharma.github.io/graphicalMCP/apple-touch-icon.png">
+<link rel="apple-touch-icon" type="image/png" sizes="120x120" href="https://openpharma.github.io/graphicalMCP/apple-touch-icon-120x120.png">
+<link rel="apple-touch-icon" type="image/png" sizes="76x76" href="https://openpharma.github.io/graphicalMCP/apple-touch-icon-76x76.png">
+<link rel="apple-touch-icon" type="image/png" sizes="60x60" href="https://openpharma.github.io/graphicalMCP/apple-touch-icon-60x60.png">
+<script src="https://openpharma.github.io/graphicalMCP/deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<link href="https://openpharma.github.io/graphicalMCP/deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
+<script src="https://openpharma.github.io/graphicalMCP/deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="https://openpharma.github.io/graphicalMCP/deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet">
+<link href="https://openpharma.github.io/graphicalMCP/deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet">
+<script src="https://openpharma.github.io/graphicalMCP/deps/headroom-0.11.0/headroom.min.js"></script><script src="https://openpharma.github.io/graphicalMCP/deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="https://openpharma.github.io/graphicalMCP/deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="https://openpharma.github.io/graphicalMCP/deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="https://openpharma.github.io/graphicalMCP/deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="https://openpharma.github.io/graphicalMCP/deps/search-1.0.0/fuse.min.js"></script><script src="https://openpharma.github.io/graphicalMCP/deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="https://openpharma.github.io/graphicalMCP/pkgdown.js"></script><meta property="og:title" content="Page not found (404)">
+<meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png">
 </head>
 <body>
-    <a href="https://gilead-biostats.github.io/graphicalMCP/#main" class="visually-hidden-focusable">Skip to contents</a>
+    <a href="https://openpharma.github.io/graphicalMCP/#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
     <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="light" aria-label="Site navigation"><div class="container">
 
-    <a class="navbar-brand me-2" href="https://gilead-biostats.github.io/graphicalMCP/index.html">graphicalMCP</a>
+    <a class="navbar-brand me-2" href="https://openpharma.github.io/graphicalMCP/index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -36,28 +36,28 @@
 
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto">
-<li class="nav-item"><a class="nav-link" href="https://gilead-biostats.github.io/graphicalMCP/articles/graphicalMCP.html">Get started</a></li>
-<li class="nav-item"><a class="nav-link" href="https://gilead-biostats.github.io/graphicalMCP/articles/glossary.html">Glossary</a></li>
-<li class="nav-item"><a class="nav-link" href="https://gilead-biostats.github.io/graphicalMCP/reference/index.html">Function reference</a></li>
+<li class="nav-item"><a class="nav-link" href="https://openpharma.github.io/graphicalMCP/articles/graphicalMCP.html">Get started</a></li>
+<li class="nav-item"><a class="nav-link" href="https://openpharma.github.io/graphicalMCP/articles/glossary.html">Glossary</a></li>
+<li class="nav-item"><a class="nav-link" href="https://openpharma.github.io/graphicalMCP/reference/index.html">Function reference</a></li>
 <li class="nav-item dropdown">
   <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button>
   <ul class="dropdown-menu" aria-labelledby="dropdown-articles">
-<li><a class="dropdown-item" href="https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html">Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests</a></li>
-    <li><a class="dropdown-item" href="https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html">Graphical multiple comparison procedures based on the closure principle</a></li>
-    <li><a class="dropdown-item" href="https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html">Common multiple comparison procedures illustrated using graphicalMCP</a></li>
-    <li><a class="dropdown-item" href="https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html">Comparisons with other packages</a></li>
-    <li><a class="dropdown-item" href="https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html">Rationales to generate the closure and the weighting strategy of a graph</a></li>
+<li><a class="dropdown-item" href="https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html">Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests</a></li>
+    <li><a class="dropdown-item" href="https://openpharma.github.io/graphicalMCP/articles/closed-testing.html">Graphical multiple comparison procedures based on the closure principle</a></li>
+    <li><a class="dropdown-item" href="https://openpharma.github.io/graphicalMCP/articles/graph-examples.html">Common multiple comparison procedures illustrated using graphicalMCP</a></li>
+    <li><a class="dropdown-item" href="https://openpharma.github.io/graphicalMCP/articles/comparisons.html">Comparisons with other packages</a></li>
+    <li><a class="dropdown-item" href="https://openpharma.github.io/graphicalMCP/articles/generate-closure.html">Rationales to generate the closure and the weighting strategy of a graph</a></li>
     <li><hr class="dropdown-divider"></li>
-    <li><a class="dropdown-item" href="https://gilead-biostats.github.io/graphicalMCP/articles/index.html">More articles...</a></li>
+    <li><a class="dropdown-item" href="https://openpharma.github.io/graphicalMCP/articles/index.html">More articles...</a></li>
   </ul>
 </li>
-<li class="nav-item"><a class="nav-link" href="https://gilead-biostats.github.io/graphicalMCP/news/index.html">Changelog</a></li>
+<li class="nav-item"><a class="nav-link" href="https://openpharma.github.io/graphicalMCP/news/index.html">Changelog</a></li>
       </ul>
 <ul class="navbar-nav">
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -66,7 +66,7 @@
 </nav><div class="container template-title-body">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
-      <img src="https://gilead-biostats.github.io/graphicalMCP/logo.png" class="logo" alt=""><h1>Page not found (404)</h1>
+      <img src="https://openpharma.github.io/graphicalMCP/logo.png" class="logo" alt=""><h1>Page not found (404)</h1>
 
     </div>
 
@@ -81,7 +81,7 @@
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/LICENSE.html b/LICENSE.html
index 56a2e6b..ef0c5a0 100644
--- a/LICENSE.html
+++ b/LICENSE.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Apache License • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Apache License"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Apache License • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Apache License"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -31,7 +31,7 @@
 <li class="nav-item"><a class="nav-link" href="news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -40,7 +40,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="logo.png" class="logo" alt=""><h1>Apache License</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/LICENSE.md" class="external-link"><code>LICENSE.md</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/LICENSE.md" class="external-link"><code>LICENSE.md</code></a></small>
     </div>
 
 <div id="apache-license" class="section level1">
@@ -132,7 +132,7 @@ <h3 id="appendix-how-to-apply-the-apache-license-to-your-work">APPENDIX: How to
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/articles/closed-testing.html b/articles/closed-testing.html
index 2808830..cdb98d4 100644
--- a/articles/closed-testing.html
+++ b/articles/closed-testing.html
@@ -26,7 +26,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -56,7 +56,7 @@
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -72,7 +72,7 @@
       <img src="../logo.png" class="logo" alt=""><h1>Graphical multiple comparison procedures based on the closure principle</h1>
             
       
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/vignettes/closed-testing.Rmd" class="external-link"><code>vignettes/closed-testing.Rmd</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/vignettes/closed-testing.Rmd" class="external-link"><code>vignettes/closed-testing.Rmd</code></a></small>
       <div class="d-none name"><code>closed-testing.Rmd</code></div>
     </div>
 
@@ -82,7 +82,7 @@
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://gt.rstudio.com" class="external-link">gt</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/kornl/gMCP" class="external-link">gMCP</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">lrstat</span><span class="op">)</span></span>
-<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://gilead-biostats.github.io/graphicalMCP/">graphicalMCP</a></span><span class="op">)</span></span></code></pre></div>
+<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/openpharma/graphicalMCP" class="external-link">graphicalMCP</a></span><span class="op">)</span></span></code></pre></div>
 <div class="section level2">
 <h2 id="motivating-example">Motivating example<a class="anchor" aria-label="anchor" href="#motivating-example"></a>
 </h2>
@@ -1071,7 +1071,7 @@ <h2 class="unnumbered" id="reference">Reference<a class="anchor" aria-label="anc
 <div id="ref-sarkar-1998-some" class="csl-entry">
 Sarkar, Sanat K. 1998. <span>“Some Probability Inequalities for Ordered
 MTP2 Random Variables: A Proof of the Simes Conjecture.”</span>
-<em>Annals of Statistics</em> 26 (2): 494–504. <a href="https://www.jstor.org/stable/120038" class="external-link">https://www.jstor.org/stable/120038</a>.
+<em>Annals of Statistics</em> 26 (2): 494–504.
 </div>
 <div id="ref-xi-2017-unified" class="csl-entry">
 Xi, Dong, Ekkehard Glimm, Willi Maurer, and Frank Bretz. 2017. <span>“A
@@ -1091,7 +1091,7 @@ <h2 class="unnumbered" id="reference">Reference<a class="anchor" aria-label="anc
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/articles/comparisons.html b/articles/comparisons.html
index ccbd800..2c4eda3 100644
--- a/articles/comparisons.html
+++ b/articles/comparisons.html
@@ -26,7 +26,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -56,7 +56,7 @@
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -72,14 +72,14 @@
       <img src="../logo.png" class="logo" alt=""><h1>Comparisons with other packages</h1>
             
       
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/vignettes/comparisons.Rmd" class="external-link"><code>vignettes/comparisons.Rmd</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/vignettes/comparisons.Rmd" class="external-link"><code>vignettes/comparisons.Rmd</code></a></small>
       <div class="d-none name"><code>comparisons.Rmd</code></div>
     </div>
 
     
     
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://gilead-biostats.github.io/graphicalMCP/">graphicalMCP</a></span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/openpharma/graphicalMCP" class="external-link">graphicalMCP</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">lrstat</span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/kornl/gMCP" class="external-link">gMCP</a></span><span class="op">)</span></span></code></pre></div>
 <div class="section level2">
@@ -521,7 +521,7 @@ <h2 class="unnumbered" id="reference">Reference<a class="anchor" aria-label="anc
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/articles/generate-closure.html b/articles/generate-closure.html
index fe09c67..c269a72 100644
--- a/articles/generate-closure.html
+++ b/articles/generate-closure.html
@@ -26,7 +26,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -56,7 +56,7 @@
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -72,7 +72,7 @@
       <img src="../logo.png" class="logo" alt=""><h1>Rationales to generate the closure and the weighting strategy of a graph</h1>
             
       
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/vignettes/generate-closure.Rmd" class="external-link"><code>vignettes/generate-closure.Rmd</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/vignettes/generate-closure.Rmd" class="external-link"><code>vignettes/generate-closure.Rmd</code></a></small>
       <div class="d-none name"><code>generate-closure.Rmd</code></div>
     </div>
 
@@ -472,7 +472,7 @@ <h2 class="unnumbered" id="reference">Reference<a class="anchor" aria-label="anc
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/articles/glossary.html b/articles/glossary.html
index 6132dba..69ff8cb 100644
--- a/articles/glossary.html
+++ b/articles/glossary.html
@@ -26,7 +26,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -56,7 +56,7 @@
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -72,7 +72,7 @@
       <img src="../logo.png" class="logo" alt=""><h1>Glossary</h1>
             
       
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/vignettes/glossary.Rmd" class="external-link"><code>vignettes/glossary.Rmd</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/vignettes/glossary.Rmd" class="external-link"><code>vignettes/glossary.Rmd</code></a></small>
       <div class="d-none name"><code>glossary.Rmd</code></div>
     </div>
 
@@ -315,7 +315,7 @@
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/articles/graph-examples.html b/articles/graph-examples.html
index 558ccb3..91584da 100644
--- a/articles/graph-examples.html
+++ b/articles/graph-examples.html
@@ -26,7 +26,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -56,7 +56,7 @@
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -72,14 +72,14 @@
       <img src="../logo.png" class="logo" alt=""><h1>Common multiple comparison procedures illustrated using graphicalMCP</h1>
             
       
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/vignettes/graph-examples.Rmd" class="external-link"><code>vignettes/graph-examples.Rmd</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/vignettes/graph-examples.Rmd" class="external-link"><code>vignettes/graph-examples.Rmd</code></a></small>
       <div class="d-none name"><code>graph-examples.Rmd</code></div>
     </div>
 
     
     
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://gilead-biostats.github.io/graphicalMCP/">graphicalMCP</a></span><span class="op">)</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/openpharma/graphicalMCP" class="external-link">graphicalMCP</a></span><span class="op">)</span></span></code></pre></div>
 <div class="section level2">
 <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
 </h2>
@@ -765,7 +765,7 @@ <h2 class="unnumbered" id="reference">Reference<a class="anchor" aria-label="anc
 <div id="ref-holm-1979-simple" class="csl-entry">
 Holm, Sture. 1979. <span>“A Simple Sequentially Rejective Multiple Test
 Procedure.”</span> <em>Scandinavian Journal of Statistics</em> 75:
-65–70. <a href="http://www.jstor.org/stable/4615733" class="external-link">http://www.jstor.org/stable/4615733</a>.
+65–70.
 </div>
 <div id="ref-hommel-1988-stagewise" class="csl-entry">
 Hommel, Gerhard. 1988. <span>“A Stagewise Rejective Multiple Test
@@ -812,7 +812,7 @@ <h2 class="unnumbered" id="reference">Reference<a class="anchor" aria-label="anc
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/articles/graphicalMCP.html b/articles/graphicalMCP.html
index 63788f7..55d9ba6 100644
--- a/articles/graphicalMCP.html
+++ b/articles/graphicalMCP.html
@@ -26,7 +26,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -56,7 +56,7 @@
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -72,7 +72,7 @@
       <img src="../logo.png" class="logo" alt=""><h1>Get started</h1>
             
       
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/vignettes/graphicalMCP.Rmd" class="external-link"><code>vignettes/graphicalMCP.Rmd</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/vignettes/graphicalMCP.Rmd" class="external-link"><code>vignettes/graphicalMCP.Rmd</code></a></small>
       <div class="d-none name"><code>graphicalMCP.Rmd</code></div>
     </div>
 
@@ -107,7 +107,7 @@ <h3 id="initial-graph">Initial graph<a class="anchor" aria-label="anchor" href="
 end hypothesis. The edge is weighted by a transition weight indicating
 the proportion of propagation.</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://gilead-biostats.github.io/graphicalMCP/">graphicalMCP</a></span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/openpharma/graphicalMCP" class="external-link">graphicalMCP</a></span><span class="op">)</span></span>
 <span><span class="co"># A graph of two primary hypotheses (H1 and H2) and two secondary hypotheses (H3 and H4)</span></span>
 <span><span class="va">hypotheses</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">0.5</span>, <span class="fl">0</span>, <span class="fl">0</span><span class="op">)</span></span>
 <span><span class="va">transitions</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span></span>
@@ -287,7 +287,7 @@ <h2 class="unnumbered" id="references">References<a class="anchor" aria-label="a
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/articles/index.html b/articles/index.html
index 4d4dbb6..b0cf85f 100644
--- a/articles/index.html
+++ b/articles/index.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Articles • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Articles"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Articles • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Articles"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -31,7 +31,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -73,7 +73,7 @@ <h3>Glossary</h3>
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/articles/shortcut-testing.html b/articles/shortcut-testing.html
index 9e91c5a..2838650 100644
--- a/articles/shortcut-testing.html
+++ b/articles/shortcut-testing.html
@@ -26,7 +26,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -56,7 +56,7 @@
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -72,7 +72,7 @@
       <img src="../logo.png" class="logo" alt=""><h1>Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests</h1>
             
       
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/vignettes/shortcut-testing.Rmd" class="external-link"><code>vignettes/shortcut-testing.Rmd</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/vignettes/shortcut-testing.Rmd" class="external-link"><code>vignettes/shortcut-testing.Rmd</code></a></small>
       <div class="d-none name"><code>shortcut-testing.Rmd</code></div>
     </div>
 
@@ -80,7 +80,7 @@
     
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://gt.rstudio.com" class="external-link">gt</a></span><span class="op">)</span></span>
-<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://gilead-biostats.github.io/graphicalMCP/">graphicalMCP</a></span><span class="op">)</span></span></code></pre></div>
+<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/openpharma/graphicalMCP" class="external-link">graphicalMCP</a></span><span class="op">)</span></span></code></pre></div>
 <div class="section level2">
 <h2 id="motivating-example">Motivating example<a class="anchor" aria-label="anchor" href="#motivating-example"></a>
 </h2>
@@ -766,7 +766,7 @@ <h2 class="unnumbered" id="reference">Reference<a class="anchor" aria-label="anc
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/authors.html b/authors.html
index a87189a..22c29ed 100644
--- a/authors.html
+++ b/authors.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Authors and Citation • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Authors and Citation"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Authors and Citation • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Authors and Citation"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -31,7 +31,7 @@
 <li class="nav-item"><a class="nav-link" href="news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -61,18 +61,18 @@ <h2>Authors</h2>
 
     <div class="section level2">
       <h2 id="citation">Citation</h2>
-      <p><small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/inst/CITATION" class="external-link"><code>inst/CITATION</code></a></small></p>
+      <p><small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/inst/CITATION" class="external-link"><code>inst/CITATION</code></a></small></p>
 
       <p>Xi D, Brockmann E (2024).
-<em>graphicalMCP: Graphical multiple comparison procedures</em>, version 0.2.5 edition.
-<a href="https://github.com/Gilead-BioStats/graphicalMCP" class="external-link">https://github.com/Gilead-BioStats/graphicalMCP</a>.
+<em>graphicalMCP: Graphical multiple comparison procedures</em>, version 0.2.6 edition.
+<a href="https://CRAN.R-project.org/package=graphicalMCP" class="external-link">https://CRAN.R-project.org/package=graphicalMCP</a>.
 </p>
       <pre>@Manual{,
   title = {{graphicalMCP}: Graphical multiple comparison procedures},
   author = {Dong Xi and Ethan Brockmann},
-  edition = {version 0.2.5},
+  edition = {version 0.2.6},
   year = {2024},
-  url = {https://github.com/Gilead-BioStats/graphicalMCP},
+  url = {https://CRAN.R-project.org/package=graphicalMCP},
 }</pre>
     </div>
 
@@ -85,7 +85,7 @@ <h2 id="citation">Citation</h2>
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/index.html b/index.html
index 204cd40..10e15ea 100644
--- a/index.html
+++ b/index.html
@@ -19,7 +19,7 @@
 <script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Graphical Multiple Comparison Procedures">
 <meta name="description" content="Multiple comparison procedures (MCPs) control the familywise error rate in clinical trials. Graphical MCPs include many commonly used procedures as special cases; see Bretz et al. (2011) &lt;doi:10.1002/bimj.201000239&gt;, Lu (2016) &lt;doi:10.1002/sim.6985&gt;, and Xi et al. (2017) &lt;doi:10.1002/bimj.201600233&gt;. This package is a low-dependency implementation of graphical MCPs which allow mixed types of tests. It also includes power simulations and visualization of graphical MCPs.">
 <meta property="og:description" content="Multiple comparison procedures (MCPs) control the familywise error rate in clinical trials. Graphical MCPs include many commonly used procedures as special cases; see Bretz et al. (2011) &lt;doi:10.1002/bimj.201000239&gt;, Lu (2016) &lt;doi:10.1002/sim.6985&gt;, and Xi et al. (2017) &lt;doi:10.1002/bimj.201600233&gt;. This package is a low-dependency implementation of graphical MCPs which allow mixed types of tests. It also includes power simulations and visualization of graphical MCPs.">
-<meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png">
+<meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png">
 </head>
 <body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -29,7 +29,7 @@
 
     <a class="navbar-brand me-2" href="index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -59,7 +59,7 @@
 <li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json">
 </form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul>
 </div>
 
@@ -84,10 +84,21 @@ <h1 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#i
 <div class="section level1">
 <h1 id="installation">Installation<a class="anchor" aria-label="anchor" href="#installation"></a>
 </h1>
-<p><code>graphicalMCP</code> is currently not on CRAN but can be installed from GitHub using the following code:</p>
+<div class="section level3">
+<h3 id="release">Release<a class="anchor" aria-label="anchor" href="#release"></a>
+</h3>
+<p>You can install the current release version from <em>CRAN</em> with:</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/install.packages.html" class="external-link">install.packages</a></span><span class="op">(</span><span class="st">"graphicalMCP"</span><span class="op">)</span></span></code></pre></div>
+</div>
+<div class="section level3">
+<h3 id="development">Development<a class="anchor" aria-label="anchor" href="#development"></a>
+</h3>
+<p>You can install the current development version from <em>GitHub</em> with:</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># install.packages("pak")</span></span>
-<span><span class="fu">pak</span><span class="fu">::</span><span class="fu"><a href="https://pak.r-lib.org/reference/pak.html" class="external-link">pak</a></span><span class="op">(</span><span class="st">"Gilead-BioStats/graphicalMCP"</span><span class="op">)</span></span></code></pre></div>
+<span><span class="fu">pak</span><span class="fu">::</span><span class="fu"><a href="https://pak.r-lib.org/reference/pak.html" class="external-link">pak</a></span><span class="op">(</span><span class="st">"openpharma/graphicalMCP"</span><span class="op">)</span></span></code></pre></div>
+</div>
 </div>
 <div class="section level1">
 <h1 id="documentation">Documentation<a class="anchor" aria-label="anchor" href="#documentation"></a>
@@ -107,7 +118,7 @@ <h1 id="documentation">Documentation<a class="anchor" aria-label="anchor" href="
 <li>see <code><a href="articles/comparisons.html">vignette("comparisons")</a></code> for comparisons to other R packages</li>
 </ul>
 </li>
-<li>To view vignettes in R after properly installing <code>graphicalMCP</code> from GitHub, we can build vignettes by <code>devtools::install(build_vignettes = TRUE)</code>, and then use <code>browseVignettes("graphicalMCP")</code> to view the full list of vignettes</li>
+<li>To view vignettes in R after properly installing <code>graphicalMCP</code>, we can build vignettes by <code>devtools::install(build_vignettes = TRUE)</code>, and then use <code>browseVignettes("graphicalMCP")</code> to view the full list of vignettes</li>
 </ul>
 </div>
 <div class="section level1">
@@ -127,15 +138,16 @@ <h1 id="related-work">Related work<a class="anchor" aria-label="anchor" href="#r
 <h1 id="acknowledgments">Acknowledgments<a class="anchor" aria-label="anchor" href="#acknowledgments"></a>
 </h1>
 <p>Along with the authors and contributors, thanks to the following people for their suggestions and inspirations on the package:</p>
-<p>Frank Bretz, Willi Maurer, Ekkehard Glimm, Nan Chen, Jeremy Wildfire, Spencer Childress, Colleen McLaughlin, Matt Roumaya, Chelsea Dickens, and Ron Yu</p>
+<p>Frank Bretz, Willi Maurer, Ekkehard Glimm, Nan Chen, Jeremy Wildfire, Spencer Childress, Colleen McLaughlin, Matt Roumaya, Chelsea Dickens, Nan Xiao, Keaven Anderson, and Ron Yu</p>
 <p>We owe a debt of gratitude to the authors of <a href="https://cran.r-project.org/package=gMCP" class="external-link">gMCP</a> for their pioneering work, without which this package would not be nearly as extensive as it is.</p>
 </div>
 
   </main><aside class="col-md-3"><div class="links">
 <h2 data-toc-skip>Links</h2>
 <ul class="list-unstyled">
-<li><a href="https://github.com/Gilead-BioStats/graphicalMCP/" class="external-link">Browse source code</a></li>
-<li><a href="https://github.com/Gilead-BioStats/graphicalMCP/issues" class="external-link">Report a bug</a></li>
+<li><a href="https://cloud.r-project.org/package=graphicalMCP" class="external-link">View on CRAN</a></li>
+<li><a href="https://github.com/openpharma/graphicalMCP/" class="external-link">Browse source code</a></li>
+<li><a href="https://github.com/openpharma/graphicalMCP/issues" class="external-link">Report a bug</a></li>
 </ul>
 </div>
 
@@ -167,7 +179,10 @@ <h2 data-toc-skip>Developers</h2>
 <div class="dev-status">
 <h2 data-toc-skip>Dev status</h2>
 <ul class="list-unstyled">
+<li><a href="https://www.repostatus.org/#active" class="external-link"><img src="https://www.repostatus.org/badges/latest/active.svg" alt="Project Status: Active – The project has reached a stable, usable state and is being actively developed."></a></li>
 <li><a href="https://cran.r-project.org/package=graphicalMCP" class="external-link"><img src="https://www.r-pkg.org/badges/version/graphicalMCP" alt="CRAN status"></a></li>
+<li><a href="https://cranlogs.r-pkg.org/badges/graphicalMCP" class="external-link"><img src="https://cranlogs.r-pkg.org/badges/graphicalMCP" alt="CRAN monthly downloads"></a></li>
+<li><a href="https://cranlogs.r-pkg.org/badges/grand-total/graphicalMCP" class="external-link"><img src="https://cranlogs.r-pkg.org/badges/grand-total/graphicalMCP" alt="CRAN total downloads"></a></li>
 </ul>
 </div>
 
@@ -180,7 +195,7 @@ <h2 data-toc-skip>Dev status</h2>
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer>
diff --git a/news/index.html b/news/index.html
index df687c3..495029c 100644
--- a/news/index.html
+++ b/news/index.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Changelog • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Changelog"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Changelog • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Changelog"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -31,7 +31,7 @@
 <li class="active nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -40,7 +40,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Changelog</h1>
-      <small>Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/NEWS.md" class="external-link"><code>NEWS.md</code></a></small>
+      <small>Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/NEWS.md" class="external-link"><code>NEWS.md</code></a></small>
     </div>
 
     <div class="section level2">
@@ -49,8 +49,8 @@ <h2 class="pkg-version" data-toc-text="0.1.0" id="graphicalmcp-010">graphicalMCP
 </ul></div>
     <div class="section level2">
 <h2 class="pkg-version" data-toc-text="0.1.1" id="graphicalmcp-011">graphicalMCP 0.1.1<a class="anchor" aria-label="anchor" href="#graphicalmcp-011"></a></h2>
-<ul><li>Added compilation of vignettes (<a href="https://github.com/Gilead-BioStats/graphicalMCP/issues/73" class="external-link">#73</a>)</li>
-<li>Removed duplicated columns of “*” in test values (<a href="https://github.com/Gilead-BioStats/graphicalMCP/issues/75" class="external-link">#75</a>)</li>
+<ul><li>Added compilation of vignettes (<a href="https://github.com/openpharma/graphicalMCP/issues/73" class="external-link">#73</a>)</li>
+<li>Removed duplicated columns of “*” in test values (<a href="https://github.com/openpharma/graphicalMCP/issues/75" class="external-link">#75</a>)</li>
 </ul></div>
     <div class="section level2">
 <h2 class="pkg-version" data-toc-text="0.1.2" id="graphicalmcp-012">graphicalMCP 0.1.2<a class="anchor" aria-label="anchor" href="#graphicalmcp-012"></a></h2>
@@ -79,13 +79,18 @@ <h2 class="pkg-version" data-toc-text="0.2.3" id="graphicalmcp-023">graphicalMCP
 </ul></div>
     <div class="section level2">
 <h2 class="pkg-version" data-toc-text="0.2.4" id="graphicalmcp-024">graphicalMCP 0.2.4<a class="anchor" aria-label="anchor" href="#graphicalmcp-024"></a></h2>
-<ul><li>Updated documentation according to issue <a href="https://github.com/Gilead-BioStats/graphicalMCP/issues/84" class="external-link">#84</a></li>
+<ul><li>Updated documentation according to issue <a href="https://github.com/openpharma/graphicalMCP/issues/84" class="external-link">#84</a></li>
 <li>Resubmission for first CRAN release</li>
 </ul></div>
     <div class="section level2">
-<h2 class="pkg-version" data-toc-text="0.2.5" id="graphicalmcp-025">graphicalMCP 0.2.5<a class="anchor" aria-label="anchor" href="#graphicalmcp-025"></a></h2>
+<h2 class="pkg-version" data-toc-text="0.2.5" id="graphicalmcp-025">graphicalMCP 0.2.5<a class="anchor" aria-label="anchor" href="#graphicalmcp-025"></a></h2><p class="text-muted">CRAN release: 2024-07-13</p>
 <ul><li>Updated adjust_weights_parametric_util.Rd</li>
 <li>Resubmission for first CRAN release</li>
+</ul></div>
+    <div class="section level2">
+<h2 class="pkg-version" data-toc-text="0.2.6" id="graphicalmcp-026">graphicalMCP 0.2.6<a class="anchor" aria-label="anchor" href="#graphicalmcp-026"></a></h2>
+<ul><li>Github repo transferred to openpharma</li>
+<li>Submission for CRAN release</li>
 </ul></div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
@@ -96,7 +101,7 @@ <h2 class="pkg-version" data-toc-text="0.2.5" id="graphicalmcp-025">graphicalMCP
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/pkgdown.js b/pkgdown.js
index 9757bf9..1a99c65 100644
--- a/pkgdown.js
+++ b/pkgdown.js
@@ -152,3 +152,11 @@ async function searchFuse(query, callback) {
   });
   });
 })(window.jQuery || window.$)
+
+document.addEventListener('keydown', function(event) {
+  // Check if the pressed key is '/'
+  if (event.key === '/') {
+    event.preventDefault();  // Prevent any default action associated with the '/' key
+    document.getElementById('search-input').focus();  // Set focus to the search input
+  }
+});
diff --git a/pkgdown.yml b/pkgdown.yml
index 4f0a376..b1ee1eb 100644
--- a/pkgdown.yml
+++ b/pkgdown.yml
@@ -1,5 +1,5 @@
 pandoc: 3.1.11
-pkgdown: 2.1.0
+pkgdown: 2.1.1
 pkgdown_sha: ~
 articles:
   closed-testing: closed-testing.html
@@ -9,7 +9,7 @@ articles:
   graph-examples: graph-examples.html
   graphicalMCP: graphicalMCP.html
   shortcut-testing: shortcut-testing.html
-last_built: 2024-07-11T22:02Z
+last_built: 2024-11-08T20:25Z
 urls:
-  reference: https://gilead-biostats.github.io/graphicalMCP/reference
-  article: https://gilead-biostats.github.io/graphicalMCP/articles
+  reference: https://openpharma.github.io/graphicalMCP/reference
+  article: https://openpharma.github.io/graphicalMCP/articles
diff --git a/reference/adjust_p.html b/reference/adjust_p.html
index 4153e4a..3c56fdc 100644
--- a/reference/adjust_p.html
+++ b/reference/adjust_p.html
@@ -21,7 +21,7 @@
 
 Simes tests for adjust_p_simes().
 
-"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -29,7 +29,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -53,7 +53,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -62,7 +62,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Calculate adjusted p-values</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/adjust_p.R" class="external-link"><code>R/adjust_p.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/adjust_p.R" class="external-link"><code>R/adjust_p.R</code></a></small>
       <div class="d-none name"><code>adjust_p.Rd</code></div>
     </div>
 
@@ -184,7 +184,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/adjust_p_parametric.html b/reference/adjust_p_parametric.html
index 9e6de89..a1ac717 100644
--- a/reference/adjust_p_parametric.html
+++ b/reference/adjust_p_parametric.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/adjust_p.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/adjust_p.html">
   </head>
 </html>
 
diff --git a/reference/adjust_p_simes.html b/reference/adjust_p_simes.html
index 9e6de89..a1ac717 100644
--- a/reference/adjust_p_simes.html
+++ b/reference/adjust_p_simes.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/adjust_p.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/adjust_p.html">
   </head>
 </html>
 
diff --git a/reference/adjust_weights.html b/reference/adjust_weights.html
index a71bb55..ee160b1 100644
--- a/reference/adjust_weights.html
+++ b/reference/adjust_weights.html
@@ -19,7 +19,7 @@
 
 Simes tests for adjust_weights_simes().
 
-"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -27,7 +27,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -51,7 +51,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -60,7 +60,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Calculate adjusted hypothesis weights</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/adjust_weights.R" class="external-link"><code>R/adjust_weights.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/adjust_weights.R" class="external-link"><code>R/adjust_weights.R</code></a></small>
       <div class="d-none name"><code>adjust_weights.Rd</code></div>
     </div>
 
@@ -249,7 +249,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/adjust_weights_parametric_util.html b/reference/adjust_weights_parametric_util.html
index 145a14a..a4a4955 100644
--- a/reference/adjust_weights_parametric_util.html
+++ b/reference/adjust_weights_parametric_util.html
@@ -17,7 +17,7 @@
 Note that one-sided tests are required for parametric tests.
 
 
-"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -25,7 +25,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -49,7 +49,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -58,7 +58,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Calculate adjusted hypothesis weights for parametric tests</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/adjust_weights_parametric_util.R" class="external-link"><code>R/adjust_weights_parametric_util.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/adjust_weights_parametric_util.R" class="external-link"><code>R/adjust_weights_parametric_util.R</code></a></small>
       <div class="d-none name"><code>adjust_weights_parametric_util.Rd</code></div>
     </div>
 
@@ -172,7 +172,7 @@ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/adjust_weights_simes.html b/reference/adjust_weights_simes.html
index 7259bae..18c3592 100644
--- a/reference/adjust_weights_simes.html
+++ b/reference/adjust_weights_simes.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html">
   </head>
 </html>
 
diff --git a/reference/as_graph.html b/reference/as_graph.html
index b75663d..11ee2a0 100644
--- a/reference/as_graph.html
+++ b/reference/as_graph.html
@@ -11,7 +11,7 @@
 Note that igraph and gMCP have additional attributes for vertices, edges,
 or a graph itself. These conversion functions only handle attributes related
 to hypothesis names, hypothesis weights and transition weights. Other
-attributes will be dropped when converting."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+attributes will be dropped when converting."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -19,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -43,7 +43,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -52,7 +52,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Convert between graphicalMCP, gMCP, and igraph graph classes</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/as_graph.R" class="external-link"><code>R/as_graph.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/as_graph.R" class="external-link"><code>R/as_graph.R</code></a></small>
       <div class="d-none name"><code>as_graph.Rd</code></div>
     </div>
 
@@ -147,7 +147,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/as_graphMCP.html b/reference/as_graphMCP.html
index 61f423c..90fdd6d 100644
--- a/reference/as_graphMCP.html
+++ b/reference/as_graphMCP.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/as_graph.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/as_graph.html">
   </head>
 </html>
 
diff --git a/reference/as_graphMCP.initial_graph.html b/reference/as_graphMCP.initial_graph.html
index 61f423c..90fdd6d 100644
--- a/reference/as_graphMCP.initial_graph.html
+++ b/reference/as_graphMCP.initial_graph.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/as_graph.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/as_graph.html">
   </head>
 </html>
 
diff --git a/reference/as_igraph.html b/reference/as_igraph.html
index 61f423c..90fdd6d 100644
--- a/reference/as_igraph.html
+++ b/reference/as_igraph.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/as_graph.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/as_graph.html">
   </head>
 </html>
 
diff --git a/reference/as_igraph.initial_graph.html b/reference/as_igraph.initial_graph.html
index 61f423c..90fdd6d 100644
--- a/reference/as_igraph.initial_graph.html
+++ b/reference/as_igraph.initial_graph.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/as_graph.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/as_graph.html">
   </head>
 </html>
 
diff --git a/reference/as_initial_graph.graphMCP.html b/reference/as_initial_graph.graphMCP.html
index 61f423c..90fdd6d 100644
--- a/reference/as_initial_graph.graphMCP.html
+++ b/reference/as_initial_graph.graphMCP.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/as_graph.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/as_graph.html">
   </head>
 </html>
 
diff --git a/reference/as_initial_graph.igraph.html b/reference/as_initial_graph.igraph.html
index 61f423c..90fdd6d 100644
--- a/reference/as_initial_graph.igraph.html
+++ b/reference/as_initial_graph.igraph.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/as_graph.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/as_graph.html">
   </head>
 </html>
 
diff --git a/reference/bonferroni_holm.html b/reference/bonferroni_holm.html
index 5389be1..981a7e9 100644
--- a/reference/bonferroni_holm.html
+++ b/reference/bonferroni_holm.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/edge_pairs.html b/reference/edge_pairs.html
index a2b76fd..cb85c1d 100644
--- a/reference/edge_pairs.html
+++ b/reference/edge_pairs.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Find pairs of vertices that are connected in both directions — edge_pairs • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Find pairs of vertices that are connected in both directions — edge_pairs"><meta name="description" content="For an initial graph, find pairs of hypotheses that are connected in both
 directions. This is used to plot graphs using plot.initial_graph()."><meta property="og:description" content="For an initial graph, find pairs of hypotheses that are connected in both
-directions. This is used to plot graphs using plot.initial_graph()."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+directions. This is used to plot graphs using plot.initial_graph()."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -33,7 +33,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -42,7 +42,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Find pairs of vertices that are connected in both directions</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/edge_pairs.R" class="external-link"><code>R/edge_pairs.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/edge_pairs.R" class="external-link"><code>R/edge_pairs.R</code></a></small>
       <div class="d-none name"><code>edge_pairs.Rd</code></div>
     </div>
 
@@ -79,7 +79,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/example_graphs.html b/reference/example_graphs.html
index 9ec7b43..c7abc00 100644
--- a/reference/example_graphs.html
+++ b/reference/example_graphs.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Example graphs of commonly used multiple comparison procedures — bonferroni • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Example graphs of commonly used multiple comparison procedures — bonferroni"><meta name="description" content="Built-in functions to quickly generate select graphical multiple comparison
 procedures."><meta property="og:description" content="Built-in functions to quickly generate select graphical multiple comparison
-procedures."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+procedures."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -33,7 +33,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -42,7 +42,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Example graphs of commonly used multiple comparison procedures</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/example_graphs.R" class="external-link"><code>R/example_graphs.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/example_graphs.R" class="external-link"><code>R/example_graphs.R</code></a></small>
       <div class="d-none name"><code>example_graphs.Rd</code></div>
     </div>
 
@@ -348,7 +348,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/fallback.html b/reference/fallback.html
index 5389be1..981a7e9 100644
--- a/reference/fallback.html
+++ b/reference/fallback.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/fallback_improved_1.html b/reference/fallback_improved_1.html
index 5389be1..981a7e9 100644
--- a/reference/fallback_improved_1.html
+++ b/reference/fallback_improved_1.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/fallback_improved_2.html b/reference/fallback_improved_2.html
index 5389be1..981a7e9 100644
--- a/reference/fallback_improved_2.html
+++ b/reference/fallback_improved_2.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/fixed_sequence.html b/reference/fixed_sequence.html
index 5389be1..981a7e9 100644
--- a/reference/fixed_sequence.html
+++ b/reference/fixed_sequence.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/graph_calculate_power.html b/reference/graph_calculate_power.html
index 77f00fc..e7ec386 100644
--- a/reference/graph_calculate_power.html
+++ b/reference/graph_calculate_power.html
@@ -15,7 +15,7 @@
 hypothesis, the probability to reject all hypotheses, the expected number of
 rejections, and the probability of user-defined success criteria. See
 vignette("shortcut-testing") and vignette("closed-testing") for more
-illustration of power calculation.'><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+illustration of power calculation.'><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -23,7 +23,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -47,7 +47,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -56,7 +56,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Calculate power values for a graphical multiple comparison procedure</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/graph_calculate_power.R" class="external-link"><code>R/graph_calculate_power.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/graph_calculate_power.R" class="external-link"><code>R/graph_calculate_power.R</code></a></small>
       <div class="d-none name"><code>graph_calculate_power.Rd</code></div>
     </div>
 
@@ -341,7 +341,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graph_create.html b/reference/graph_create.html
index da816b6..5ba17de 100644
--- a/reference/graph_create.html
+++ b/reference/graph_create.html
@@ -5,7 +5,7 @@
 object using hypothesis weights and transition weights."><meta property="og:description" content="A graphical multiple comparison procedure is represented by 1) a vector of
 initial hypothesis weights hypotheses, and 2) a matrix of initial
 transition weights transitions. This function creates the initial graph
-object using hypothesis weights and transition weights."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+object using hypothesis weights and transition weights."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -37,7 +37,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -46,7 +46,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Create the initial graph for a multiple comparison procedure</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/graph_create.R" class="external-link"><code>R/graph_create.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/graph_create.R" class="external-link"><code>R/graph_create.R</code></a></small>
       <div class="d-none name"><code>graph_create.Rd</code></div>
     </div>
 
@@ -215,9 +215,11 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-in"><span>  H3 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">0</span>, <span class="fl">0</span><span class="op">)</span>,</span></span>
 <span class="r-in"><span>  H4 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1</span>, <span class="fl">0</span>, <span class="fl">0</span>, <span class="fl">0</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="op">)</span></span></span>
-<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="cn">FALSE</span><span class="op">)</span> <span class="op">{</span> <span class="co"># \dontrun{</span></span></span>
+<span class="r-in"><span><span class="kw"><a href="https://rdrr.io/r/base/try.html" class="external-link">try</a></span><span class="op">(</span></span></span>
 <span class="r-in"><span><span class="va">g</span> <span class="op">&lt;-</span> <span class="fu">graph_create</span><span class="op">(</span><span class="va">hypotheses</span>, <span class="va">transitions</span><span class="op">)</span></span></span>
-<span class="r-in"><span><span class="op">}</span> <span class="co"># }</span></span></span>
+<span class="r-in"><span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Error in graph_create(hypotheses, transitions) : </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>   Names provided in `hypotheses` and `transitions` should match</span>
 <span class="r-in"><span></span></span>
 <span class="r-in"><span><span class="co"># When names are not specified, hypotheses are numbered sequentially as</span></span></span>
 <span class="r-in"><span><span class="co"># H1, H2, ...</span></span></span>
@@ -255,7 +257,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graph_generate_weights.html b/reference/graph_generate_weights.html
index b038c2f..137e6de 100644
--- a/reference/graph_generate_weights.html
+++ b/reference/graph_generate_weights.html
@@ -23,7 +23,7 @@
 initial graph (the overall intersection hypothesis). The weighting strategy
 of this graph consists of hypothesis weights from all \(2^{m}-1\) updated
 graphs (intersection hypotheses). The algorithm to derive the weighting
-strategy is based on Algorithm 1 in Bretz et al. (2011)."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+strategy is based on Algorithm 1 in Bretz et al. (2011)."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -31,7 +31,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -55,7 +55,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -64,7 +64,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Generate the weighting strategy based on a graphical multiple comparison procedure</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/graph_generate_weights.R" class="external-link"><code>R/graph_generate_weights.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/graph_generate_weights.R" class="external-link"><code>R/graph_generate_weights.R</code></a></small>
       <div class="d-none name"><code>graph_generate_weights.Rd</code></div>
     </div>
 
@@ -174,7 +174,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graph_rejection_orderings.html b/reference/graph_rejection_orderings.html
index d1358f2..dded5b5 100644
--- a/reference/graph_rejection_orderings.html
+++ b/reference/graph_rejection_orderings.html
@@ -15,7 +15,7 @@
 (or sequences) of rejections. Although the order of rejection does not affect
 the final rejection decisions Bretz et al. (2009), different sequences could
 offer different ways to explain the step-by-step process of shortcut
-graphical multiple comparison procedures."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+graphical multiple comparison procedures."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -23,7 +23,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -47,7 +47,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -56,7 +56,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Find alternate rejection orderings (sequences) for shortcut tests</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/graph_rejection_orderings.R" class="external-link"><code>R/graph_rejection_orderings.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/graph_rejection_orderings.R" class="external-link"><code>R/graph_rejection_orderings.R</code></a></small>
       <div class="d-none name"><code>graph_rejection_orderings.Rd</code></div>
     </div>
 
@@ -270,7 +270,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graph_test_closure.html b/reference/graph_test_closure.html
index 048e84d..3df407a 100644
--- a/reference/graph_test_closure.html
+++ b/reference/graph_test_closure.html
@@ -25,7 +25,7 @@
 Current choices of test types include Bonferroni, Simes and parametric. This
 implementation offers a more general framework covering Bretz et al. (2011),
 Lu (2016), and Xi et al. (2017). See vignette("closed-testing") for more
-illustration of closed test procedures and interpretation of their outputs.'><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+illustration of closed test procedures and interpretation of their outputs.'><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -33,7 +33,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -57,7 +57,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -66,7 +66,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Perform closed graphical multiple comparison procedures</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/graph_test_closure.R" class="external-link"><code>R/graph_test_closure.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/graph_test_closure.R" class="external-link"><code>R/graph_test_closure.R</code></a></small>
       <div class="d-none name"><code>graph_test_closure.Rd</code></div>
     </div>
 
@@ -483,7 +483,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graph_test_fast.html b/reference/graph_test_fast.html
index 10c6a67..4279eee 100644
--- a/reference/graph_test_fast.html
+++ b/reference/graph_test_fast.html
@@ -5,7 +5,7 @@
 only once. Vectorization has been applied where possible."><meta property="og:description" content="These functions performs similarly to graph_test_closure() or
 graph_test_shortcut() but are optimized for efficiently calculating power.
 For example, generating weights and calculating adjusted weights can be done
-only once. Vectorization has been applied where possible."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+only once. Vectorization has been applied where possible."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -37,7 +37,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -46,7 +46,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Perform graphical multiple comparison procedures efficiently for power calculation</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/power_tests.R" class="external-link"><code>R/power_tests.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/power_tests.R" class="external-link"><code>R/power_tests.R</code></a></small>
       <div class="d-none name"><code>graph_test_fast.Rd</code></div>
     </div>
 
@@ -115,7 +115,7 @@ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graph_test_shortcut.html b/reference/graph_test_shortcut.html
index 01d9b1a..efb884f 100644
--- a/reference/graph_test_shortcut.html
+++ b/reference/graph_test_shortcut.html
@@ -11,7 +11,7 @@
 equivalent to closed graphical multiple comparison procedures using
 Bonferroni tests for intersection hypotheses, but shortcut procedures are
 faster to perform. See vignette("shortcut-testing") for more illustration
-of shortcut procedures and interpretation of their outputs.'><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+of shortcut procedures and interpretation of their outputs.'><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -19,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -43,7 +43,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -52,7 +52,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Perform shortcut (sequentially rejective) graphical multiple comparison procedures</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/graph_test_shortcut.R" class="external-link"><code>R/graph_test_shortcut.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/graph_test_shortcut.R" class="external-link"><code>R/graph_test_shortcut.R</code></a></small>
       <div class="d-none name"><code>graph_test_shortcut.Rd</code></div>
     </div>
 
@@ -228,7 +228,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graph_test_shortcut_fast.html b/reference/graph_test_shortcut_fast.html
index c85cc73..53831ee 100644
--- a/reference/graph_test_shortcut_fast.html
+++ b/reference/graph_test_shortcut_fast.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_fast.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/graph_test_fast.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_fast.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/graph_test_fast.html">
   </head>
 </html>
 
diff --git a/reference/graph_update.html b/reference/graph_update.html
index c775d66..13347ad 100644
--- a/reference/graph_update.html
+++ b/reference/graph_update.html
@@ -5,7 +5,7 @@
 weights according to Algorithm 1 of Bretz et al. (2009)."><meta property="og:description" content="After a hypothesis is deleted, an initial graph will be updated. The deleted
 hypothesis will have the hypothesis weight of 0 and the transition weight of
 0. Remaining hypotheses will have updated hypothesis weights and transition
-weights according to Algorithm 1 of Bretz et al. (2009)."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+weights according to Algorithm 1 of Bretz et al. (2009)."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -13,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -37,7 +37,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -46,7 +46,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Obtain an updated graph by updating an initial graphical after deleting hypotheses</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/graph_update.R" class="external-link"><code>R/graph_update.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/graph_update.R" class="external-link"><code>R/graph_update.R</code></a></small>
       <div class="d-none name"><code>graph_update.Rd</code></div>
     </div>
 
@@ -284,7 +284,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graphicalMCP-package.html b/reference/graphicalMCP-package.html
index f737a9d..6ea90ad 100644
--- a/reference/graphicalMCP-package.html
+++ b/reference/graphicalMCP-package.html
@@ -7,7 +7,7 @@
 Multiple comparison procedures (MCPs) control the familywise error rate in clinical trials. Graphical MCPs include many commonly used procedures as special cases; see Bretz et al. (2011) doi:10.1002/bimj.201000239
 , Lu (2016) doi:10.1002/sim.6985
 , and Xi et al. (2017) doi:10.1002/bimj.201600233
-. This package is a low-dependency implementation of graphical MCPs which allow mixed types of tests. It also includes power simulations and visualization of graphical MCPs."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+. This package is a low-dependency implementation of graphical MCPs which allow mixed types of tests. It also includes power simulations and visualization of graphical MCPs."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -15,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -39,7 +39,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -48,7 +48,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>graphicalMCP: Graphical Multiple Comparison Procedures</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/graphicalMCP-package.R" class="external-link"><code>R/graphicalMCP-package.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/graphicalMCP-package.R" class="external-link"><code>R/graphicalMCP-package.R</code></a></small>
       <div class="d-none name"><code>graphicalMCP-package.Rd</code></div>
     </div>
 
@@ -63,8 +63,8 @@
 
     <div class="section level2">
     <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
-    <div class="dont-index"><p>Useful links:</p><ul><li><p><a href="https://gilead-biostats.github.io/graphicalMCP/">https://gilead-biostats.github.io/graphicalMCP/</a></p></li>
-<li><p>Report bugs at <a href="https://github.com/Gilead-BioStats/graphicalMCP/issues" class="external-link">https://github.com/Gilead-BioStats/graphicalMCP/issues</a></p></li>
+    <div class="dont-index"><p>Useful links:</p><ul><li><p><a href="https://github.com/openpharma/graphicalMCP" class="external-link">https://github.com/openpharma/graphicalMCP</a></p></li>
+<li><p>Report bugs at <a href="https://github.com/openpharma/graphicalMCP/issues" class="external-link">https://github.com/openpharma/graphicalMCP/issues</a></p></li>
 </ul></div>
     </div>
     <div class="section level2">
@@ -83,7 +83,7 @@ <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a><
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/graphicalMCP.html b/reference/graphicalMCP.html
index 9cc4ebb..70e6b8a 100644
--- a/reference/graphicalMCP.html
+++ b/reference/graphicalMCP.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/graphicalMCP-package.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/graphicalMCP-package.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/graphicalMCP-package.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/graphicalMCP-package.html">
   </head>
 </html>
 
diff --git a/reference/huque_etal.html b/reference/huque_etal.html
index 5389be1..981a7e9 100644
--- a/reference/huque_etal.html
+++ b/reference/huque_etal.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/index.html b/reference/index.html
index 86ae6f1..2438182 100644
--- a/reference/index.html
+++ b/reference/index.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Package index • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Package index"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Package index • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Package index"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -31,7 +31,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -220,7 +220,7 @@ <h2 id="example-graphs">Example graphs<a class="anchor" aria-label="anchor" href
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/input_val.html b/reference/input_val.html
index 30d2bd8..279838b 100644
--- a/reference/input_val.html
+++ b/reference/input_val.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Validate inputs for testing and power simulations — test_input_val • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Validate inputs for testing and power simulations — test_input_val"><meta name="description" content="Validate inputs for testing and power simulations"><meta property="og:description" content="Validate inputs for testing and power simulations"><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Validate inputs for testing and power simulations — test_input_val • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Validate inputs for testing and power simulations — test_input_val"><meta name="description" content="Validate inputs for testing and power simulations"><meta property="og:description" content="Validate inputs for testing and power simulations"><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +7,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -31,7 +31,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -40,7 +40,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Validate inputs for testing and power simulations</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/test_power_input_val.R" class="external-link"><code>R/test_power_input_val.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/test_power_input_val.R" class="external-link"><code>R/test_power_input_val.R</code></a></small>
       <div class="d-none name"><code>input_val.Rd</code></div>
     </div>
 
@@ -158,7 +158,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/plot.initial_graph-1.png b/reference/plot.initial_graph-1.png
index bd3c81a..f159a44 100644
Binary files a/reference/plot.initial_graph-1.png and b/reference/plot.initial_graph-1.png differ
diff --git a/reference/plot.initial_graph-2.png b/reference/plot.initial_graph-2.png
index 2bba724..7128285 100644
Binary files a/reference/plot.initial_graph-2.png and b/reference/plot.initial_graph-2.png differ
diff --git a/reference/plot.initial_graph.html b/reference/plot.initial_graph.html
index 1b82e1d..8bb3171 100644
--- a/reference/plot.initial_graph.html
+++ b/reference/plot.initial_graph.html
@@ -7,7 +7,7 @@
 transitions into edges to create a network plot. Vertices are labeled with
 hypothesis names and hypothesis weights, and edges are labeled with
 transition weights. See vignette("graph-examples") for more illustration
-of commonly used multiple comparison procedure using graphs.'><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+of commonly used multiple comparison procedure using graphs.'><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -15,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -39,7 +39,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -48,7 +48,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>S3 plot method for class <code>initial_graph</code></h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/plot.initial_graph.R" class="external-link"><code>R/plot.initial_graph.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/plot.initial_graph.R" class="external-link"><code>R/plot.initial_graph.R</code></a></small>
       <div class="d-none name"><code>plot.initial_graph.Rd</code></div>
     </div>
 
@@ -242,7 +242,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/plot.updated_graph-1.png b/reference/plot.updated_graph-1.png
index 1f3b327..8f613b9 100644
Binary files a/reference/plot.updated_graph-1.png and b/reference/plot.updated_graph-1.png differ
diff --git a/reference/plot.updated_graph.html b/reference/plot.updated_graph.html
index 9af5212..9cde975 100644
--- a/reference/plot.updated_graph.html
+++ b/reference/plot.updated_graph.html
@@ -3,7 +3,7 @@
 plot.initial_graph(), only changing the default vertex color to use gray
 for deleted hypotheses."><meta property="og:description" content="Plotting an updated graph is a very light wrapper around
 plot.initial_graph(), only changing the default vertex color to use gray
-for deleted hypotheses."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+for deleted hypotheses."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -11,7 +11,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -35,7 +35,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -44,7 +44,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>S3 plot method for the class <code>updated_graph</code></h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/plot.updated_graph.R" class="external-link"><code>R/plot.updated_graph.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/plot.updated_graph.R" class="external-link"><code>R/plot.updated_graph.R</code></a></small>
       <div class="d-none name"><code>plot.updated_graph.Rd</code></div>
     </div>
 
@@ -170,7 +170,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/power_input_val.html b/reference/power_input_val.html
index 5cffa50..df524a9 100644
--- a/reference/power_input_val.html
+++ b/reference/power_input_val.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/input_val.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/input_val.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/input_val.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/input_val.html">
   </head>
 </html>
 
diff --git a/reference/print.graph_report.html b/reference/print.graph_report.html
index c3cb3bb..d287a74 100644
--- a/reference/print.graph_report.html
+++ b/reference/print.graph_report.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>S3 print method for the class graph_report — print.graph_report • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="S3 print method for the class graph_report — print.graph_report"><meta name="description" content="A printed graph_report displays the initial graph, p-values and
 significance levels, rejection decisions, and optional detailed test results."><meta property="og:description" content="A printed graph_report displays the initial graph, p-values and
-significance levels, rejection decisions, and optional detailed test results."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+significance levels, rejection decisions, and optional detailed test results."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -33,7 +33,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -42,7 +42,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>S3 print method for the class <code>graph_report</code></h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/print.graph_report.R" class="external-link"><code>R/print.graph_report.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/print.graph_report.R" class="external-link"><code>R/print.graph_report.R</code></a></small>
       <div class="d-none name"><code>print.graph_report.Rd</code></div>
     </div>
 
@@ -171,7 +171,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/print.initial_graph.html b/reference/print.initial_graph.html
index c90b346..5c67543 100644
--- a/reference/print.initial_graph.html
+++ b/reference/print.initial_graph.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>S3 print method for the class initial_graph — print.initial_graph • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="S3 print method for the class initial_graph — print.initial_graph"><meta name="description" content='A printed initial_graph displays a header stating "Initial graph",
 hypothesis weights, and transition weights.'><meta property="og:description" content='A printed initial_graph displays a header stating "Initial graph",
-hypothesis weights, and transition weights.'><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+hypothesis weights, and transition weights.'><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -33,7 +33,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -42,7 +42,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>S3 print method for the class <code>initial_graph</code></h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/print.initial_graph.R" class="external-link"><code>R/print.initial_graph.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/print.initial_graph.R" class="external-link"><code>R/print.initial_graph.R</code></a></small>
       <div class="d-none name"><code>print.initial_graph.Rd</code></div>
     </div>
 
@@ -136,7 +136,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/print.power_report.html b/reference/print.power_report.html
index 99c0149..0a7030f 100644
--- a/reference/print.power_report.html
+++ b/reference/print.power_report.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>S3 print method for the class power_report — print.power_report • graphicalMCP</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="S3 print method for the class power_report — print.power_report"><meta name="description" content="A printed power_report displays the initial graph, testing and simulation
 options, power outputs, and optional detailed simulations and test results."><meta property="og:description" content="A printed power_report displays the initial graph, testing and simulation
-options, power outputs, and optional detailed simulations and test results."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+options, power outputs, and optional detailed simulations and test results."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -9,7 +9,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -33,7 +33,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -42,7 +42,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>S3 print method for the class <code>power_report</code></h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/print.power_report.R" class="external-link"><code>R/print.power_report.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/print.power_report.R" class="external-link"><code>R/print.power_report.R</code></a></small>
       <div class="d-none name"><code>print.power_report.Rd</code></div>
     </div>
 
@@ -150,7 +150,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/print.updated_graph.html b/reference/print.updated_graph.html
index 84c2844..5206b13 100644
--- a/reference/print.updated_graph.html
+++ b/reference/print.updated_graph.html
@@ -3,7 +3,7 @@
 graph, and the sequence of intermediate updated graphs after hypotheses are
 deleted (if available)."><meta property="og:description" content="A printed updated_graph displays the initial graph, the (final) updated
 graph, and the sequence of intermediate updated graphs after hypotheses are
-deleted (if available)."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+deleted (if available)."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -11,7 +11,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -35,7 +35,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -44,7 +44,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>S3 print method for the class <code>updated_graph</code></h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/print.updated_graph.R" class="external-link"><code>R/print.updated_graph.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/print.updated_graph.R" class="external-link"><code>R/print.updated_graph.R</code></a></small>
       <div class="d-none name"><code>print.updated_graph.Rd</code></div>
     </div>
 
@@ -255,7 +255,7 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/random_graph.html b/reference/random_graph.html
index 5389be1..981a7e9 100644
--- a/reference/random_graph.html
+++ b/reference/random_graph.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/simple_successive_1.html b/reference/simple_successive_1.html
index 5389be1..981a7e9 100644
--- a/reference/simple_successive_1.html
+++ b/reference/simple_successive_1.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/simple_successive_2.html b/reference/simple_successive_2.html
index 5389be1..981a7e9 100644
--- a/reference/simple_successive_2.html
+++ b/reference/simple_successive_2.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/solve_c_parametric.html b/reference/solve_c_parametric.html
index 11c8fa4..d14ba38 100644
--- a/reference/solve_c_parametric.html
+++ b/reference/solve_c_parametric.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html">
   </head>
 </html>
 
diff --git a/reference/test_values.html b/reference/test_values.html
index 26e8306..097f346 100644
--- a/reference/test_values.html
+++ b/reference/test_values.html
@@ -3,7 +3,7 @@
 Bonferroni, parametric and Simes tests. This function organize outputs of
 testing and prepare them for graph_report."><meta property="og:description" content="An intersection hypothesis can be tested by a mixture of test types including
 Bonferroni, parametric and Simes tests. This function organize outputs of
-testing and prepare them for graph_report."><meta property="og:image" content="https://gilead-biostats.github.io/graphicalMCP/logo.png"></head><body>
+testing and prepare them for graph_report."><meta property="og:image" content="https://openpharma.github.io/graphicalMCP/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -11,7 +11,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">graphicalMCP</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.5</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.2.6</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -35,7 +35,7 @@
 <li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
-<li class="nav-item"><a class="external-link nav-link" href="https://github.com/Gilead-BioStats/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/openpharma/graphicalMCP/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
       </ul></div>
 
 
@@ -44,7 +44,7 @@
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.png" class="logo" alt=""><h1>Organize outputs for testing an intersection hypothesis</h1>
-      <small class="dont-index">Source: <a href="https://github.com/Gilead-BioStats/graphicalMCP/blob/main/R/test_values.R" class="external-link"><code>R/test_values.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/openpharma/graphicalMCP/blob/main/R/test_values.R" class="external-link"><code>R/test_values.R</code></a></small>
       <div class="d-none name"><code>test_values.Rd</code></div>
     </div>
 
@@ -143,7 +143,7 @@ <h2 id="references">References<a class="anchor" aria-label="anchor" href="#refer
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
 </div>
 
     </footer></div>
diff --git a/reference/test_values_parametric.html b/reference/test_values_parametric.html
index 0c0339e..666ce43 100644
--- a/reference/test_values_parametric.html
+++ b/reference/test_values_parametric.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/test_values.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/test_values.html">
   </head>
 </html>
 
diff --git a/reference/test_values_simes.html b/reference/test_values_simes.html
index 0c0339e..666ce43 100644
--- a/reference/test_values_simes.html
+++ b/reference/test_values_simes.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/test_values.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/test_values.html">
   </head>
 </html>
 
diff --git a/reference/three_doses_two_primary_two_secondary.html b/reference/three_doses_two_primary_two_secondary.html
index 5389be1..981a7e9 100644
--- a/reference/three_doses_two_primary_two_secondary.html
+++ b/reference/three_doses_two_primary_two_secondary.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/reference/two_doses_two_primary_two_secondary.html b/reference/two_doses_two_primary_two_secondary.html
index 5389be1..981a7e9 100644
--- a/reference/two_doses_two_primary_two_secondary.html
+++ b/reference/two_doses_two_primary_two_secondary.html
@@ -1,8 +1,8 @@
 <html>
   <head>
-    <meta http-equiv="refresh" content="0;URL=https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html" />
+    <meta http-equiv="refresh" content="0;URL=https://openpharma.github.io/graphicalMCP/reference/example_graphs.html" />
     <meta name="robots" content="noindex">
-    <link rel="canonical" href="https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html">
+    <link rel="canonical" href="https://openpharma.github.io/graphicalMCP/reference/example_graphs.html">
   </head>
 </html>
 
diff --git a/search.json b/search.json
index 1a229a8..660ba4a 100644
--- a/search.json
+++ b/search.json
@@ -1 +1 @@
-[{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"Apache License","title":"Apache License","text":"Version 2.0, January 2004 <http://www.apache.org/licenses/>","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_1-definitions","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"1. Definitions","title":"Apache License","text":"“License” shall mean terms conditions use, reproduction, distribution defined Sections 1 9 document. “Licensor” shall mean copyright owner entity authorized copyright owner granting License. “Legal Entity” shall mean union acting entity entities control, controlled , common control entity. purposes definition, “control” means () power, direct indirect, cause direction management entity, whether contract otherwise, (ii) ownership fifty percent (50%) outstanding shares, (iii) beneficial ownership entity. “” (“”) shall mean individual Legal Entity exercising permissions granted License. “Source” form shall mean preferred form making modifications, including limited software source code, documentation source, configuration files. “Object” form shall mean form resulting mechanical transformation translation Source form, including limited compiled object code, generated documentation, conversions media types. “Work” shall mean work authorship, whether Source Object form, made available License, indicated copyright notice included attached work (example provided Appendix ). “Derivative Works” shall mean work, whether Source Object form, based (derived ) Work editorial revisions, annotations, elaborations, modifications represent, whole, original work authorship. purposes License, Derivative Works shall include works remain separable , merely link (bind name) interfaces , Work Derivative Works thereof. “Contribution” shall mean work authorship, including original version Work modifications additions Work Derivative Works thereof, intentionally submitted Licensor inclusion Work copyright owner individual Legal Entity authorized submit behalf copyright owner. purposes definition, “submitted” means form electronic, verbal, written communication sent Licensor representatives, including limited communication electronic mailing lists, source code control systems, issue tracking systems managed , behalf , Licensor purpose discussing improving Work, excluding communication conspicuously marked otherwise designated writing copyright owner “Contribution.” “Contributor” shall mean Licensor individual Legal Entity behalf Contribution received Licensor subsequently incorporated within Work.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_2-grant-of-copyright-license","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"2. Grant of Copyright License","title":"Apache License","text":"Subject terms conditions License, Contributor hereby grants perpetual, worldwide, non-exclusive, -charge, royalty-free, irrevocable copyright license reproduce, prepare Derivative Works , publicly display, publicly perform, sublicense, distribute Work Derivative Works Source Object form.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_3-grant-of-patent-license","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"3. Grant of Patent License","title":"Apache License","text":"Subject terms conditions License, Contributor hereby grants perpetual, worldwide, non-exclusive, -charge, royalty-free, irrevocable (except stated section) patent license make, made, use, offer sell, sell, import, otherwise transfer Work, license applies patent claims licensable Contributor necessarily infringed Contribution(s) alone combination Contribution(s) Work Contribution(s) submitted. institute patent litigation entity (including cross-claim counterclaim lawsuit) alleging Work Contribution incorporated within Work constitutes direct contributory patent infringement, patent licenses granted License Work shall terminate date litigation filed.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_4-redistribution","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"4. Redistribution","title":"Apache License","text":"may reproduce distribute copies Work Derivative Works thereof medium, without modifications, Source Object form, provided meet following conditions: () must give recipients Work Derivative Works copy License; (b) must cause modified files carry prominent notices stating changed files; (c) must retain, Source form Derivative Works distribute, copyright, patent, trademark, attribution notices Source form Work, excluding notices pertain part Derivative Works; (d) Work includes “NOTICE” text file part distribution, Derivative Works distribute must include readable copy attribution notices contained within NOTICE file, excluding notices pertain part Derivative Works, least one following places: within NOTICE text file distributed part Derivative Works; within Source form documentation, provided along Derivative Works; , within display generated Derivative Works, wherever third-party notices normally appear. contents NOTICE file informational purposes modify License. may add attribution notices within Derivative Works distribute, alongside addendum NOTICE text Work, provided additional attribution notices construed modifying License. may add copyright statement modifications may provide additional different license terms conditions use, reproduction, distribution modifications, Derivative Works whole, provided use, reproduction, distribution Work otherwise complies conditions stated License.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_5-submission-of-contributions","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"5. Submission of Contributions","title":"Apache License","text":"Unless explicitly state otherwise, Contribution intentionally submitted inclusion Work Licensor shall terms conditions License, without additional terms conditions. Notwithstanding , nothing herein shall supersede modify terms separate license agreement may executed Licensor regarding Contributions.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_6-trademarks","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"6. Trademarks","title":"Apache License","text":"License grant permission use trade names, trademarks, service marks, product names Licensor, except required reasonable customary use describing origin Work reproducing content NOTICE file.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_7-disclaimer-of-warranty","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"7. Disclaimer of Warranty","title":"Apache License","text":"Unless required applicable law agreed writing, Licensor provides Work (Contributor provides Contributions) “” BASIS, WITHOUT WARRANTIES CONDITIONS KIND, either express implied, including, without limitation, warranties conditions TITLE, NON-INFRINGEMENT, MERCHANTABILITY, FITNESS PARTICULAR PURPOSE. solely responsible determining appropriateness using redistributing Work assume risks associated exercise permissions License.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_8-limitation-of-liability","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"8. Limitation of Liability","title":"Apache License","text":"event legal theory, whether tort (including negligence), contract, otherwise, unless required applicable law (deliberate grossly negligent acts) agreed writing, shall Contributor liable damages, including direct, indirect, special, incidental, consequential damages character arising result License use inability use Work (including limited damages loss goodwill, work stoppage, computer failure malfunction, commercial damages losses), even Contributor advised possibility damages.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"id_9-accepting-warranty-or-additional-liability","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"9. Accepting Warranty or Additional Liability","title":"Apache License","text":"redistributing Work Derivative Works thereof, may choose offer, charge fee , acceptance support, warranty, indemnity, liability obligations /rights consistent License. However, accepting obligations, may act behalf sole responsibility, behalf Contributor, agree indemnify, defend, hold Contributor harmless liability incurred , claims asserted , Contributor reason accepting warranty additional liability. END TERMS CONDITIONS","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/LICENSE.html","id":"appendix-how-to-apply-the-apache-license-to-your-work","dir":"","previous_headings":"","what":"APPENDIX: How to apply the Apache License to your work","title":"Apache License","text":"apply Apache License work, attach following boilerplate notice, fields enclosed brackets [] replaced identifying information. (Don’t include brackets!) text enclosed appropriate comment syntax file format. also recommend file class name description purpose included “printed page” copyright notice easier identification within third-party archives.","code":"Copyright 2023 Gilead Sciences  Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at    http://www.apache.org/licenses/LICENSE-2.0  Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License."},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"motivating-example","dir":"Articles","previous_headings":"","what":"Motivating example","title":"Graphical multiple comparison procedures based on the closure principle","text":"Consider confirmatory clinical trial comparing test treatment (treatment) control treatment (control) disease. two doses treatment: low dose high dose. three endpoints included multiplicity adjustment strategy, primary endpoint (PE) two secondary endpoints (SE1 SE2). total, six null hypotheses: H1H_1, H3H_3 H5H_5 primary hypothesis two secondary hypotheses respectively low dose versus control; H2H_2, H4H_4 H6H_6 primary hypothesis two secondary hypotheses respectively high dose versus control. clinical considerations constrain structure multiple comparison procedures, can flexibly incorporated using graphical approaches. First, low high doses considered equally important, means rejecting primary hypothesis either dose versus control leads successful trial. Regarding secondary hypotheses, one tested corresponding primary hypothesis rejected. means H3H_3 H5H_5 tested H1H_1 rejected; H4H_4 H6H_6 tested H2H_2 rejected. addition, statistical considerations complete graph. primary hypotheses H1H_1 H2H_2 equal hypothesis weight 0.5. secondary hypotheses hypothesis weight 0. primary hypothesis rejected, weight propagate along three outgoing edges: one primary hypothesis two descendant secondary hypotheses. edge primary hypothesis transition weight 0.5; two edges descendant secondary hypotheses equal transition weight 0.25. secondary hypotheses dose-control comparison, edge transition weight 1 (close 1 allow ϵ\\epsilon edges). hypothesis weights dose-control comparison group propagated primary hypothesis dose-control comparison, hypotheses first dose-control comparison group deleted. specifications, can create following graph.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"create-a-graph","dir":"Articles","previous_headings":"Motivating example","what":"Create a graph","title":"Graphical multiple comparison procedures based on the closure principle","text":"","code":"hypotheses <- c(0.5, 0.5, 0, 0, 0, 0)  epsilon <- 1e-5 transitions <- rbind(   c(0, 0.5, 0.25, 0, 0.25, 0),   c(0.5, 0, 0, 0.25, 0, 0.25),   c(0, 0, 0, 0, 1, 0),   c(epsilon, 0, 0, 0, 0, 1 - epsilon),   c(0, epsilon, 1 - epsilon, 0, 0, 0),   c(0, 0, 0, 1, 0, 0) )  hyp_names <- c(\"H1\", \"H2\", \"H3\", \"H4\", \"H5\", \"H6\") g <- graph_create(hypotheses, transitions, hyp_names)  plot_layout <- rbind(   c(0.15, 0.5),   c(0.65, 0.5),   c(0, 0),   c(0.5, 0),   c(0.3, 0),   c(0.8, 0) )  plot(   g,   layout = plot_layout,   eps = epsilon,   edge_curves = c(pairs = 0.8),   vertex.size = 35 )"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"bonferroni-tests","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle","what":"Bonferroni tests","title":"Graphical multiple comparison procedures based on the closure principle","text":"Given set p-values H1,…,H6H_1, \\ldots, H_6, graphical multiple comparison procedure can performed control family-wise error rate (FWER) significance level alpha. one-sided p-values, alpha often set 0.025 (default). First, perform Bonferroni-based procedure using closure principle (Bretz et al. 2009). running procedure, none hypotheses rejected. results identical using graph_test_shortcut().","code":"p_values <- c(0.015, 0.013, 0.01, 0.007, 0.1, 0.0124) test_results <- graph_test_closure(   g,   p = p_values,   alpha = 0.025,   verbose = TRUE,   test_values = TRUE )  test_results$outputs$adjusted_p #>    H1    H2    H3    H4    H5    H6  #> 0.026 0.026 0.028 0.028 0.100 0.028  test_results$outputs$rejected #>    H1    H2    H3    H4    H5    H6  #> FALSE FALSE FALSE FALSE FALSE FALSE # Same testing results as # 'graph_test_shortcut(g, p = p_values, alpha = 0.025)$outputs$rejected'"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"obtain-the-closure","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Bonferroni tests","what":"Obtain the closure","title":"Graphical multiple comparison procedures based on the closure principle","text":"investigate closure every intersection hypothesis rejected, one obtain detailed output specifying verbose = TRUE. hypotheses tested using Bonferroni tests, adjusted p-value every intersection hypothesis adjusted p-value group 1 (meaning hypotheses group Bonferroni tests). intersection hypothesis rejected adjusted p-value less equal alpha. Adjusted p-values initially calculated groups hypotheses. case one group, includes hypotheses, can . adjusted p-value intersection hypothesis minimum across groups within intersection. Finally, adjusted p-value individual hypothesis whole procedure equal maximum adjusted p-values across intersections involving hypothesis.","code":"test_results_verbose <-   graph_test_closure(     g,     p = p_values,     alpha = 0.025,     verbose = TRUE   )  head(test_results_verbose$details$results) #>   Intersection  H1  H2 H3 H4 H5 H6 adj_p_grp1 adj_p_inter reject_intersection #> 1       111111 0.5 0.5  0  0  0  0      0.026       0.026               FALSE #> 2       111110 0.5 0.5  0  0  0 NA      0.026       0.026               FALSE #> 3       111101 0.5 0.5  0  0 NA  0      0.026       0.026               FALSE #> 4       111100 0.5 0.5  0  0 NA NA      0.026       0.026               FALSE #> 5       111011 0.5 0.5  0 NA  0  0      0.026       0.026               FALSE #> 6       111010 0.5 0.5  0 NA  0 NA      0.026       0.026               FALSE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"obtain-adjusted-significance-levels","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Bonferroni tests","what":"Obtain adjusted significance levels","title":"Graphical multiple comparison procedures based on the closure principle","text":"equivalent way obtain rejections via adjusting significance levels. hypothesis rejected p-value less equal adjusted significance level. One can obtain adjusted significance levels every hypothesis every intersection hypothesis closure specifying test_values = TRUE. hypothesis rejected closed testing procedure intersection hypotheses involving rejected. intersection hypothesis rejected null hypotheses within rejected.","code":"test_results_test_values <-   graph_test_closure(     g,     test_types = \"b\",     p = p_values,     alpha = 0.025,     test_values = TRUE   )  head(test_results_test_values$test_values$results) #>   Intersection Hypothesis       Test      p Weight Alpha Inequality_holds #> 1       111111         H1 bonferroni 0.0150    0.5 0.025            FALSE #> 2       111111         H2 bonferroni 0.0130    0.5 0.025            FALSE #> 3       111111         H3 bonferroni 0.0100    0.0 0.025            FALSE #> 4       111111         H4 bonferroni 0.0070    0.0 0.025            FALSE #> 5       111111         H5 bonferroni 0.1000    0.0 0.025            FALSE #> 6       111111         H6 bonferroni 0.0124    0.0 0.025            FALSE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"mixed-procedures-for-graphical-approaches","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle","what":"Mixed procedures for graphical approaches","title":"Graphical multiple comparison procedures based on the closure principle","text":"framework graphicalMCP allows mixture tests improve performance Bonferroni-based graphical approaches. can group hypotheses multiple subgroups perform separate test every subgroup. Currently, graphicalMCP supports Bonferroni, parametric Simes tests. connect results different subgroups hypotheses, Bonferroni tests used. , show two examples. first example applies parametric tests primary hypotheses (Xi et al. 2017), second example applies Simes tests two subgroups secondary hypotheses addition parametric tests primary hypotheses.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"parametric-tests-for-primary-hypotheses","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Mixed procedures for graphical approaches","what":"Parametric tests for primary hypotheses","title":"Graphical multiple comparison procedures based on the closure principle","text":"example, assume test statistics primary hypotheses follow asymptotic bivariate normal distribution. null hypotheses H1H_1 H2H_2, mean distribution 0. correlation test statistics H1H_1 H2H_2 can calculated function sample size. Assume sample size control, low high doses n0n_0, n1n_1 n2n_2, respectively. correlation test statistics H1H_1 H2H_2 ρ12=(n1n1+n0)1/2(n2n2+n0)1/2\\rho_{12}=\\left(\\frac{n_1}{n_1+n_0}\\right)^{1/2}\\left(\\frac{n_2}{n_2+n_0}\\right)^{1/2}. equal randomization, correlation 0.5. intersection hypothesis H1∩H2∩H3∩H4∩H5∩H6H_1\\cap H_2\\cap H_3\\cap H_4\\cap H_5\\cap H_6, hypothesis weights 0.5, 0.5, 0, 0, 0, 0, respectively H1,…,H6H_1,\\ldots, H_6. Assume one-sided p-values hypotheses p1,…,p6p_1,\\ldots,p_6, respectively. intersection hypothesis rejected Bonferroni test p1≤0.5αp_1\\leq 0.5\\alpha p2≤0.5αp_2\\leq 0.5\\alpha. Alternatively, parametric test utilizes correlation test statistics t1=Φ−1(1−p1)t_1=\\Phi^{-1}(1 - p_1) t2=Φ−1(1−p2)t_2=\\Phi^{-1}(1 - p_2). intersection hypothesis can rejected p1≤c×0.5αp_1\\leq c\\times 0.5\\alpha p2≤c×0.5αp_2\\leq c\\times 0.5\\alpha, cc value adjustment due correlation t1t_1 t2t_2. specifically, cc can solved solution Pr{(p1≤c×0.5α)∪(p2≤c×0.5α)}=αPr\\{(p_1\\leq c\\times 0.5\\alpha)\\cup (p_2\\leq c\\times 0.5\\alpha)\\}=\\alpha. given correlation ρ12\\rho_{12}, cc value can solved using uniroot function mvtnorm package. example, ρ12=0.5\\rho_{12}=0.5, cc value 1.078. can obtain adjusted significance level H1H_1 H2H_2 c×0.5αc\\times 0.5\\alpha. Alternatively, can calculate adjusted p-value H1∩H2∩H3∩H4∩H5∩H6H_1\\cap H_2\\cap H_3\\cap H_4\\cap H_5\\cap H_6 Pr{(P1≤min{p1,p2})∪(P2≤min{p1,p2})}Pr\\{(P_1\\leq \\min{\\{p_1, p_2\\}})\\cup (P_2\\leq \\min{\\{p_1, p_2\\}})\\}. implement procedure, need create two subgroups: one H1H_1 H2H_2, one rest hypotheses. first subgroup hypotheses, apply parametric tests; second subgroup (subsets), apply Bonferroni tests. Three additional inputs needed: specify grouping information test_groups, identify types tests every subgroup test_types, provide correlation matrix parametric tests test_corr. Assume correlation 0.5 test statistics primary hypotheses. procedure rejects H1H_1 H2H_2, others. Compared Bonferroni-based graphical approach didn’t rejected hypothesis, illustrates power improvement using parametric tests Bonferroni tests.","code":"corr_12 <- matrix(0.5, nrow = 2, ncol = 2) diag(corr_12) <- 1  test_results_parametric <-   graph_test_closure(     g,     p = p_values,     alpha = 0.025,     test_groups = list(c(1, 2), 3:6),     test_types = c(\"parametric\", \"bonferroni\"),     test_corr = list(corr_12, NA),     test_values = TRUE   )  test_results_parametric$outputs$adjusted_p #>         H1         H2         H3         H4         H5         H6  #> 0.02413846 0.02413846 0.02800000 0.02800000 0.10000000 0.02800000 test_results_parametric$outputs$rejected #>    H1    H2    H3    H4    H5    H6  #>  TRUE  TRUE FALSE FALSE FALSE FALSE  head(test_results_parametric$test_values$results) #>   Intersection Hypothesis       Test      p      c_value Weight Alpha #> 1       111111         H1 parametric 0.0150 1.0782936582    0.5 0.025 #> 2       111111         H2 parametric 0.0130 1.0782936582    0.5 0.025 #> 3       111111         H3 bonferroni 0.0100                 0.0 0.025 #> 4       111111         H4 bonferroni 0.0070                 0.0 0.025 #> 5       111111         H5 bonferroni 0.1000                 0.0 0.025 #> 6       111111         H6 bonferroni 0.0124                 0.0 0.025 #>   Inequality_holds #> 1            FALSE #> 2             TRUE #> 3            FALSE #> 4            FALSE #> 5            FALSE #> 6            FALSE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"parametric-tests-for-primary-hypotheses-and-simes-tests-for-secondary-hypotheses","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Mixed procedures for graphical approaches","what":"Parametric tests for primary hypotheses and Simes tests for secondary hypotheses","title":"Graphical multiple comparison procedures based on the closure principle","text":"addition using parametric tests primary hypotheses, ways improve Bonferroni-based graphical approaches. One way apply Simes tests secondary hypotheses(Bretz et al. 2011; Lu 2016). Simes tests improve Bonferroni tests may reject intersection hypothesis p-values relatively small, even ’re larger adjusted significance levels Bonferroni tests. intersection hypothesis H3∩H5H_3\\cap H_5, hypothesis weights 0.5 0.5, respectively H3H_3 H5H_5. intersection hypothesis rejected Bonferroni test p3≤0.5αp_3\\leq 0.5\\alpha p5≤0.5αp_5\\leq 0.5\\alpha. addition conditions, Simes test can also reject intersection hypothesis p3p_3 p5p_5 less equal α\\alpha. order control Type error Simes test, distributional requirement needed, called MTP2MTP_2(Sarkar 1998). case, means correlation test statistics H3H_3 H5H_5 non-negative. illustrate possibility using mixed tests example, keep parametric tests primary hypotheses apply Simes tests secondary hypotheses. two sets secondary hypotheses: H3H_3 H5H_5 secondary hypotheses low dose versus control, H4H_4 H6H_6 secondary hypotheses high dose versus control. believed correlation test statistics H3H_3 H5H_5 non-negative case H4H_4 H6H_6. Thus one can apply Simes tests H3H_3 H5H_5, separately H4H_4 H6H_6. Note different applying Simes tests H3…,H6H_3\\ldots,H_6 requires stronger MTP2MTP_2 condition. implement procedure, create three subgroups: one H1H_1 H2H_2, one H3H_3 H5H_5, one H4H_4 H6H_6. first subgroup hypotheses, apply parametric tests; second third subgroups, apply separate Simes tests. Assume correlation 0.5 test statistics primary hypotheses. procedure rejects H1H_1, H2H_2, H4H_4, H6H_6, H3H_3. Compared results using parametric tests primary hypotheses (Bonferroni tests secondary hypotheses), H3H_3, H4H_4 H6H_6 additional hypotheses rejected using Simes tests, showing power improvement using Simes tests.","code":"test_results_parametric_simes <-   graph_test_closure(     g,     p = p_values, alpha = 0.025,     test_groups = list(c(1, 2), c(3, 5), c(4, 6)),     test_types = c(\"parametric\", \"simes\", \"simes\"),     test_corr = list(corr_12, NA, NA),     test_values = TRUE   )  test_results_parametric_simes$outputs$adjusted_p #>         H1         H2         H3         H4         H5         H6  #> 0.02413846 0.02413846 0.02480008 0.02480000 0.10000000 0.02480008 test_results_parametric_simes$outputs$rejected #>    H1    H2    H3    H4    H5    H6  #>  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  head(test_results_parametric_simes$test_values$results) #>   Intersection Hypothesis       Test      p      c_value Weight Alpha #> 1       111111         H1 parametric 0.0150 1.0782936582    0.5 0.025 #> 2       111111         H2 parametric 0.0130 1.0782936582    0.5 0.025 #> 3       111111         H3      simes 0.0100                 0.0 0.025 #> 4       111111         H5      simes 0.1000                 0.0 0.025 #> 5       111111         H4      simes 0.0070                 0.0 0.025 #> 6       111111         H6      simes 0.0124                 0.0 0.025 #>   Inequality_holds #> 1            FALSE #> 2             TRUE #> 3            FALSE #> 4            FALSE #> 5            FALSE #> 6            FALSE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"power-calculation","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle","what":"Power calculation","title":"Graphical multiple comparison procedures based on the closure principle","text":"Given graph, trial team often interested power trial. single null hypothesis, power probability reject null hypothesis significance level alpha alternative hypothesis true (.e. true positive). multiple null hypotheses, multiple version power. example, power reject least one hypothesis power reject hypotheses, given alternative hypotheses true. graphical multiple comparison procedures, also important understand power reject hypothesis, given multiplicity adjustment. Sometimes, team may want customize definitions power define success. Thus power calculation important aspect trial design.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"input-marginal-power-for-primary-hypotheses","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"Input: Marginal power for primary hypotheses","title":"Graphical multiple comparison procedures based on the closure principle","text":"Assume primary endpoint occurrence unfavorable clinical event. evaluate treatment effect, proportion patients event calculated lower better. Assume proportions 0.181 low high doses, 0.3 control. Using equal randomization among three treatment groups, clinical trial team chooses total sample size 600 200 per group. leads marginal power 80% H1H_1 H2H_2, respectively, using two-sample test difference proportions unpooled variance one-sided significance level 0.025. calculation, use marginal power combine information treatment effect, nuisance parameter, sample sizes hypothesis. Note significance level used marginal power alpha used power calculation significance level FWER control. addition, marginal power one--one relationship noncentrality parameter, illustrated .","code":"alpha <- 0.025 prop <- c(0.3, 0.181, 0.181) sample_size <- rep(200, 3)  unpooled_variance <-   prop[-1] * (1 - prop[-1]) / sample_size[-1] +   prop[1] * (1 - prop[1]) / sample_size[1]  noncentrality_parameter_primary <-   -(prop[-1] - prop[1]) / sqrt(unpooled_variance)  marginal_power_primary <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_primary,   sd = 1,   lower.tail = FALSE )  names(marginal_power_primary) <- c(\"H1\", \"H2\") marginal_power_primary #>        H1        H2  #> 0.8028315 0.8028315"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"input-marginal-power-for-secondary-hypotheses","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"Input: Marginal power for secondary hypotheses","title":"Graphical multiple comparison procedures based on the closure principle","text":"Assume secondary endpoint (SE1) change total medication score baseline, continuous outcome. Also assume secondary endpoint (SE2) change another medication score baseline, continuous outcome contains fewer categories compared SE1. evaluate treatment effect, mean change calculated reduction better. Assume mean change baseline SE1 reduction 7.5 8.25, respectively low high doses, 5 control. Also assume mean change baseline SE2 reduction 8 9, respectively low high doses, 6 control. assume known common standard deviation 10. Given sample size 200 per treatment group, marginal power 71% 90% H3H_3 H4H_4, respectively 52% 85% H5H_5 H6H_6, respectively using two-sample zz-test difference means one-sided significance level 0.025.","code":"mean_change_se1 <- c(5, 7.5, 8.25) sd <- rep(10, 3) variance <- sd[-1]^2 / sample_size[-1] + sd[1]^2 / sample_size[1]  noncentrality_parameter_se1 <-   (mean_change_se1[-1] - mean_change_se1[1]) /     sqrt(variance)  marginal_power_se1 <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_se1,   sd = 1,   lower.tail = FALSE )  names(marginal_power_se1) <- c(\"H3\", \"H4\") marginal_power_se1 #>        H3        H4  #> 0.7054139 0.9014809  mean_change_se2 <- c(6, 8, 9)  noncentrality_parameter_se2 <-   (mean_change_se2[-1] - mean_change_se2[1]) /     sqrt(variance)  marginal_power_se2 <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_se2,   sd = 1,   lower.tail = FALSE )  names(marginal_power_se2) <- c(\"H5\", \"H6\") marginal_power_se2 #>        H5        H6  #> 0.5159678 0.8508384"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"input-correlation-structure-to-simulate-test-statistics","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"Input: Correlation structure to simulate test statistics","title":"Graphical multiple comparison procedures based on the closure principle","text":"addition marginal power, also need make assumptions joint distribution test statistics. example, assume follow multivariate normal distribution means ’re defined noncentrality parameters correlation matrix RR. obtain correlations, helpful understand two types correlations example. correlation two dose-control comparisons endpoint correlation endpoints. former correlation can calculated function sample size. example, correlation test statistics H1H_1 H2H_2 ρ12=(n1n1+n0)1/2(n2n3+n0)1/2\\rho_{12}=\\left(\\frac{n_1}{n_1+n_0}\\right)^{1/2}\\left(\\frac{n_2}{n_3+n_0}\\right)^{1/2}. equal randomization, correlation 0.5. correlation test statistics H3H_3 H4H_4 H5H_5 H6H_6 . hand, correlation endpoints dose-control comparison often estimated based prior knowledge previous trials. Without information, assume ρ13=ρ15=ρ24=ρ26=ρ35=ρ46=0.5\\rho_{13}=\\rho_{15}=\\rho_{24}=\\rho_{26}=\\rho_{35}=\\rho_{46}=0.5. practice, one set correlation parameter try multiple values assess sensitivity assumption. Regarding correlation test statistics H1H_1 H4(H6)H_4 (H_6) H2H_2 H3(H5)H_3 (H_5), even difficult estimate. use simple product rule, means correlation product correlations two previously assumed correlations. example, ρ14=ρ12*ρ24\\rho_{14}=\\rho_{12}*\\rho_{24} ρ23=ρ12*ρ13\\rho_{23}=\\rho_{12}*\\rho_{13}. practice, assumptions may made tested, instead using product rule.","code":"corr <- matrix(0, nrow = 6, ncol = 6)  corr[1, 2] <-   corr[3, 4] <-   corr[5, 6] <-   sqrt(     sample_size[2] / sum(sample_size[1:2]) *       sample_size[3] / sum(sample_size[c(1, 3)])   )  rho <- 0.5  corr[1, 3] <-   corr[1, 5] <-   corr[2, 4] <-   corr[2, 6] <-   corr[3, 5] <-   corr[4, 6] <-   rho  corr[1, 4] <- corr[1, 6] <- corr[2, 3] <- corr[2, 5] <- corr[1, 2] * rho  corr[3, 6] <- corr[1, 3] * corr[1, 6] corr[4, 5] <- corr[1, 4] * corr[1, 6]  corr <- corr + t(corr) diag(corr) <- 1 colnames(corr) <- hyp_names rownames(corr) <- hyp_names corr #>      H1   H2    H3     H4     H5    H6 #> H1 1.00 0.50 0.500 0.2500 0.5000 0.250 #> H2 0.50 1.00 0.250 0.5000 0.2500 0.500 #> H3 0.50 0.25 1.000 0.5000 0.5000 0.125 #> H4 0.25 0.50 0.500 1.0000 0.0625 0.500 #> H5 0.50 0.25 0.500 0.0625 1.0000 0.500 #> H6 0.25 0.50 0.125 0.5000 0.5000 1.000"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"user-defined-success-criteria","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"User-defined success criteria","title":"Graphical multiple comparison procedures based on the closure principle","text":"mentioned earlier, multiple versions “power” multiple hypotheses. Commonly used “power” definitions include: - Local power: probability hypothesis rejected (multiplicity adjustment) - Expected . rejections: expected number rejections - Power reject 1 : probability reject least one hypothesis - Power reject : probability reject hypotheses default outputs graph_calculate_power function. addition, user customize success criteria define versions “power”.","code":"success_fns <- list(   # Probability to reject H1   H1 = function(x) x[1],    # Expected number of rejections   `Expected no. of rejections` =     function(x) x[1] + x[2] + x[3] + x[4] + x[5] + x[6],    # Probability to reject at least one hypothesis   `AtLeast1` = function(x) x[1] | x[2] | x[3] | x[4] | x[5] | x[6],    # Probability to reject all hypotheses   `All` = function(x) x[1] & x[2] & x[3] & x[4] & x[5] & x[6],    # Probability to reject both H1 and H2   `H1andH2` = function(x) x[1] & x[2],    # Probability to reject all hypotheses for the low dose or the high dose   `(H1andH3andH5)or(H2andH4andH6)` <-     function(x) (x[1] & x[3] & x[5]) | (x[2] & x[4] & x[6]) )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html","id":"output-calculate-power","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"Output: Calculate power","title":"Graphical multiple comparison procedures based on the closure principle","text":"Given inputs, can calculate power via simulation graphical multiple comparison procedure one-sided significance level alpha = 0.025 using sim_n = 1e5 simulations random seed 1234. three procedures compare: Bonferroni-based procedure, procedure using parametric tests primary hypotheses, procedure using parametric tests primary hypotheses Simes tests two sets secondary hypotheses separately. local power hypotheses H1,…,H6H_1, \\ldots, H_6 - 0.760, 0.752, 0.510, 0.665, 0.391, 0.625, respectively using Bonferroni-based procedure, - 0.764, 0.756, 0.511, 0.668, 0.392, 0.628, respectively using procedure using parametric tests primary hypotheses, - 0.764, 0.757, 0.521, 0.673, 0.402, 0.633, respectively using procedure using parametric tests primary hypotheses Simes tests two sets secondary hypotheses separately. Note local power improved hypotheses parametric tests Simes tests applied Bonferroni-based procedure. see detailed outputs simulated p-values rejection decisions hypotheses, can specify verbose = TRUE. produce lot outputs. allow flexible printing functions, user can change following: - indented space default setting indent = 2 - precision numeric values (.e., number decimal places) default setting precision = 6","code":"set.seed(1234) power_bonferroni <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(     marginal_power_primary,     marginal_power_se1,     marginal_power_se2   ),   sim_success = success_fns )  round(power_bonferroni$power$power_local, 3) #>    H1    H2    H3    H4    H5    H6  #> 0.760 0.752 0.510 0.665 0.391 0.625  set.seed(1234) power_parametric <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(     marginal_power_primary,     marginal_power_se1,     marginal_power_se2   ),   test_groups = list(c(1, 2), 3:6),   test_types = c(\"parametric\", \"bonferroni\"),   test_corr = list(corr_12, NA),   sim_success = success_fns )  round(power_parametric$power$power_local, 3) #>    H1    H2    H3    H4    H5    H6  #> 0.764 0.756 0.511 0.668 0.392 0.628  set.seed(1234) power_parametric_simes <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(     marginal_power_primary,     marginal_power_se1,     marginal_power_se2   ),   test_groups = list(c(1, 2), c(3, 5), c(4, 6)),   test_types = c(\"parametric\", \"simes\", \"simes\"),   test_corr = list(corr_12, NA, NA),   sim_success = success_fns )  round(power_parametric_simes$power$power_local, 3) #>    H1    H2    H3    H4    H5    H6  #> 0.764 0.757 0.521 0.673 0.402 0.633 set.seed(1234) power_verbose_output_parametric_simes <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(     marginal_power_primary,     marginal_power_se1,     marginal_power_se2   ),   test_groups = list(c(1, 2), c(3, 5), c(4, 6)),   test_types = c(\"parametric\", \"simes\", \"simes\"),   test_corr = list(corr_12, NA, NA),   sim_success = success_fns,   verbose = TRUE )  head(power_verbose_output_parametric_simes$details$p_sim, 10) #>                 H1           H2           H3           H4           H5 #>  [1,] 0.0236514114 6.962444e-03 3.835101e-03 0.0615622415 0.0034034237 #>  [2,] 0.0367030430 4.681135e-02 6.857853e-02 0.0284812435 0.1496042440 #>  [3,] 0.0157541925 6.543826e-03 1.152738e-03 0.0007655046 0.0836186744 #>  [4,] 0.0053369856 8.699959e-07 9.952719e-03 0.0002429371 0.0369937655 #>  [5,] 0.0342665326 1.788794e-01 6.202961e-03 0.0305855529 0.0461642736 #>  [6,] 0.0011139852 1.783703e-02 6.083855e-02 0.0087065723 0.3865009844 #>  [7,] 0.2540774514 2.101193e-01 2.616673e-02 0.0277425681 0.0092489689 #>  [8,] 0.0908135583 4.433230e-02 1.903718e-01 0.0418782572 0.3996511810 #>  [9,] 0.0739568465 4.728371e-02 3.778643e-01 0.0296172396 0.4446759145 #> [10,] 0.0003353917 1.048743e-03 1.246528e-05 0.0032298980 0.0001601294 #>                 H6 #>  [1,] 0.0018417304 #>  [2,] 0.0552141940 #>  [3,] 0.0255279965 #>  [4,] 0.0001345536 #>  [5,] 0.0666051161 #>  [6,] 0.0867387423 #>  [7,] 0.0297658510 #>  [8,] 0.1097032475 #>  [9,] 0.0620564532 #> [10,] 0.0114581872  print(power_verbose_output_parametric_simes,   indent = 4,   precision = 6 ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>     Initial graph #>  #>     --- Hypothesis weights --- #>     H1: 0.5 #>     H2: 0.5 #>     H3: 0.0 #>     H4: 0.0 #>     H5: 0.0 #>     H6: 0.0 #>  #>     --- Transition weights --- #>             H1      H2      H3      H4      H5      H6 #>     H1 0.00000 0.50000 0.25000 0.00000 0.25000 0.00000 #>     H2 0.50000 0.00000 0.00000 0.25000 0.00000 0.25000 #>     H3 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 #>     H4 0.00001 0.00000 0.00000 0.00000 0.00000 0.99999 #>     H5 0.00000 0.00001 0.99999 0.00000 0.00000 0.00000 #>     H6 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 #>  #>     Alpha = 0.025 #>  #>     Parametric testing correlation:     H1  H2 #>                                     H1 1.0 0.5 #>                                     H2 0.5 1.0 #>  #>     Test types #>     parametric: (H1, H2) #>          simes: (H3, H5) #>          simes: (H4, H6) #>  #> Simulation parameters ($inputs) ------------------------------------------------ #>     Testing 100,000 simulations with multivariate normal params: #>  #>                           H1       H2       H3       H4       H5       H6 #>     Marginal power: 0.802831 0.802831 0.705414 0.901481 0.515968 0.850838 #>  #>     Correlation:        H1     H2     H3     H4     H5     H6 #>                  H1 1.0000 0.5000 0.5000 0.2500 0.5000 0.2500 #>                  H2 0.5000 1.0000 0.2500 0.5000 0.2500 0.5000 #>                  H3 0.5000 0.2500 1.0000 0.5000 0.5000 0.1250 #>                  H4 0.2500 0.5000 0.5000 1.0000 0.0625 0.5000 #>                  H5 0.5000 0.2500 0.5000 0.0625 1.0000 0.5000 #>                  H6 0.2500 0.5000 0.1250 0.5000 0.5000 1.0000 #>  #> Power calculation ($power) ----------------------------------------------------- #>                                      H1      H2      H3      H4      H5      H6 #>                    Local power: 0.76437 0.75656 0.52086 0.67302 0.40234 0.63292 #>  #>     Expected no. of rejections: 3.75007 #>      Power to reject 1 or more: 0.86277 #>            Power to reject all: 0.32537 #>  #>                Success measure   Power #>                             H1 0.76437 #>     Expected no. of rejections 3.75007 #>                       AtLeast1 0.86277 #>                            All 0.32537 #>                        H1andH2 0.65816 #>                                0.63324 #>  #> Simulation details ($details) -------------------------------------------------- #>         p_sim_H1    p_sim_H2    p_sim_H3    p_sim_H4    p_sim_H5    p_sim_H6 rej_H1 #>      2.36514e-02 6.96244e-03 3.83510e-03 6.15622e-02 3.40342e-03 1.84173e-03  FALSE #>      3.67030e-02 4.68113e-02 6.85785e-02 2.84812e-02 1.49604e-01 5.52142e-02  FALSE #>      1.57542e-02 6.54383e-03 1.15274e-03 7.65505e-04 8.36187e-02 2.55280e-02   TRUE #>      5.33699e-03 8.69996e-07 9.95272e-03 2.42937e-04 3.69938e-02 1.34554e-04   TRUE #>      3.42665e-02 1.78879e-01 6.20296e-03 3.05856e-02 4.61643e-02 6.66051e-02  FALSE #>      1.11399e-03 1.78370e-02 6.08385e-02 8.70657e-03 3.86501e-01 8.67387e-02   TRUE #>      2.54077e-01 2.10119e-01 2.61667e-02 2.77426e-02 9.24897e-03 2.97659e-02  FALSE #>      9.08136e-02 4.43323e-02 1.90372e-01 4.18783e-02 3.99651e-01 1.09703e-01  FALSE #>      7.39568e-02 4.72837e-02 3.77864e-01 2.96172e-02 4.44676e-01 6.20565e-02  FALSE #>      3.35392e-04 1.04874e-03 1.24653e-05 3.22990e-03 1.60129e-04 1.14582e-02   TRUE #>      rej_H2 rej_H3 rej_H4 rej_H5 rej_H6 #>        TRUE  FALSE  FALSE  FALSE   TRUE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>        TRUE   TRUE   TRUE  FALSE  FALSE #>        TRUE   TRUE   TRUE  FALSE   TRUE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>        TRUE  FALSE  FALSE  FALSE  FALSE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>        TRUE   TRUE   TRUE   TRUE   TRUE #>     ... (Use `print(x, rows = <nn>)` for more)"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Comparisons with other packages","text":"two R packages cover graphical multiple comparison procedures (MCPs): gMCP (Rohmeyer Klinglmueller 2024) lrstat (Lu 2023). development graphicalMCP benefited two packages. provide comparisons graphicalMCP packages respect key functions.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"list-of-comparisons","dir":"Articles","previous_headings":"","what":"List of comparisons","title":"Comparisons with other packages","text":"graphicalMCP::graph_generate_weights() gMCP::generateWeights() graphicalMCP::graph_test_shortcut() gMCP::gMCP() graphicalMCP::graph_calculate_power() gMCP::calcPower() graphicalMCP::graph_test_closure() gMCP::gMCP() graphicalMCP::graph_calculate_power() gMCP::calcPower() graphicalMCP::graph_test_closure() gMCP::gMCP() graphicalMCP::graph_calculate_power() gMCP::calcPower()","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"comparisons-of-weighting-strategies","dir":"Articles","previous_headings":"","what":"Comparisons of weighting strategies","title":"Comparisons with other packages","text":"random graph five hypotheses generated used comparison. Weighting strategies following two functions compared: graphicalMCP::graph_generate_weights() gMCP::generateWeights(). process repeated 1000 times. Weighting strategies matched 1000 cases.","code":"set.seed(1234) identical <- NULL for (i in 1:1000) {   graph <- random_graph(5)   graphicalmcp_weights <- graphicalMCP::graph_generate_weights(graph)   dimnames(graphicalmcp_weights) <- list(NULL, NULL)   gmcp_weights <-     gMCP::generateWeights(graph$transitions, graph$hypotheses)   gmcp_weights <- gmcp_weights[nrow(gmcp_weights):1, ] # Reorder rows   identical <- c(     identical,     all.equal(gmcp_weights, graphicalmcp_weights, tolerance = 1e-7)   ) } all(identical) #> [1] TRUE"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"adjusted-p-values-for-testing","dir":"Articles","previous_headings":"Comparisons of sequentially rejective procedures based on Bonferroni tests","what":"Adjusted p-values for testing","title":"Comparisons with other packages","text":"random graph five hypotheses generated used comparison. set p-values randomly generated used graphical MCP. Adjusted p-values calculated compared using following functions: graphicalMCP::graph_test_shortcut() gMCP::gMCP(). process repeated 10000 times. Adjusted p-values matched 10000 cases.","code":"set.seed(1234) alpha <- 0.025 identical <- NULL for (i in 1:10000) {   graph <- random_graph(5)   p <- runif(5, 0, alpha)   graphicalmcp_test_shortcut <-     graph_test_shortcut(graph, p, alpha = alpha)$outputs$adjusted_p   gmcp_test_shortcut <-     gMCP(as_graphMCP(graph), p, alpha = alpha)@adjPValues   identical <- c(     identical,     all.equal(graphicalmcp_test_shortcut, gmcp_test_shortcut, tolerance = 1e-7)   ) } all(identical) #> [1] TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"power-simulations","dir":"Articles","previous_headings":"Comparisons of sequentially rejective procedures based on Bonferroni tests","what":"Power simulations","title":"Comparisons with other packages","text":"random graph five hypotheses generated used comparison. set marginal power (without multiplicity adjustment) randomly generated. Local power (multiplicity adjustment) calculated compared using following functions: graphicalMCP::graph_calculate_power() gMCP::calcPower(). Since different simulation methods used, results slightly different. maximum absolute difference local power 0.0051 (0.51%) among 1000 cases, relatively small.","code":"set.seed(1234) alpha <- 0.025 sim_corr <- matrix(.5, 5, 5) diag(sim_corr) <- 1 graphicalmcp_power <- NULL gmcp_power <- NULL for (i in 1:1000) {   graph <- random_graph(5)   marginal_power <- runif(5, 0.5, 0.9)   noncentrality_parameter <-     qnorm(1 - 0.025, lower.tail = TRUE) -     qnorm(1 - marginal_power, lower.tail = TRUE)    set.seed(1234 + i - 1)   graphicalmcp_power <- rbind(     graphicalmcp_power,     graph_calculate_power(       graph,       alpha = alpha,       power_marginal = marginal_power,       sim_corr = sim_corr,       sim_n = 2^17     )$power$power_local   )    set.seed(1234 + i - 1)   gmcp_power <- rbind(     gmcp_power,     calcPower(       graph$hypotheses,       alpha = alpha,       graph$transitions,       mean = noncentrality_parameter,       corr.sim = sim_corr,       n.sim = 2^17     )$LocalPower   ) }  diff <- data.frame(   rbind(graphicalmcp_power, gmcp_power),   procedure = rep(c(\"graphicalMCP\", \"gMCP\"), each = nrow(graphicalmcp_power)) )  write.csv(   diff,   here::here(\"vignettes/cache/comparisons_power_shortcut.csv\"),   row.names = FALSE )  diff <- read.csv(here::here(\"vignettes/cache/comparisons_power_shortcut.csv\")) graphicalmcp_power <- subset(diff, procedure == \"graphicalMCP\") gmcp_power <- subset(diff, procedure == \"gMCP\") round(   max(     abs(       graphicalmcp_power[, -ncol(graphicalmcp_power)] -         gmcp_power[, -ncol(gmcp_power)]     )   ),   4 ) # Maximum difference in local power among 1000 cases"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"adjusted-p-values-for-testing-1","dir":"Articles","previous_headings":"Comparisons of closed test procedures with parametric tests","what":"Adjusted p-values for testing","title":"Comparisons with other packages","text":"successive graph two primary two secondary hypotheses generated used comparison. set p-values randomly generated used graphical MCP. Adjusted p-values calculated compared using following functions: graphicalMCP::graph_test_closure() gMCP::gMCP(). Parametric tests used two primary hypotheses. process repeated 10000 times. Adjusted p-values matched 10000 cases.","code":"hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0.5, 0.5, 0),   c(0.5, 0, 0, 0.5),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) graph <- graph_create(hypotheses, transitions)  set.seed(1234) alpha <- 0.025 identical <- NULL test_corr <- rbind(   c(1, 0.5, NA, NA),   c(0.5, 1, NA, NA),   c(NA, NA, 1, NA),   c(NA, NA, NA, 1) ) for (i in 1:10000) {   p <- runif(4, 0, alpha)   graphicalmcp_test_parametric <- graph_test_closure(     graph,     p,     alpha = alpha,     test_groups = list(1:2, 3:4),     test_types = c(\"parametric\", \"bonferroni\"),     test_corr = list(test_corr[1:2, 1:2], NA)   )$outputs$adjusted_p   gmcp_test_parametric <- gMCP(     as_graphMCP(graph),     p,     alpha = 0.025,     correlation = test_corr   )@adjPValues   identical <- c(     identical,     all.equal(graphicalmcp_test_parametric, gmcp_test_parametric, tolerance = 1e-7)   ) } all(identical) #> [1] TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"power-simulations-1","dir":"Articles","previous_headings":"Comparisons of closed test procedures with parametric tests","what":"Power simulations","title":"Comparisons with other packages","text":"successive graph two primary two secondary hypotheses generated used comparison. set marginal power (without multiplicity adjustment) randomly generated. Local power (multiplicity adjustment) calculated compared using following functions: graphicalMCP::graph_calculate_power() gMCP::calcPower(). Parametric tests used two primary hypotheses. process repeated 100 times. Since different simulation methods used, results slightly different. maximum absolute difference local power 0.0142 (1.42%) among 100 cases, small.","code":"hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0.5, 0.5, 0),   c(0.5, 0, 0, 0.5),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) graph <- graph_create(hypotheses, transitions) test_corr <- rbind(   c(1, 0.5, NA, NA),   c(0.5, 1, NA, NA),   c(NA, NA, 1, NA),   c(NA, NA, NA, 1) ) sim_corr <- matrix(0.5, 4, 4) diag(sim_corr) <- 1 set.seed(1234) alpha <- 0.025 graphicalmcp_power_parametric <- NULL gmcp_power_parametric <- NULL for (i in 1:100) {   marginal_power <- runif(4, 0.5, 0.9)   noncentrality_parameter <-     qnorm(1 - 0.025, lower.tail = TRUE) -     qnorm(1 - marginal_power, lower.tail = TRUE)    set.seed(1234 + i - 1)   graphicalmcp_power_parametric <- rbind(     graphicalmcp_power_parametric,     graph_calculate_power(       graph,       alpha = alpha,       test_groups = list(1:2, 3:4),       test_types = c(\"parametric\", \"bonferroni\"),       test_corr = list(test_corr[1:2, 1:2], NA),       power_marginal = marginal_power,       sim_corr = sim_corr,       sim_n = 2^14     )$power$power_local   )    set.seed(1234 + i - 1)   gmcp_power_parametric <- rbind(     gmcp_power_parametric,     calcPower(       graph$hypotheses,       alpha = alpha,       graph$transitions,       corr.test = test_corr,       mean = noncentrality_parameter,       corr.sim = sim_corr,       n.sim = 2^14     )$LocalPower   ) }  diff <- data.frame(   rbind(graphicalmcp_power_parametric, gmcp_power_parametric),   procedure = rep(c(\"graphicalMCP\", \"gMCP\"), each = nrow(gmcp_power_parametric)) )  write.csv(   diff,   here::here(\"vignettes/cache/comparisons_power_parametric.csv\"),   row.names = FALSE )  diff <- read.csv(here::here(\"vignettes/cache/comparisons_power_parametric.csv\")) graphicalmcp_power <- subset(diff, procedure == \"graphicalMCP\") gmcp_power <- subset(diff, procedure == \"gMCP\") round(   max(     abs(       graphicalmcp_power_parametric[, -ncol(graphicalmcp_power_parametric)] -         gmcp_power_parametric[, -ncol(gmcp_power)]     )   ),   4 ) # Maximum difference in local power among 100 cases"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"adjusted-p-values-for-testing-2","dir":"Articles","previous_headings":"Comparisons of closed test procedures with Simes tests","what":"Adjusted p-values for testing","title":"Comparisons with other packages","text":"successive graph two primary two secondary hypotheses generated used comparison. set p-values randomly generated used graphical MCP. Adjusted p-values calculated compared using following functions: graphicalMCP::graph_test_closure() lrstat::fadjpsim(). Simes tests used two primary hypotheses. process repeated 10000 times. Adjusted p-values matched 10000 cases.","code":"hypotheses <- c(0.5, 0.5, 0, 0) eps <- 0.0001 transitions <- rbind(   c(0, 1 - eps, eps, 0),   c(1 - eps, 0, 0, eps),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) graph <- graph_create(hypotheses, transitions)  set.seed(1234) alpha <- 0.025 identical <- NULL family <- rbind(   c(1, 1, 0, 0),   c(0, 0, 1, 0),   c(0, 0, 0, 1) ) for (i in 1:10000) {   p <- runif(4, 0, alpha)   graphicalmcp_test_simes <- graph_test_closure(     graph,     p,     alpha = alpha,     test_groups = list(1:2, 3:4),     test_types = c(\"simes\", \"bonferroni\")   )$outputs$adjusted_p   names(graphicalmcp_test_simes) <- NULL   lrstat_test_simes <-     fadjpsim(       fwgtmat(graph$hypotheses, graph$transitions),       p,       family     )    identical <- c(     identical,     all.equal(graphicalmcp_test_simes, lrstat_test_simes, tolerance = 1e-7)   ) } all(identical) #> [1] TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html","id":"power-simulations-2","dir":"Articles","previous_headings":"Comparisons of closed test procedures with Simes tests","what":"Power simulations","title":"Comparisons with other packages","text":"Power simulations available lrstat. Thus comparison done compare graphicalMCP::graph_calculate_power() manual repetition lrstat::fadjpsim() many sets marginal power. process comparison adjusted p-values, thus omitted.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"motivating-example","dir":"Articles","previous_headings":"","what":"Motivating example","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"Consider simple successive graph four hypotheses. two primary hypotheses H1H_1 H2H_2 two secondary hypotheses H3H_3 H4H_4. Initially, hypothesis weights split equally H1H_1 H2H_2 0.5. Hypotheses H3H_3 H4H_4 receive 0 hypothesis weights H3(H4)H_3 (H_4) tested H1(H2)H_1 (H_2) rejected. Thus edge H1(H2)H_1 (H_2) H3(H4)H_3 (H_4) transition weight 1. H1H_1 H3H_3 rejected, hypothesis weights propagated H2H_2; similarly, H2H_2 H4H_4 rejected, hypothesis weights propagated H1H_1. Thus edge H3(H4)H_3 (H_4) H2(H1)H_2 (H_1) transition weight 1. graphical multiple comparison procedure illustrated .","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"generating-the-closure","dir":"Articles","previous_headings":"","what":"Generating the closure","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"closure multiple comparison procedure collection intersection hypotheses H1∩H2∩H3∩H4H_1\\cap H_2\\cap H_3\\cap H_4, H1∩H2∩H3H_1\\cap H_2\\cap H_3, H1∩H2∩H4H_1\\cap H_2\\cap H_4, H1∩H3∩H4H_1\\cap H_3\\cap H_4, H2∩H3∩H4…,H1,H2,H3H_2\\cap H_3\\cap H_4\\ \\ldots, H_1, H_2, H_3, H4H_4. words, intersection hypotheses consist intersections based non-empty subsets {1,2,3,4}\\{1, 2, 3, 4\\}, e.g., {1,2,3}\\{1, 2, 3\\}, {1,2,4}\\{1, 2, 4\\}, {1,3,4}\\{1, 3, 4\\}, {2,3,4}\\{2, 3, 4\\}, …\\ldots. Thus 24−12^4-1 intersection hypotheses. equivalent way generate intersection hypotheses use binary representation. example, intersection hypothesis H1∩H2∩H3∩H4H_1\\cap H_2\\cap H_3\\cap H_4 corresponds (1,1,1,1)(1, 1, 1, 1) H1∩H2∩H3H_1\\cap H_2\\cap H_3 corresponds (1,1,1,0)(1, 1, 1, 0). closure can indexed power set {1,2,3,4}\\{1, 2, 3, 4\\} . general, one can use rev(expand.grid(rep(list(1:0), m))) general closure, mm number hypotheses.","code":"#>    H1 H2 H3 H4 #> 1   1  1  1  1 #> 2   1  1  1  0 #> 3   1  1  0  1 #> 4   1  1  0  0 #> 5   1  0  1  1 #> 6   1  0  1  0 #> 7   1  0  0  1 #> 8   1  0  0  0 #> 9   0  1  1  1 #> 10  0  1  1  0 #> 11  0  1  0  1 #> 12  0  1  0  0 #> 13  0  0  1  1 #> 14  0  0  1  0 #> 15  0  0  0  1"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"calculating-the-weighting-strategy","dir":"Articles","previous_headings":"Generating the closure","what":"Calculating the weighting strategy","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"Given closure, one can calculate hypothesis weight associated every hypothesis every intersection hypothesis using Algorithm 1 (Bretz et al. 2011). whole collection hypothesis weights called weighting strategy. example, hypothesis weights (0.5,0.5,0,0)(0.5, 0.5, 0, 0) intersection hypothesis H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4. hypothesis weights intersection hypothesis H1∩H2∩H3H_1\\cap H_2 \\cap H_3 (0.5,0.5,0,0)(0.5, 0.5, 0, 0), can calculated removing H4H_4 initial graph applying Algorithm 1 (Bretz et al. 2011). algorithm calculates hypothesis weights step--step fashion. example, intersection hypothesis H1∩H2H_1\\cap H_2, can start H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 calculates hypothesis weights H1∩H2∩H3H_1\\cap H_2 \\cap H_3 removing H4H_4 calculates hypothesis weights H1∩H2H_1\\cap H_2 removing H3H_3; can also start H1∩H2∩H3H_1\\cap H_2 \\cap H_3 (assuming hypotheses weights stored) calculates hypothesis weights H1∩H2H_1\\cap H_2 removing H3H_3. Therefore, two strategies calculate weighting strategy.","code":"#>      H1   H2   H3   H4 #> 1  0.50 0.50 0.00 0.00 #> 2  0.50 0.50 0.00 0.00 #> 3  0.50 0.50 0.00 0.00 #> 4  0.50 0.50 0.00 0.00 #> 5  0.75 0.00 0.00 0.25 #> 6  1.00 0.00 0.00 0.00 #> 7  0.75 0.00 0.00 0.25 #> 8  1.00 0.00 0.00 0.00 #> 9  0.00 0.75 0.25 0.00 #> 10 0.00 0.75 0.25 0.00 #> 11 0.00 1.00 0.00 0.00 #> 12 0.00 1.00 0.00 0.00 #> 13 0.00 0.00 0.50 0.50 #> 14 0.00 0.00 1.00 0.00 #> 15 0.00 0.00 0.00 1.00"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"approach-1-simple-approach","dir":"Articles","previous_headings":"Generating the closure > Calculating the weighting strategy","what":"Approach 1: Simple approach","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"first strategy utilizes initial graph starting point calculates hypothesis weights intersection hypotheses. example, calculate hypothesis weights H1∩H2H_1\\cap H_2, start intersection hypothesis H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 sequentially remove H4H_4 H3H_3 (order). approach simple implement since hypothesis weights H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 determined initial graph always available. approach similar one implemented gMCP R package. drawback use information reduce number calculations. example, possible hypothesis weights H1∩H2∩H3H_1\\cap H_2 \\cap H_3 calculated calculating H1∩H2H_1\\cap H_2. Using information H1∩H2∩H3H_1\\cap H_2 \\cap H_3 need one-step calculation, compared two-step calculation using H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"approach-2-parent-child-approach","dir":"Articles","previous_headings":"Generating the closure > Calculating the weighting strategy","what":"Approach 2: Parent-child approach","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"approach tries avoid drawback Approach 1 saving intermediate graphs. performs one-step calculation save time. general, intersection hypothesis parent intersection hypothesis, involves hypotheses involved first intersection one extra hypothesis. example, second row matrix_intersections H1∩H2∩H3H_1\\cap H_2 \\cap H_3 parent intersection H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 first row; third row matrix_intersections H1∩H2∩H4H_1\\cap H_2 \\cap H_4 parent intersection H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 first row. Thus can identify parent intersection hypothesis row matrix_intersections (except row 1) row number 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7. Given sequence parent hypotheses, simple obtain hypothesis weights intersection hypothesis based parent intersection hypothesis via one-step calculation. interest understand pattern obtain efficiently. First, bottom half (rows 9 - 15) top half (rows 1 - 7), row’s parent bottom half corresponding row top half, eight rows , difference flipping H1H_1 1 top half 0 bottom half. example, row 15’s parent row 15 - 8 = 7. Using observation, can determine parent hypotheses rows 9 15 1, 2, 3, 4, 5, 6, 7. similar pattern can observed rows 5 8. parent hypotheses rows 1, 2, 3, 4, respectively, flipping H2H_2 1 0. rows 3 - 4, parent hypotheses rows 1, 2, respectively, flipping H3H_3 1 0. Lastly row 2, parent hypothesis row 1. row number parent hypothesis can efficiently generated running .call(c, lapply(2^(seq_len(m) - 1), seq_len))[-2^m, ], mm number hypotheses.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"comparing-different-approaches-to-calculating-weighting-strategies","dir":"Articles","previous_headings":"Generating the closure","what":"Comparing different approaches to calculating weighting strategies","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"benchmark existing approaches calculating weighting strategies, compare following approaches: gMCP::generateWeights() (Rohmeyer Klinglmueller 2024), lrstat::fwgtmat() (Lu 2016), Approach 1 (graphicalMCP simple) Approach 2 (graphicalMCP parent-child). Random graphs generated numbers hypotheses 4, 8, 12, 16. Computing time (median log-10 milliseconds) plotted . can see gMCP::generateWeights() slowest lrstat::fwgtmat() fastest. Approach 2 (graphicalMCP parent-child) faster Approach 1 (graphicalMCP simple). Note lrstat::fwgtmat() implements calculation using C++, known faster R. less stable approaches, e.g., giving errors often others. Given computing time R-based approaches acceptable, adding Rcpp dependency considered graphicalMCP. considerations, implement Approach 2 graphicalMCP::graph_generate_weights().","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"conventional-approach-for-power-simulations","dir":"Articles","previous_headings":"Improving power simulations using parent-child relationships","what":"Conventional approach for power simulations","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"conventional approach power simulations repeat following process many times, e.g., 100,000 times. Simulate set p-values Determine hypothesis can rejected Remove rejected hypothesis update graph Repeat hypotheses can rejected Note step update graph may repeat many replications, may repetitive. mm hypotheses, 2m−12^m-1 graphs depending hypotheses rejected. graphs correspond closure weighting strategy. Thus idea avoid redundant updating graphs utilize weighting strategy.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"power-simulations-using-parent-child-relationships","dir":"Articles","previous_headings":"Improving power simulations using parent-child relationships","what":"Power simulations using parent-child relationships","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"key allow approach efficiently identify row weighting strategy, given hypotheses rejected. Remembering pattern found Approach 2, bottom half (rows 9 - 15) matrix_intersections top half (rows 1 - 7), except flipping H1H_1 1 0. means H1H_1 rejected (1 H1H_1 matrix_intersections), row number index top half. example, assume H2H_2 H4H_4 rejected index matrix_intersections (1,0,1,0)(1, 0, 1, 0). Since H1H_1 1, corresponding row top half (rows 1- 7). H2H_2 0 thus corresponding row bottom half within top half (rows 5 - 7). Since H3H_3 1 thus corresponding row top half (rows 5 - 6). H4H_4 0 thus corresponding row 6. useful way calculate row number index XXXX 2^m - sum(XXXX * 2^(m:1 - 1)). example XXXX=1010, row number (1 - 1) * 8 + (1 - 0) * 4 + (1 - 1) * 2 + (1 - 0) * 1 + 1 = 16 - 10 = 6. way efficiently identifying rows weighting_strategy, power simulations implemented follows: Obtain weighting strategy (simulations) Simulate set p-values Determine hypothesis can rejected Remove rejected hypothesis identify row weighting strategy Repeat hypotheses can rejected small modification Step 3b makes approach much faster conventional approach power simulations.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html","id":"comparing-different-approaches-to-power-simulations","dir":"Articles","previous_headings":"Improving power simulations using parent-child relationships","what":"Comparing different approaches to power simulations","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"benchmark existing approaches calculating weighting strategies, compare following approaches: gMCP::calcPower(), Approach 1 (graphicalMCP conventional), Approach 2 (graphicalMCP parent-child). Holm fixed sequence procedures considered numbers hypotheses 4, 8, 12, 16. Computing time (median log-10 seconds) plotted . can see gMCP::calcPower() fastest Approach 1 (graphicalMCP conventional) lowest. Note gMCP::calcPower() implements simulation using C, known faster R easy extend situations. Given computing time Approach 2 (graphicalMCP parent-child) acceptable, implement graphicalMCP::graph_calculate_power().","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"confirmatory clinical trials, regulatory guidelines mandate strong control family-wise error rate prespecified level α\\alpha. Many multiple comparison procedures (MCPs) proposed purpose. graphical approaches general framework include many common MCPs special cases. vignette, illustrate use graphicalMCP perform common MCPs. test mm hypotheses using graphical MCP, hypothesis HiH_i receives weight 0≤wi≤10\\leq w_i\\leq 1 (called hypothesis weight), ∑=1mwi≤1\\sum_{=1}^{m}w_i\\leq 1. HiH_i HjH_j, directed weighted edge 0≤gij≤10\\leq g_{ij}\\leq 1, means HiH_i rejected, hypothesis weight propagated (transferred) HjH_j gijg_{ij} determines much propagation. also require ∑j=1mgij≤1\\sum_{j=1}^{m}g_{ij}\\leq 1 gii=0g_{ii}=0.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"weighted-bonferroni-test","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Weighted Bonferroni test","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"weighted Bonferroni test splits α\\alpha among hypotheses testing every hypothesis significance level wiαw_i\\alpha. Thus rejects hypothesis p-value less equal significance level. wi=wjw_i=w_j ,ji,j, means equal split test Bonferroni test. propagation pair hypothesis.","code":"set.seed(1234) alpha <- 0.025 m <- 3 bonferroni_graph <- bonferroni(rep(1 / m, m)) # transitions <- matrix(0, m, m) # bonferroni_graph <- graph_create(rep(1 / m, m), transitions)  plot(   bonferroni_graph,   layout = igraph::layout_in_circle(     as_igraph(bonferroni_graph),     order = c(2, 1, 3)   ),   vertex.size = 70 ) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     bonferroni_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3  #>  TRUE FALSE FALSE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"holm-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Holm Procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Holm (Bonferroni-Holm) procedures improve Bonferroni tests allowing propagation (Holm 1979). words, transition weights hypotheses may zero. uniformly powerful Bonferroni tests.","code":"set.seed(1234) alpha <- 0.025 m <- 3 holm_graph <- bonferroni_holm(rep(1 / m, m)) # transitions <- matrix(1 / (m - 1), m, m) # diag(transitions) <- 0 # holm_graph <- graph_create(rep(1 / m, m), transitions)  plot(holm_graph,   layout = igraph::layout_in_circle(     as_igraph(holm_graph),     order = c(2, 1, 3)   ),   vertex.size = 70 ) p_values <- runif(m, 0, alpha)  test_results <- graph_test_shortcut(holm_graph, p = p_values, alpha = alpha)  test_results$outputs$rejected #>    H1    H2    H3  #>  TRUE FALSE FALSE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"fixed-sequence-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Fixed sequence procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Fixed sequence (hierarchical) procedures pre-specify order testing [Maurer, Hothorn, Lehmacher (1995);westfall-2001-optimally]. example, procedure test H1H_1 first. rejected, test H2H_2; otherwise testing stops. H2H_2 rejected, test H3H_3; otherwise testing stops. hypothesis, tested full α\\alpha level, can tested.","code":"set.seed(1234) alpha <- 0.025 m <- 3 fixed_sequence_graph <- fixed_sequence(m) # transitions <- rbind( #   c(0, 1, 0), #   c(0, 0, 1), #   c(0, 0, 0) # ) # fixed_sequence_graph <- graph_create(c(1, 0, 0), transitions)  plot(fixed_sequence_graph, nrow = 1, asp = 0.05, vertex.size = 40) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     fixed_sequence_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"fallback-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Fallback procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Fallback procedures one-way propagation (like fixed sequence procedures) allow hypotheses tested different significance levels (Wiens 2003).  can improved allow propagation later hypotheses earlier hypotheses, possible later hypothesis rejected earlier hypothesis can rejected. two versions improvement: fallback_improved_1 due (Wiens Dmitrienko 2005) fallback_improved_2 due (Bretz et al. 2009) respectively.","code":"set.seed(1234) alpha <- 0.025 m <- 3 fallback_graph <- fallback(rep(1 / 3, 3)) # transitions <- rbind( #   c(0, 1, 0), #   c(0, 0, 1), #   c(0, 0, 0) # ) # fallback_graph <- graph_create(rep(1 / 3, 3), transitions)  plot(fallback_graph, nrow = 1, asp = 0.05, vertex.size = 40) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     fallback_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE set.seed(1234) alpha <- 0.025 m <- 3 fallback_improved_1_graph <- fallback_improved_1(rep(1 / 3, 3)) # hypotheses <- rep(1 / 3, 3) # transitions <- rbind( #   c(0, 1, 0), #   c(0, 0, 1), #   c(hypotheses[seq_len(m - 1)] / sum(hypotheses[seq_len(m - 1)]), 0) # ) # fallback_improved_1_graph <- graph_create(rep(1 / 3, 3), transitions)  plot(   fallback_improved_1_graph,   nrow = 1,   asp = 0.05,   vertex.size = 40,   edge_curves = c(\"pairs\" = 7, \"H3|H1\" = -10) ) epsilon <- 0.0001 fallback_improved_2_graph <- fallback_improved_2(rep(1 / 3, 3), epsilon) # hypotheses <- rep(1 / 3, 3) # transitions <- rbind( #   c(0, 1, 0), #   c(1 - epsilon, 0, epsilon), #   c(1, 0, 0) # ) # fallback_improved_2_graph <- graph_create(rep(1 / 3, 3), transitions)  plot(   fallback_improved_2_graph,   nrow = 1,   asp = 0.05,   eps = 0.0001,   edge_curves = c(\"pairs\" = 7, \"H3|H1\" = -10),   vertex.size = 40 ) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     fallback_improved_2_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"serial-gatekeeping-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Serial gatekeeping procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Serial gatekeeping procedures involve ordered multiple families hypotheses, hypotheses family hypotheses must rejected proceeding test sequence. example considers primary family consisting two hypotheses H1H_1 H2H_2 secondary family consisting single hypothesis H3H_3. primary family, Holm procedure applied. H1H_1 H2H_2 rejected, H3H_3 can tested level α\\alpha; otherwise H3H_3 rejected. allow conditional propagation H3H_3, ε\\varepsilon edge used H2H_2 H3H_3. small transition weight H2H_2 propagates hypothesis weight H1H_1 (already rejected) retains small (non-zero) weight H3H_3 H1H_1 rejected, hypothesis weight H2H_2 propagated H3H_3. ε\\varepsilon assigned 0.0001 practice, value adjusted much smaller smallest p-value observed.","code":"set.seed(1234) alpha <- 0.025 m <- 3 epsilon <- 0.0001  transitions <- rbind(   c(0, 1, 0),   c(1 - epsilon, 0, epsilon),   c(0, 0, 0) )  serial_gatekeeping_graph <- graph_create(c(0.5, 0.5, 0), transitions)  plot(   serial_gatekeeping_graph,   nrow = 1,   asp = 0.05,   eps = 0.0001,   edge_curves = c(\"pairs\" = 7, \"H3|H1\" = -10),   vertex.size = 40 ) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     serial_gatekeeping_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"parallel-gatekeeping-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Parallel gatekeeping procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Parallel gatekeeping procedures also involve multiple ordered families hypotheses, null hypotheses family hypotheses must rejected proceeding test sequence (Dmitrienko, Offen, Westfall 2003). example considers primary family consisting two hypotheses H1H_1 H2H_2 secondary family consisting two hypotheses H3H_3 H4H_4. primary family, Bonferroni test applied. H1H_1 H2H_2 rejected, H3H_3 H4H_4 can tested level α/2\\alpha/2 using Holm procedure; H1H_1 H2H_2 rejected, H3H_3 H4H_4 can tested level α\\alpha using Holm procedure; otherwise H3H_3 H4H_4 rejected.  parallel gatekeeping procedure can improved adding ε\\varepsilon edges secondary hypotheses primary hypotheses, possible secondary hypotheses rejected still remaining primary hypothesis rejected (Bretz et al. 2009).","code":"set.seed(1234) alpha <- 0.025 m <- 4  transitions <- rbind(   c(0, 0, 0.5, 0.5),   c(0, 0, 0.5, 0.5),   c(0, 0, 0, 1),   c(0, 0, 1, 0) )  parallel_gatekeeping_graph <- graph_create(c(0.5, 0.5, 0, 0), transitions)  plot(parallel_gatekeeping_graph, vertex.size = 70) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     parallel_gatekeeping_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE FALSE FALSE FALSE set.seed(1234) alpha <- 0.025 m <- 4 epsilon <- 0.0001  transitions <- rbind(   c(0, 0, 0.5, 0.5),   c(0, 0, 0.5, 0.5),   c(epsilon, 0, 0, 1 - epsilon),   c(0, epsilon, 1 - epsilon, 0) )  parallel_gatekeeping_improved_graph <-   graph_create(c(0.5, 0.5, 0, 0), transitions)  plot(parallel_gatekeeping_improved_graph, eps = 0.0001, vertex.size = 70) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     parallel_gatekeeping_improved_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE FALSE FALSE FALSE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"successive-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Successive procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Successive procedures incorporate successive relationships hypotheses. example, secondary hypothesis tested primary hypothesis rejected. similar using fixed sequence procedure component graph. example considers two primary hypotheses H1H_1 H2H_2 two secondary hypotheses H3H_3 H4H_4. Primary hypotheses H1H_1 H2H_2 receive equal hypothesis weight 0.5; secondary hypotheses H3H_3 H4H_4 receive hypothesis weight 0. secondary hypothesis H3(H4)H_3 (H_4) can tested corresponding primary hypothesis H1(H2)H_1 (H_2) rejected. represents successive relationships H1H_1 H3H_3, H2H_2 H4H_4, respectively (Maurer, Glimm, Bretz 2011). H1H_1 H3H_3 rejected, hypothesis weights propagated H2H_2 H4H_4, vice versa.  graph generalized allow propagation primary hypotheses (Maurer, Glimm, Bretz 2011). general successive graph illustrate variable determine propagation H1H_1 H2H_2.","code":"set.seed(1234) alpha <- 0.025 m <- 4 simple_successive_graph <- simple_successive_1() # transitions <- rbind( #   c(0, 0, 1, 0), #   c(0, 0, 0, 1), #   c(0, 1, 0, 0), #   c(1, 0, 0, 0) # ) # simple_successive_graph <- graph_create(c(0.5, 0.5, 0, 0), transitions)  plot(simple_successive_graph, layout = \"grid\", nrow = 2, vertex.size = 70) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     simple_successive_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE FALSE FALSE FALSE set.seed(1234) alpha <- 0.025 m <- 4  successive_var <- simple_successive_var <- function(gamma) {   graph_create(     c(0.5, 0.5, 0, 0),     rbind(       c(0, gamma, 1 - gamma, 0),       c(gamma, 0, 0, 1 - gamma),       c(0, 1, 0, 0),       c(1, 0, 0, 0)     )   ) }  successive_var_graph <- successive_var(0.5) plot(successive_var_graph, layout = \"grid\", nrow = 2, vertex.size = 70) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     successive_var_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE FALSE"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"hommel-procedure","dir":"Articles","previous_headings":"Simes-based procedures","what":"Hommel procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Hommel procedure (Hommel 1988) closed test procedure uses Simes tests every intersection hypothesis. According Xi Bretz (2019), graph Hommel procedures graph Holm procedures. Thus perform Hommel procedure, just need specify test_type simes.","code":"set.seed(1234) alpha <- 0.025 m <- 3 hommel_graph <- bonferroni_holm(rep(1 / m, m))  plot(   hommel_graph,   layout = igraph::layout_in_circle(     as_igraph(hommel_graph),     order = c(2, 1, 3)   ),   vertex.size = 70 ) p_values <- runif(m, 0, alpha)  test_results <- graph_test_closure(   hommel_graph,   p = p_values,   alpha = alpha,   test_types = \"simes\" )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html","id":"dunnett-procedure","dir":"Articles","previous_headings":"Parametric procedures","what":"Dunnett procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Step-Dunnett procedures closed test procedure improvement Holm procedures incorporating correlation structure test statistics (Dunnett Tamhane 1991). Thus graph Holm procedures. Assume equi-correlated case, correlation pair test statistics , e.g., 0.5. can perform step-Dunnett procedure specifying test_type parametric providing correlation matrix.","code":"set.seed(1234) alpha <- 0.025 m <- 3 dunnett_graph <- bonferroni_holm(rep(1 / m, m))  plot(   dunnett_graph,   layout = igraph::layout_in_circle(     as_igraph(dunnett_graph),     order = c(2, 1, 3)   ),   vertex.size = 70 ) p_values <- runif(m, 0, alpha) corr <- matrix(0.5, m, m) diag(corr) <- 1  test_results <- graph_test_closure(   dunnett_graph,   p = p_values, alpha = alpha,   test_types = \"parametric\",   test_corr = list(corr) )  test_results$outputs$rejected #>    H1    H2    H3  #>  TRUE FALSE FALSE"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graphicalMCP.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Get started","text":"Graphical approaches multiple comparison procedures (MCPs) general framework control familywise error rate strongly pre-specified significance level 0<α<10<\\alpha<1. approach includes many commonly used MCPs special cases transparent visualizing MCPs better communications. graphicalMCP designed design analyze graphical MCPs flexible, informative efficient way.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graphicalMCP.html","id":"initial-graph","dir":"Articles","previous_headings":"Basic usage","what":"Initial graph","title":"Get started","text":"base object graphicalMCP initial_graph, consists vector hypothesis weights matrix transition weights (Bretz et al. 2009). object can created via graph_create(). graphical representation, hypotheses denoted nodes (vertices) associated hypothesis weights. directed edge hypothesis another indicates direction propagation hypothesis weight origin hypothesis end hypothesis. edge weighted transition weight indicating proportion propagation.","code":"library(graphicalMCP) # A graph of two primary hypotheses (H1 and H2) and two secondary hypotheses (H3 and H4) hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) hyp_names <- c(\"H1\", \"H2\", \"H3\", \"H4\") example_graph <- graph_create(hypotheses, transitions, hyp_names) example_graph #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 plot(example_graph, vertex.size = 60)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graphicalMCP.html","id":"update-graph","dir":"Articles","previous_headings":"Basic usage","what":"Update graph","title":"Get started","text":"hypothesis removed graph, hypothesis transition weights remaining hypotheses updated according Algorithm 1 Bretz et al. (2011). example, assume hypotheses H1, H2 H4 removed graph. updated graph removing three hypotheses .","code":"updated_example <- graph_update(   example_graph,   delete = c(TRUE, TRUE, FALSE, TRUE) )  updated_example #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 1, 2, 4 #>  #> --- Hypothesis weights --- #> H1: NA #> H2: NA #> H3:  1 #> H4: NA #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1 NA NA NA NA #>  H2 NA NA NA NA #>  H3 NA NA  0 NA #>  H4 NA NA NA NA plot(updated_example, vertex.size = 60)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graphicalMCP.html","id":"perform-graphical-mcps","dir":"Articles","previous_headings":"","what":"Perform graphical MCPs","title":"Get started","text":"Given set p-values hypotheses, graphical MCPs can performed using graph_test_shortcut() determine hypotheses can rejected significance level alpha. Assume p-values 0.01, 0.005, 0.03, 0.01 hypotheses H1-H4. one-sided significance level alpha = 0.025, rejected hypotheses H1, H2, H4. details shortcut testing can found vignette(\"shortcut-testing\"). similar testing procedure can performed using closure principle. allow tests intersection hypotheses, e.g., Simes, parametric mixture . test type Bonferroni, resulting closed procedure equivalent shortcut procedure . Additional details closed testing can found vignette(\"closed-testing\").","code":"test_results <- graph_test_shortcut(   example_graph,   p = c(0.01, 0.005, 0.03, 0.01),   alpha = 0.025 ) test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE  TRUE test_results_closed <- graph_test_closure(   example_graph,   p = c(0.01, 0.005, 0.03, 0.01),   alpha = 0.025,   test_types = \"bonferroni\",   test_groups = list(1:4) ) test_results_closed$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE  TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/graphicalMCP.html","id":"power-simulations","dir":"Articles","previous_headings":"","what":"Power simulations","title":"Get started","text":"multiplicity adjustment, graphical MCPs, “power” reject hypothesis affected, compared marginal power. latter power rejected hypothesis significance level alpha without multiplicity adjustment. marginal power usually obtained pieces statistical software. graph_calculate_power() performs power simulations assess power adjusting graphical MCP (Bretz, Maurer, Hommel 2011). Assume marginal power reject H1-H4 90%, 90%, 80%, 80% test statistics independent . local power multiplicity adjustment 87.7%, 87.7%, 67.2%, 67.2% respectively H1-H4. Additional details power simulations can found vignette(\"shortcut-testing\") vignette(\"closed-testing\").","code":"set.seed(1234) power_results <- graph_calculate_power(   example_graph,   sim_n = 1e6,   power_marginal = c(0.9, 0.9, 0.8, 0.8) ) power_results$power$power_local #>       H1       H2       H3       H4  #> 0.875760 0.876295 0.670470 0.671431"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"motivating-example","dir":"Articles","previous_headings":"","what":"Motivating example","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Consider confirmatory clinical trial comparing test treatment (treatment) control treatment (control) disease. two doses treatment: low dose high dose. two endpoints included multiplicity adjustment strategy, primary endpoint (PE) secondary endpoint (SE). total, four null hypotheses: H1H_1 H3H_3 primary secondary hypotheses respectively low dose versus control; H2H_2 H4H_4 primary secondary hypotheses respectively high dose versus control. clinical considerations constrain structure multiple comparison procedures, can flexibly incorporated using graphical approaches. First, low high doses considered equally important, means rejecting primary hypothesis either dose versus control leads successful trial. Regarding secondary hypotheses, one tested corresponding primary hypothesis rejected. means H3H_3 tested H1H_1 rejected; H4H_4 tested H2H_2 rejected. addition, statistical considerations complete graph. primary hypotheses H1H_1 H2H_2 equal hypothesis weight 0.5. secondary hypotheses hypothesis weight 0. primary hypothesis rejected, weight propagated along two outgoing edges: One primary hypothesis one descendant secondary hypothesis. two edges equal transition weight 0.5. primary secondary hypotheses rejected dose-control comparison, hypothesis weights propagated primary hypothesis dose-control comparison. specifications, can create following graph.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"create-the-graph","dir":"Articles","previous_headings":"","what":"Create the graph","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"","code":"hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0.5, 0.5, 0),   c(0.5, 0, 0, 0.5),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) hyp_names <- c(\"H1\", \"H2\", \"H3\", \"H4\")  g <- graph_create(hypotheses, transitions, hyp_names)  plot(g, vertex.size = 60)"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"adjusted-p-values-and-rejections","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure","what":"Adjusted p-values and rejections","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Given set p-values H1,…,H4H_1, \\ldots, H_4, graphical multiple comparison procedure can performed control familywise error rate (FWER) significance level alpha. graph_test_shortcut function agnostic one-sided two-sided tests. one-sided p-values, alpha often set 0.025 (default); two-sided p-values, alpha often set 0.05. consider one-sided tests . hypothesis rejected adjusted p-value less equal alpha. running procedure, hypotheses H1H_1, H2H_2, H4H_4 rejected adjusted p-value calculated.","code":"p_values <- c(0.018, 0.01, 0.105, 0.006) test_results <- graph_test_shortcut(g, p = p_values, alpha = 0.025)  test_results$outputs$adjusted_p # Adjusted p-values #>    H1    H2    H3    H4  #> 0.024 0.020 0.105 0.024 test_results$outputs$rejected # Rejections #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE  TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"obtain-final-and-intermediate-graphs-after-rejections","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure","what":"Obtain final and intermediate graphs after rejections","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"final graph graph removing rejected hypotheses H1H_1, H2H_2, H4H_4. can obtained via test_results$outputs$graph. Rejected hypotheses get hypothesis weight NA transition weight NA. based printing method print.updated_graph. can also obtain non-NA graph calling hypothesis weights transition weights separately via test_results$outputs$graph$hypotheses test_results$outputs$graph$transitions. Note case, rejected hypotheses get 0 hypothesis weight 0 transition weight. mainly internal calculation updating graphs. also interested intermediate graphs - example, graph H2H_2 H1H_1 rejected - can specify verbose = TRUE graph_test_shortcut. Note intermediate graphs depend order rejections, .e., sequence hypotheses rejected. default order defined increasing adjusted p-values, followed earlier hypothesis numbering case ties. example, default order rejection H2→H1→H4H_2\\rightarrow H_1\\rightarrow H_4. obtain intermediate graphs based order rejection, one can specify test_results_verbose$details$results. example, graph H2H_2 H1H_1 rejected given test_results_verbose$details$results[[3]].","code":"test_results$outputs$graph # Final graph after H1, H2 and H4 rejected (as NA's) #> Updated graph #>  #> --- Hypothesis weights --- #> H1: NA #> H2: NA #> H3:  1 #> H4: NA #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1 NA NA NA NA #>  H2 NA NA NA NA #>  H3 NA NA  0 NA #>  H4 NA NA NA NA test_results$outputs$graph$hypotheses # Hypothesis weights of the final graph #> H1 H2 H3 H4  #>  0  0  1  0 test_results$outputs$graph$transitions # Transition weights of the final graph #>    H1 H2 H3 H4 #> H1  0  0  0  0 #> H2  0  0  0  0 #> H3  0  0  0  0 #> H4  0  0  0  0  test_results_verbose <- graph_test_shortcut(   g,   p = p_values,   alpha = 0.025,   verbose = TRUE )  # Intermediate graph after H1 and H2 rejected test_results_verbose$details$results[[3]] #> Updated graph #>  #> --- Hypothesis weights --- #> H1:  NA #> H2:  NA #> H3: 0.5 #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1 NA NA NA NA #>  H2 NA NA NA NA #>  H3 NA NA  0  1 #>  H4 NA NA  1  0"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"obtain-possible-orders-of-rejections","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure","what":"Obtain possible orders of rejections","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"order rejections may unique orders valid. example, rejected hypotheses H1H_1, H2H_2 H4H_4. default order rejections H2→H1→H4H_2 \\rightarrow H_1 \\rightarrow H_4. Another valid order rejections H2→H4→H1H_2 \\rightarrow H_4 \\rightarrow H_1. However, first rejected hypothesis can H1H_1 H4H_4. obtain possible rejection orders, one can use function graph_rejection_orderings. intermediate final graphs can obtained using function graph_update particular order rejections.","code":"# Obtain all valid orders of rejections orders <- graph_rejection_orderings(test_results)$valid_orderings orders #> [[1]] #> H2 H1 H4  #>  2  1  4  #>  #> [[2]] #> H2 H4 H1  #>  2  4  1  # Intermediate graphs following the order of H2 and H4 graph_update(g, delete = orders[[2]])$intermediate_graphs[[3]] #> Updated graph #>  #> --- Hypothesis weights --- #> H1:  1 #> H2: NA #> H3:  0 #> H4: NA #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA  1 NA #>  H2 NA NA NA NA #>  H3  1 NA  0 NA #>  H4 NA NA NA NA"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"obtain-adjusted-significance-levels","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure","what":"Obtain adjusted significance levels","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"equivalent way obtain rejections adjusting significance levels. hypothesis rejected p-value less equal adjusted significance level. adjusted significance levels calculated order adjusted p-values: H2→H1→H4H_2 \\rightarrow H_1 \\rightarrow H_4, four steps checking rejections. First, H2H_2 rejected adjusted significance level 0.5 * alpha. Second, H1H_1 rejected adjusted significance level 0.75 * alpha, H2H_2 rejected. Third, H4H_4 rejected adjusted significance level 0.5 * alpha, H1H_1 H2H_2 rejected. Fourth finally, H3H_3 rejected adjusted significance level alpha, H1H_1, H2H_2 H4H_4 rejected. results can obtained specifying test_values = TRUE.","code":"test_results_test_values <- graph_test_shortcut(   g,   p = p_values,   alpha = 0.025,   test_values = TRUE )  test_results_test_values$test_values$results #>   Step Hypothesis     p Weight Alpha Inequality_holds #> 1    1         H2 0.010   0.50 0.025             TRUE #> 2    2         H1 0.018   0.75 0.025             TRUE #> 3    3         H4 0.006   0.50 0.025             TRUE #> 4    4         H3 0.105   1.00 0.025            FALSE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"power-simulation","dir":"Articles","previous_headings":"","what":"Power simulation","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Given graph, interested “power” trial. single null hypothesis, power probability true positive - , rejecting null hypothesis significance level alpha alternative hypothesis true. multiple null hypotheses, multiple versions “power”. example, power reject least one hypothesis vs power reject hypotheses, given alternative hypotheses true. graphical multiple comparison procedures, also important understand power reject hypothesis, given multiplicity adjustment. Sometimes, may want customize definitions power define success. Thus power calculation important aspect trial design.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"input-marginal-power-for-primary-hypotheses","dir":"Articles","previous_headings":"Power simulation","what":"Input: Marginal power for primary hypotheses","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Assume primary endpoint occurrence unfavorable clinical event. evaluate treatment effect, proportion patients event calculated, lower proportion preferred. Assume proportions 0.181 low high doses, 0.3 control. Using equal randomization among three treatment groups, clinical trial team chooses total sample size 600 200 per group. leads marginal power 80% H1H_1 H2H_2, respectively, using two-sample test difference proportions unpooled variance one-sided significance level 0.025. calculation, use marginal power combine information treatment effect, nuisance parameter, sample sizes hypothesis. Note significance level used marginal power calculation must alpha, used significance level FWER control. addition, marginal power one--one relationship noncentrality parameter, illustrated .","code":"alpha <- 0.025 prop <- c(0.3, 0.181, 0.181) sample_size <- rep(200, 3)  unpooled_variance <-   prop[-1] * (1 - prop[-1]) / sample_size[-1] +   prop[1] * (1 - prop[1]) / sample_size[1]  noncentrality_parameter_primary <-   -(prop[-1] - prop[1]) / sqrt(unpooled_variance)  power_marginal_primary <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_primary,   sd = 1,   lower.tail = FALSE )  names(power_marginal_primary) <- c(\"H1\", \"H2\") power_marginal_primary #>        H1        H2  #> 0.8028315 0.8028315"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"input-marginal-power-for-secondary-hypotheses","dir":"Articles","previous_headings":"Power simulation","what":"Input: Marginal power for secondary hypotheses","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Assume secondary endpoint change total medication score baseline, continuous outcome. evaluate treatment effect, mean change calculated, greater reduction preferred. Assume mean change baseline reduction 7.5 8.25, respectively low high doses, 5 control. assume known common standard deviation 10. Given sample size 200 per treatment group, marginal power 71% 90% H3H_3 H4H_4, respectively, using two-sample zz-test difference means one-sided significance level 0.025.","code":"mean_change <- c(5, 7.5, 8.25) sd <- rep(10, 3) variance <- sd[-1]^2 / sample_size[-1] + sd[1]^2 / sample_size[1]  noncentrality_parameter_secondary <-   (mean_change[-1] - mean_change[1]) / sqrt(variance)  power_marginal_secondary <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_secondary,   sd = 1,   lower.tail = FALSE )  names(power_marginal_secondary) <- c(\"H3\", \"H4\") power_marginal_secondary #>        H3        H4  #> 0.7054139 0.9014809"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"input-correlation-structure-to-simulate-test-statistics","dir":"Articles","previous_headings":"Power simulation","what":"Input: Correlation structure to simulate test statistics","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"addition marginal power, also need make assumptions joint distribution test statistics. example, assume follow multivariate normal distribution means defined noncentrality parameters correlation matrix RR. obtain correlations, helpful understand two types correlations example. correlation two dose-control comparisons endpoint correlation endpoints. former correlation can calculated function sample size. example, correlation test statistics H1H_1 H2H_2 ρ12=(n1n1+n0)1/2(n2n3+n0)1/2\\rho_{12}=\\left(\\frac{n_1}{n_1+n_0}\\right)^{1/2}\\left(\\frac{n_2}{n_3+n_0}\\right)^{1/2}. equal randomization, correlation 0.5. correlation test statistics H3H_3 H4H_4 . hand, correlation endpoints dose-control comparison often estimated based prior knowledge previous trials. Without information, assume ρ13=ρ24=0.5\\rho_{13}=\\rho_{24}=0.5. practice, one set correlation parameter try multiple values assess sensitivity assumption. Regarding correlation test statistics H1H_1 H4H_4 H2H_2 H3H_3, even difficult estimate. use simple product rule, means correlation product correlations two previously assumed correlations. example, ρ14=ρ12*ρ24\\rho_{14}=\\rho_{12}*\\rho_{24} ρ23=ρ12*ρ13\\rho_{23}=\\rho_{12}*\\rho_{13}. practice, one may make assumptions instead using product rule.","code":"corr <- matrix(0, nrow = 4, ncol = 4)  corr[1, 2] <-   corr[3, 4] <-   sqrt(     sample_size[2] / sum(sample_size[1:2]) *       sample_size[3] / sum(sample_size[c(1, 3)])   )  rho <- 0.5 corr[1, 3] <- corr[2, 4] <- rho corr[1, 4] <- corr[2, 3] <- corr[1, 2] * rho corr <- corr + t(corr) diag(corr) <- 1 colnames(corr) <- hyp_names rownames(corr) <- hyp_names corr #>      H1   H2   H3   H4 #> H1 1.00 0.50 0.50 0.25 #> H2 0.50 1.00 0.25 0.50 #> H3 0.50 0.25 1.00 0.50 #> H4 0.25 0.50 0.50 1.00"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"user-defined-success-criteria","dir":"Articles","previous_headings":"Power simulation","what":"User-defined success criteria","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"mentioned earlier, multiple versions “power” multiple hypotheses. Commonly used “power” definitions include: Local power: probability hypothesis rejected (multiplicity adjustment) Expected . rejections: expected number rejections Power reject 1 : probability reject least one hypothesis Power reject : probability reject hypotheses default outputs graph_calculate_power function. addition, user can customize success criteria define versions “power”.","code":"success_fns <- list(   # Probability to reject H1   H1 = function(x) x[1],    # Expected number of rejections   `Expected no. of rejections` = function(x) x[1] + x[2] + x[3] + x[4],    # Probability to reject at least one hypothesis   `AtLeast1` = function(x) x[1] | x[2] | x[3] | x[4],    # Probability to reject all hypotheses   `All` = function(x) x[1] & x[2] & x[3] & x[4],    # Probability to reject both H1 and H2   `H1andH2` = function(x) x[1] & x[2],    # Probability to reject both hypotheses for the low dose or the high dose   `(H1andH3)or(H2andH4)` = function(x) (x[1] & x[3]) | (x[2] & x[4]) )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html","id":"output-simulate-power","dir":"Articles","previous_headings":"Power simulation","what":"Output: Simulate power","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Given inputs, can estimate “power” via simulation graphical multiple comparison procedure one-sided significance level alpha = 0.025 using sim_n = 1e5 simulations random seed 1234. local power 0.758, 0.765, 0.689, 0.570, respectively H1,…,H4H_1, \\ldots, H_4. Note local power lower marginal power former adjusted multiplicity. power reject least one hypothesis 0.856 power reject hypotheses 0.512. expected number rejections 2.782. last two user-defined success criteria, probability reject H1H_1 H2H_2 0.667, probability reject least one pair (H1(H_1 H3)H_3) (H2(H_2 H4)H_4) 0.747. see detailed outputs simulated p-values rejection decisions hypotheses, specify verbose = TRUE. produce lot outputs. allow flexible printing functions, user can change following: indented space default setting indent = 2 precision numeric values (.e., number significant digits) default setting precision = 4","code":"set.seed(1234) power_output <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(power_marginal_primary, power_marginal_secondary),   sim_success = success_fns )  power_output$power #> $power_local #>      H1      H2      H3      H4  #> 0.76396 0.75887 0.56767 0.69133  #>  #> $rejection_expected #> [1] 2.78183 #>  #> $power_at_least_1 #> [1] 0.85557 #>  #> $power_all #> [1] 0.51205 #>  #> $power_success #>                         H1 Expected no. of rejections  #>                    0.76396                    2.78183  #>                   AtLeast1                        All  #>                    0.85557                    0.51205  #>                    H1andH2       (H1andH3)or(H2andH4)  #>                    0.66726                    0.74695 set.seed(1234) power_verbose_output <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(power_marginal_primary, power_marginal_secondary),   sim_success = success_fns,   verbose = TRUE )  head(power_verbose_output$details$p_sim, 10) #>                 H1           H2           H3           H4 #>  [1,] 0.0308204265 0.0120653993 0.0041185823 9.324338e-02 #>  [2,] 0.0007933716 0.0006499046 0.0245177515 2.965604e-03 #>  [3,] 0.0302991819 0.0595395828 0.0543082956 2.625834e-02 #>  [4,] 0.0097433244 0.0033185711 0.0007417213 4.024688e-04 #>  [5,] 0.0197134942 0.0086161835 0.0164182765 2.418325e-07 #>  [6,] 0.0031206572 0.0067023099 0.0137441457 2.751703e-04 #>  [7,] 0.0302208038 0.1423757994 0.0060382838 2.117403e-02 #>  [8,] 0.0024975725 0.0294025573 0.0004142729 2.207786e-03 #>  [9,] 0.0618994292 0.0387257108 0.3166125781 5.699791e-02 #> [10,] 0.3677921053 0.1895975134 0.0702264885 1.189651e-02  print(power_verbose_output, indent = 4, precision = 6) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>     Initial graph #>  #>     --- Hypothesis weights --- #>     H1: 0.5 #>     H2: 0.5 #>     H3: 0.0 #>     H4: 0.0 #>  #>     --- Transition weights --- #>         H1  H2  H3  H4 #>     H1 0.0 0.5 0.5 0.0 #>     H2 0.5 0.0 0.0 0.5 #>     H3 0.0 1.0 0.0 0.0 #>     H4 1.0 0.0 0.0 0.0 #>  #>     Alpha = 0.025 #>  #>     Test types #>     bonferroni: (H1, H2, H3, H4) #>  #> Simulation parameters ($inputs) ------------------------------------------------ #>     Testing 100,000 simulations with multivariate normal params: #>  #>                           H1       H2       H3       H4 #>     Marginal power: 0.802831 0.802831 0.705414 0.901481 #>  #>     Correlation:      H1   H2   H3   H4 #>                  H1 1.00 0.50 0.50 0.25 #>                  H2 0.50 1.00 0.25 0.50 #>                  H3 0.50 0.25 1.00 0.50 #>                  H4 0.25 0.50 0.50 1.00 #>  #> Power calculation ($power) ----------------------------------------------------- #>                                      H1      H2      H3      H4 #>                    Local power: 0.76396 0.75887 0.56767 0.69133 #>  #>     Expected no. of rejections: 2.78183 #>      Power to reject 1 or more: 0.85557 #>            Power to reject all: 0.51205 #>  #>                Success measure   Power #>                             H1 0.76396 #>     Expected no. of rejections 2.78183 #>                       AtLeast1 0.85557 #>                            All 0.51205 #>                        H1andH2 0.66726 #>           (H1andH3)or(H2andH4) 0.74695 #>  #> Simulation details ($details) -------------------------------------------------- #>         p_sim_H1    p_sim_H2    p_sim_H3    p_sim_H4 rej_H1 rej_H2 rej_H3 rej_H4 #>      3.08204e-02 1.20654e-02 4.11858e-03 9.32434e-02  FALSE   TRUE  FALSE  FALSE #>      7.93372e-04 6.49905e-04 2.45178e-02 2.96560e-03   TRUE   TRUE   TRUE   TRUE #>      3.02992e-02 5.95396e-02 5.43083e-02 2.62583e-02  FALSE  FALSE  FALSE  FALSE #>      9.74332e-03 3.31857e-03 7.41721e-04 4.02469e-04   TRUE   TRUE   TRUE   TRUE #>      1.97135e-02 8.61618e-03 1.64183e-02 2.41833e-07   TRUE   TRUE   TRUE   TRUE #>      3.12066e-03 6.70231e-03 1.37441e-02 2.75170e-04   TRUE   TRUE   TRUE   TRUE #>      3.02208e-02 1.42376e-01 6.03828e-03 2.11740e-02  FALSE  FALSE  FALSE  FALSE #>      2.49757e-03 2.94026e-02 4.14273e-04 2.20779e-03   TRUE  FALSE   TRUE  FALSE #>      6.18994e-02 3.87257e-02 3.16613e-01 5.69979e-02  FALSE  FALSE  FALSE  FALSE #>      3.67792e-01 1.89598e-01 7.02265e-02 1.18965e-02  FALSE  FALSE  FALSE  FALSE #>     ... (Use `print(x, rows = <nn>)` for more)"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Dong Xi. Author, maintainer. Ethan Brockmann. Author. Gilead Sciences, Inc.. Copyright holder, funder.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Xi D, Brockmann E (2024). graphicalMCP: Graphical multiple comparison procedures, version 0.2.5 edition. https://github.com/Gilead-BioStats/graphicalMCP.","code":"@Manual{,   title = {{graphicalMCP}: Graphical multiple comparison procedures},   author = {Dong Xi and Ethan Brockmann},   edition = {version 0.2.5},   year = {2024},   url = {https://github.com/Gilead-BioStats/graphicalMCP}, }"},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/index.html","id":"introduction","dir":"","previous_headings":"","what":"Introduction","title":"Graphical Multiple Comparison Procedures","text":"Graphical approaches multiple comparison procedures (MCPs) general framework control family-wise error rate strongly pre-specified significance level 0<α<10<\\alpha<1. approach includes many commonly used MCPs special cases transparent visualizing MCPs better communications. graphicalMCP designed design analyze graphical MCPs flexible, informative efficient way.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Graphical Multiple Comparison Procedures","text":"graphicalMCP currently CRAN can installed GitHub using following code:","code":"# install.packages(\"pak\") pak::pak(\"Gilead-BioStats/graphicalMCP\")"},{"path":"https://gilead-biostats.github.io/graphicalMCP/index.html","id":"documentation","dir":"","previous_headings":"","what":"Documentation","title":"Graphical Multiple Comparison Procedures","text":"basic usage instructions, see vignette(\"graphicalMCP\") become familiar graphical MCP terminologies, see vignette(\"glossary\") see vignette(\"shortcut-testing\") sequentially rejective graphical multiple comparison procedures based Bonferroni tests see vignette(\"closed-testing\") graphical multiple comparison procedures based closure principle see vignette(\"graph-examples\") common multiple comparison procedures illustrated using graphicalMCP see vignette(\"generate-closure\") rationales generate closure weighting strategy graph see vignette(\"comparisons\") comparisons R packages view vignettes R properly installing graphicalMCP GitHub, can build vignettes devtools::install(build_vignettes = TRUE), use browseVignettes(\"graphicalMCP\") view full list vignettes","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/index.html","id":"related-work","dir":"","previous_headings":"","what":"Related work","title":"Graphical Multiple Comparison Procedures","text":"Graphical MCPs - gMCP Lighter version gMCP removes rJava dependency - gMCPLite Graphical MCPs Simes tests - lrstat Built upon packages, hope implement graphical MCPs general framework, fewer dependencies simpler S3 classes, without losing computational efficiency.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/index.html","id":"acknowledgments","dir":"","previous_headings":"","what":"Acknowledgments","title":"Graphical Multiple Comparison Procedures","text":"Along authors contributors, thanks following people suggestions inspirations package: Frank Bretz, Willi Maurer, Ekkehard Glimm, Nan Chen, Jeremy Wildfire, Spencer Childress, Colleen McLaughlin, Matt Roumaya, Chelsea Dickens, Ron Yu owe debt gratitude authors gMCP pioneering work, without package nearly extensive .","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate adjusted p-values — adjust_p_bonferroni","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"intersection hypothesis, adjusted p-value smallest significance level intersection hypothesis can rejected. intersection hypothesis can rejected adjusted p-value less equal \\(\\alpha\\). Currently, three test types supported: Bonferroni tests adjust_p_bonferroni(), Parametric tests adjust_p_parametric(), Note one-sided tests required parametric tests. Simes tests adjust_p_simes().","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"","code":"adjust_p_bonferroni(p, hypotheses)  adjust_p_parametric(   p,   hypotheses,   test_corr = NULL,   maxpts = 25000,   abseps = 1e-06,   releps = 0 )  adjust_p_simes(p, hypotheses)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match length hypotheses. hypotheses numeric vector hypothesis weights. Must vector values 0 & 1 (inclusive). length match length p. sum hypothesis weights exceed 1. test_corr (Optional) numeric matrix correlations test statistics, needed perform parametric tests using adjust_p_parametric(). number rows columns correlation matrix match length p. maxpts (Optional) integer scalar maximum number function values, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 25000. abseps (Optional) numeric scalar absolute error tolerance, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 1e-6. releps (Optional) numeric scalar relative error tolerance double, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 0.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"single adjusted p-value intersection hypothesis.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"","code":"hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25) p <- c(0.019, 0.025, 0.05) adjust_p_bonferroni(p, hypotheses) #> [1] 0.038 set.seed(1234) hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25) p <- c(0.019, 0.025, 0.05) # Using the `mvtnorm::GenzBretz` algorithm corr <- matrix(0.5, nrow = 3, ncol = 3) diag(corr) <- 1 adjust_p_parametric(p, hypotheses, corr) #> [1] 0.03343516 hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25) p <- c(0.019, 0.025, 0.05) adjust_p_simes(p, hypotheses) #> [1] 0.03333333"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate adjusted hypothesis weights — adjust_weights_parametric","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"intersection hypothesis can rejected p-values less equal adjusted significance levels, adjusted hypothesis weights times \\(\\alpha\\). Bonferroni tests, adjusted hypothesis weights hypothesis weights intersection hypothesis. Additional adjustment needed parametric Simes tests: Parametric tests adjust_weights_parametric(), Note one-sided tests required parametric tests. Simes tests adjust_weights_simes().","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"","code":"adjust_weights_parametric(   matrix_weights,   matrix_intersections,   test_corr,   alpha,   test_groups,   maxpts = 25000,   abseps = 1e-06,   releps = 0 )  adjust_weights_simes(matrix_weights, p, test_groups)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"matrix_weights (Optional) matrix hypothesis weights intersection hypotheses. can obtained second half columns output graph_generate_weights(). matrix_intersections (Optional) matrix hypothesis indicators intersection hypotheses. can obtained first half columns output graph_generate_weights(). test_corr (Optional) numeric matrix correlations test statistics, needed perform parametric tests using adjust_weights_parametric(). number rows columns correlation matrix match length p. alpha (Optional) numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. test_groups (Optional) list numeric vectors specifying hypotheses test together. Grouping needed correctly perform Simes parametric tests. maxpts (Optional) integer scalar maximum number function values, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 25000. abseps (Optional) numeric scalar absolute error tolerance, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 1e-6. releps (Optional) numeric scalar relative error tolerance double, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 0. p (Optional) numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number columns matrix_weights.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"adjust_weights_parametric() returns matrix dimensions matrix_weights, whose hypothesis weights adjusted according parametric tests. adjust_weights_simes() returns matrix dimensions matrix_weights, whose hypothesis weights adjusted according Simes tests.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"","code":"alpha <- 0.025 p <- c(0.018, 0.01, 0.105, 0.006) num_hyps <- length(p) g <- bonferroni_holm(rep(1 / 4, 4)) weighting_strategy <- graph_generate_weights(g) matrix_intersections <- weighting_strategy[, seq_len(num_hyps)] matrix_weights <- weighting_strategy[, -seq_len(num_hyps)]  set.seed(1234) adjust_weights_parametric(   matrix_weights = matrix_weights,   matrix_intersections = matrix_intersections,   test_corr = diag(4),   alpha = alpha,   test_groups = list(1:4) ) #>           H1        H2        H3        H4 #> 1  0.2523785 0.2523785 0.2523785 0.2523785 #> 2  0.3361503 0.3361503 0.3361503 0.0000000 #> 3  0.3361503 0.3361503 0.0000000 0.3361503 #> 4  0.5031647 0.5031647 0.0000000 0.0000000 #> 5  0.3361503 0.0000000 0.3361503 0.3361503 #> 6  0.5031647 0.0000000 0.5031647 0.0000000 #> 7  0.5031647 0.0000000 0.0000000 0.5031647 #> 8  1.0000000 0.0000000 0.0000000 0.0000000 #> 9  0.0000000 0.3361503 0.3361503 0.3361503 #> 10 0.0000000 0.5031647 0.5031647 0.0000000 #> 11 0.0000000 0.5031647 0.0000000 0.5031647 #> 12 0.0000000 1.0000000 0.0000000 0.0000000 #> 13 0.0000000 0.0000000 0.5031647 0.5031647 #> 14 0.0000000 0.0000000 1.0000000 0.0000000 #> 15 0.0000000 0.0000000 0.0000000 1.0000000 alpha <- 0.025 p <- c(0.018, 0.01, 0.105, 0.006) num_hyps <- length(p) g <- bonferroni_holm(rep(1 / 4, 4)) weighting_strategy <- graph_generate_weights(g) matrix_intersections <- weighting_strategy[, seq_len(num_hyps)] matrix_weights <- weighting_strategy[, -seq_len(num_hyps)]  adjust_weights_simes(   matrix_weights = matrix_weights,   p = p,   test_groups = list(1:4) ) #>           H4        H2        H1 H3 #> 1  0.2500000 0.5000000 0.7500000  1 #> 2  0.0000000 0.3333333 0.6666667  1 #> 3  0.3333333 0.6666667 1.0000000  1 #> 4  0.0000000 0.5000000 1.0000000  1 #> 5  0.3333333 0.3333333 0.6666667  1 #> 6  0.0000000 0.0000000 0.5000000  1 #> 7  0.5000000 0.5000000 1.0000000  1 #> 8  0.0000000 0.0000000 1.0000000  1 #> 9  0.3333333 0.6666667 0.6666667  1 #> 10 0.0000000 0.5000000 0.5000000  1 #> 11 0.5000000 1.0000000 1.0000000  1 #> 12 0.0000000 1.0000000 1.0000000  1 #> 13 0.5000000 0.5000000 0.5000000  1 #> 14 0.0000000 0.0000000 0.0000000  1 #> 15 1.0000000 1.0000000 1.0000000  1"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"intersection hypothesis can rejected p-values less equal adjusted significance levels, adjusted hypothesis weights times \\(\\alpha\\). Bonferroni tests, adjusted hypothesis weights hypothesis weights intersection hypothesis. Additional adjustment needed parametric tests: Parametric tests adjust_weights_parametric(), Note one-sided tests required parametric tests.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"","code":"c_value_function(   x,   hypotheses,   test_corr,   alpha,   maxpts = 25000,   abseps = 1e-06,   releps = 0 )  solve_c_parametric(   hypotheses,   test_corr,   alpha,   maxpts = 25000,   abseps = 1e-06,   releps = 0 )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"x root solve stats::uniroot(). hypotheses numeric vector hypothesis weights. Must vector values 0 & 1 (inclusive). sum hypothesis weights exceed 1. test_corr (Optional) numeric matrix correlations test statistics, needed perform parametric tests using adjust_weights_parametric(). number rows columns correlation matrix match length p. alpha (Optional) numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. maxpts (Optional) integer scalar maximum number function values, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 25000. abseps (Optional) numeric scalar absolute error tolerance, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 1e-6. releps (Optional) numeric scalar relative error tolerance double, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 0.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"c_value_function() returns difference \\(\\alpha\\) Type error parametric test \\(c\\) value x, adjusted correlation test statistics using parametric tests based equation (6) Xi et al. (2017). solve_c_parametric() returns c value adjusted correlation test statistics using parametric tests based equation (6) Xi et al. (2017).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"Graph objects different structures attributes graphicalMCP, gMCP, igraph R packages. functions convert different classes increase compatibility. Note igraph gMCP additional attributes vertices, edges, graph . conversion functions handle attributes related hypothesis names, hypothesis weights transition weights. attributes dropped converting.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"","code":"as_initial_graph(graph)  # S3 method for class 'graphMCP' as_initial_graph(graph)  # S3 method for class 'igraph' as_initial_graph(graph)  as_graphMCP(graph)  # S3 method for class 'initial_graph' as_graphMCP(graph)  as_igraph(graph)  # S3 method for class 'initial_graph' as_igraph(graph)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"graph initial_graph object graphicalMCP package, graphMCP object gMCP package, igraph object igraph package, depending conversion type.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"as_graphMCP() returns graphMCP object gMCP package. as_igraph() returns igraph object igraph package. as_initial_graph() returns initial_graph object graphicalMCP package.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"Csardi, G., Nepusz, T., Traag, V., Horvat, S., Zanini, F., Noom, D., Mueller, K. (2024). igraph: Network analysis visualization R. R package version 2.0.3. https://CRAN.R-project.org/package=igraph. Rohmeyer, K., Klinglmueller, K. (2024). gMCP: Graph based multiple test procedures. R package version 0.8-17. https://cran.r-project.org/package=gMCP.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"","code":"g_graphicalMCP <- random_graph(5)  if (requireNamespace(\"gMCP\", quietly = TRUE)) {   g_gMCP <- as_graphMCP(g_graphicalMCP)    all.equal(g_graphicalMCP, as_initial_graph(g_gMCP)) } #> [1] TRUE  if (requireNamespace(\"igraph\", quietly = TRUE)) {   g_igraph <- as_igraph(g_graphicalMCP)    all.equal(g_graphicalMCP, as_initial_graph(g_igraph)) } #> [1] TRUE"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/edge_pairs.html","id":null,"dir":"Reference","previous_headings":"","what":"Find pairs of vertices that are connected in both directions — edge_pairs","title":"Find pairs of vertices that are connected in both directions — edge_pairs","text":"initial graph, find pairs hypotheses connected directions. used plot graphs using plot.initial_graph().","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/edge_pairs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find pairs of vertices that are connected in both directions — edge_pairs","text":"","code":"edge_pairs(graph)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/edge_pairs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find pairs of vertices that are connected in both directions — edge_pairs","text":"graph initial graph returned graph_create().","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/edge_pairs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find pairs of vertices that are connected in both directions — edge_pairs","text":"list vertex pairs connected directions. NULL pairs found.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html","id":null,"dir":"Reference","previous_headings":"","what":"Example graphs of commonly used multiple comparison procedures — bonferroni","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"Built-functions quickly generate select graphical multiple comparison procedures.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"","code":"bonferroni(hypotheses, hyp_names = NULL)  bonferroni_holm(hypotheses, hyp_names = NULL)  huque_etal(hyp_names = NULL)  fallback(hypotheses, hyp_names = NULL)  fallback_improved_1(hypotheses, hyp_names = NULL)  fallback_improved_2(hypotheses, epsilon = 1e-04, hyp_names = NULL)  fixed_sequence(num_hyps, hyp_names = NULL)  simple_successive_1(hyp_names = NULL)  simple_successive_2(hyp_names = NULL)  random_graph(num_hyps, hyp_names = NULL)  two_doses_two_primary_two_secondary(hyp_names = NULL)  three_doses_two_primary_two_secondary(hyp_names = NULL)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"hypotheses (Optional) numeric vector hypothesis weights graphical multiple comparison procedure. Must vector values 0 & 1 (inclusive). length match num_hyps length hyp_names. sum hypothesis weights exceed 1. hyp_names (Optional) character vector hypothesis names. length match num_hyps length hypotheses. hyp_names specified, hypotheses named sequentially H1, H2, ....... epsilon (Optional) numeric scalar indicating value \\(\\epsilon\\) edge. much smaller value hypothesis transition weights. default 1e-4. num_hyps (Optional) Number hypotheses graphical multiple comparison procedure.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"S3 object returned graph_create().","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Huque, M. F., Alosh, M., Bhore, R. (2011). Addressing multiplicity issues composite endpoint components clinical trials. Journal Biopharmaceutical Statistics, 21(4), 610-634. Maurer, W., Hothorn, L., Lehmacher, W. (1995). Multiple comparisons drug clinical trials preclinical assays: -priori ordered hypotheses. Biometrie der chemisch-pharmazeutischen Industrie, 6, 3-18. Westfall, P. H., Krishen, . (2001). Optimally weighted, fixed sequence gatekeeper multiple testing procedures. Journal Statistical Planning Inference, 99(1), 25-40. Wiens, B. L. (2003). fixed sequence Bonferroni procedure testing multiple endpoints. Pharmaceutical Statistics, 2(3), 211-215. Wiens, B. L., Dmitrienko, . (2005). fallback procedure evaluating single family hypotheses. Journal Biopharmaceutical Statistics, 15(6), 929-942. Xi, D., Bretz, F. (2019). Symmetric graphs equally weighted tests, application Hochberg procedure. Statistics Medicine, 38(27), 5268-5282.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"","code":"# Bretz et al. (2009) bonferroni(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>     H1 H2 H3 #>  H1  0  0  0 #>  H2  0  0  0 #>  H3  0  0  0 # Bretz et al. (2009) bonferroni_holm(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>      H1  H2  H3 #>  H1 0.0 0.5 0.5 #>  H2 0.5 0.0 0.5 #>  H3 0.5 0.5 0.0 # Huque et al. (2011) huque_etal() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 1 #> H2: 0 #> H3: 0 #> H4: 0 #>  #> --- Transition weights --- #>      H1  H2  H3  H4 #>  H1 0.0 0.5 0.5 0.0 #>  H2 0.0 0.0 0.0 1.0 #>  H3 0.0 0.5 0.0 0.5 #>  H4 0.0 1.0 0.0 0.0 # Wiens (2003) fallback(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>     H1 H2 H3 #>  H1  0  1  0 #>  H2  0  0  1 #>  H3  0  0  0 # Wiens and Dmitrienko (2005) fallback_improved_1(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>      H1  H2  H3 #>  H1 0.0 1.0 0.0 #>  H2 0.0 0.0 1.0 #>  H3 0.5 0.5 0.0 # Bretz et al. (2009) fallback_improved_2(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>         H1     H2     H3 #>  H1 0.0000 1.0000 0.0000 #>  H2 0.9999 0.0000 0.0001 #>  H3 1.0000 0.0000 0.0000 # Maurer et al. (1995); Westfall and Krishen (2001) fixed_sequence(num_hyps = 3) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 1 #> H2: 0 #> H3: 0 #>  #> --- Transition weights --- #>     H1 H2 H3 #>  H1  0  1  0 #>  H2  0  0  1 #>  H3  0  0  0 # Figure 1 in Bretz et al. (2011) simple_successive_1() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 # Figure 4 in Bretz et al. (2011) simple_successive_2() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>      H1  H2  H3  H4 #>  H1 0.0 0.5 0.5 0.0 #>  H2 0.5 0.0 0.0 0.5 #>  H3 0.0 1.0 0.0 0.0 #>  H4 1.0 0.0 0.0 0.0 # Create a random graph with three hypotheses random_graph(num_hyps = 3) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>         H1     H2     H3 #>  H1 0.0000 0.6000 0.4000 #>  H2 0.6667 0.0000 0.3333 #>  H3 0.7500 0.2500 0.0000 # Figure 6 in Xi and Bretz et al. (2019) two_doses_two_primary_two_secondary() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.0 #> H3: 0.0 #> H4: 0.5 #> H5: 0.0 #> H6: 0.0 #>  #> --- Transition weights --- #>         H1     H2     H3     H4     H5     H6 #>  H1 0.0000 0.5000 0.5000 0.0000 0.0000 0.0000 #>  H2 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 #>  H3 0.0000 0.9999 0.0000 0.0001 0.0000 0.0000 #>  H4 0.0000 0.0000 0.0000 0.0000 0.5000 0.5000 #>  H5 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 #>  H6 0.0001 0.0000 0.0000 0.0000 0.9999 0.0000 # Add another dose to Figure 6 in Xi and Bretz et al. (2019) three_doses_two_primary_two_secondary() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.0000 #> H3: 0.0000 #> H4: 0.3333 #> H5: 0.0000 #> H6: 0.0000 #> H7: 0.3333 #> H8: 0.0000 #> H9: 0.0000 #>  #> --- Transition weights --- #>          H1      H2      H3      H4      H5      H6      H7      H8      H9 #>  H1 0.00000 0.50000 0.50000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 #>  H2 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 #>  H3 0.00000 0.99990 0.00000 0.00005 0.00000 0.00000 0.00005 0.00000 0.00000 #>  H4 0.00000 0.00000 0.00000 0.00000 0.50000 0.50000 0.00000 0.00000 0.00000 #>  H5 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 #>  H6 0.00005 0.00000 0.00000 0.00000 0.99990 0.00000 0.00005 0.00000 0.00000 #>  H7 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.50000 0.50000 #>  H8 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 #>  H9 0.00005 0.00000 0.00000 0.00005 0.00000 0.00000 0.00000 0.99990 0.00000"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_calculate_power.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"alternative hypotheses, distribution test statistics assumed multivariate normal distribution. Given distribution, function calculates power values graphical multiple comparison procedure. default, calculate local power, probability reject individual hypothesis, probability reject least one hypothesis, probability reject hypotheses, expected number rejections, probability user-defined success criteria. See vignette(\"shortcut-testing\") vignette(\"closed-testing\") illustration power calculation.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"","code":"graph_calculate_power(   graph,   alpha = 0.025,   power_marginal = rep(alpha, length(graph$hypotheses)),   test_groups = list(seq_along(graph$hypotheses)),   test_types = c(\"bonferroni\"),   test_corr = rep(list(NA), length(test_types)),   sim_n = 1e+05,   sim_corr = diag(length(graph$hypotheses)),   sim_success = NULL,   verbose = FALSE )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"graph initial graph returned graph_create(). alpha numeric value one-sided overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing. Note one-sided tests supported. power_marginal numeric vector marginal power values use simulating p-values. See Details simulation process. test_groups list numeric vectors specifying hypotheses test together. Grouping needed correctly perform Simes parametric tests. test_types character vector test types apply test group. needed correctly perform Simes parametric tests. length match number elements test_groups. test_corr (Optional) list numeric correlation matrices. entry list correspond test group. test group using Bonferroni Simes tests, corresponding entry test_corr NA. test group using parametric tests, corresponding entry test_corr numeric correlation matrix specifying correlation test statistics hypotheses test group. length match number elements test_groups. sim_n integer scalar specifying number simulations. default 1e5. sim_corr numeric matrix correlations test statistics hypotheses. dimensions match number hypotheses graph. sim_success list user-defined functions specify success criteria. Functions must take one simulation's logical vector results input, return length-one logical vector. instance, \"success\" means rejecting hypotheses 1 2, use sim_success = list(\"1 2\" = function(x) x[1] && x[2]). list named, function body used name. Lambda functions also work starting R 4.1, e.g. sim_success = list(\\(x) x[3] || x[4]). verbose logical scalar specifying whether details power simulations included results. default verbose = FALSE.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"power_report object list 3 elements: inputs - Input parameters, list : graph - Initial graph, alpha - Overall significance level, test_groups - Groups hypotheses different types tests, test_types - Different types tests, test_corr - Correlation matrices parametric tests, sim_n - Number simulations, power_marginal - Marginal power hypotheses sim_corr - Correlation matrices simulations, sim_success - User-defined success criteria. power - list power values power_local - Local power hypotheses, proportion simulations hypothesis rejected, rejection_expected - Expected (average) number rejected hypotheses, power_at_least_1 - Power reject least one hypothesis, power_all - Power reject hypotheses, power_success - Power user-defined success, proportion simulations user-defined success criterion sim_success met. details - optional list datasets showing simulated p-values results simulation.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"simulation-details","dir":"Reference","previous_headings":"","what":"Simulation details","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"power calculation based simulations. distribution simulate determined multivariate normal distribution power_marginal sim_corr. particular, power_marginal vector marginal power values hypotheses. marginal power power reject null hypothesis significance level alpha without multiplicity adjustment. value readily available standard software R packages. can determine mean multivariate normal distribution $$\\Phi^{-1}\\left(1-\\alpha\\right)-\\Phi^{-1}\\left(1-d_i\\right)$$, often called non-centrality parameter drift parameter. \\(d_i\\) marginal power power_marginal hypothesis \\(\\). Given correlation matrix sim_corr, can simulate multivariate normal distribution using mvtnorm R package (Genz Bretz, 2009). set simulated values can used calculate corresponding one-sided p-values. set p-values plugged graphical multiple comparison procedure determine hypotheses rejected. process repeated n_sim times produce power values proportion simulations particular success criterion met.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011a). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Bretz, F., Maurer, W., Hommel, G. (2011b). Test power considerations multiple endpoint analyses using sequentially rejective graphical procedures. Statistics Medicine, 30(13), 1489-1501. Genz, ., Bretz, F. (2009). Computation Multivariate Normal t Probabilities, series Lecture Notes Statistics. Springer-Verlag, Heidelberg. Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011a). alpha <- 0.025 hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  marginal_power <- c(0.8, 0.8, 0.7, 0.9) corr1 <- matrix(0.5, nrow = 2, ncol = 2) diag(corr1) <- 1 corr <- rbind(   cbind(corr1, 0.5 * corr1),   cbind(0.5 * corr1, corr1) ) success_fns <- list(   # Probability to reject both H1 and H2   `H1andH2` = function(x) x[1] & x[2],   # Probability to reject both (H1 and H3) or (H2 and H4)   `(H1andH3)or(H2andH4)` = function(x) (x[1] & x[3]) | (x[2] & x[4]) ) set.seed(1234) # Bonferroni tests # Reduce the number of simulations to save time for package compilation power_output <- graph_calculate_power(   g,   alpha,   sim_corr = corr,   sim_n = 1e2,   power_marginal = marginal_power,   sim_success = success_fns )  # Parametric tests for H1 and H2; Simes tests for H3 and H4 # User-defined success: to reject H1 or H2; to reject H1 and H2 # Reduce the number of simulations to save time for package compilation graph_calculate_power(   g,   alpha,   test_groups = list(1:2, 3:4),   test_types = c(\"parametric\", \"simes\"),   test_corr = list(corr1, NA),   sim_n = 1e2,   sim_success = list(     function(.) .[1] || .[2],     function(.) .[1] && .[2]   ) ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>   Parametric testing correlation:     H1  H2 #>                                   H1 1.0 0.5 #>                                   H2 0.5 1.0 #>  #>   Test types #>   parametric: (H1, H2) #>        simes: (H3, H4) #>  #> Simulation parameters ($inputs) ------------------------------------------------ #>   Testing 100 simulations with multivariate normal params: #>  #>                      H1    H2    H3    H4 #>   Marginal power: 0.025 0.025 0.025 0.025 #>  #>   Correlation:    H1 H2 H3 H4 #>                H1  1  0  0  0 #>                H2  0  1  0  0 #>                H3  0  0  1  0 #>                H4  0  0  0  1 #>  #> Power calculation ($power) ----------------------------------------------------- #>                                 H1   H2   H3   H4 #>                  Local power: 0.02 0.01 0.00 0.00 #>  #>   Expected no. of rejections: 0.03 #>    Power to reject 1 or more: 0.03 #>          Power to reject all: 0 #>  #>   Success measure Power #>      .[1] || .[2]  0.03 #>      .[1] && .[2]  0.00 #>"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_create.html","id":null,"dir":"Reference","previous_headings":"","what":"Create the initial graph for a multiple comparison procedure — graph_create","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"graphical multiple comparison procedure represented 1) vector initial hypothesis weights hypotheses, 2) matrix initial transition weights transitions. function creates initial graph object using hypothesis weights transition weights.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_create.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"","code":"graph_create(hypotheses, transitions, hyp_names = NULL)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_create.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"hypotheses numeric vector hypothesis weights graphical multiple comparison procedure. Must vector values 0 & 1 (inclusive). length match row column lengths transitions. sum hypothesis weights exceed 1. transitions numeric matrix transition weights hypotheses graphical multiple comparison procedure. Must square matrix values 0 & 1 (inclusive). row column lengths match length hypotheses. row (Transition weights leaving hypothesis) can sum 1. diagonal entries (Transition weights hypothesis ) must 0s. hyp_names (Optional) character vector hypothesis names. provided, names hypotheses transitions used. names specified, hypotheses named sequentially H1, H2, .......","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_create.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"S3 object class initial_graph list 2 elements: Hypothesis weights hypotheses. Transition weights transitions.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_create.html","id":"validation-of-inputs","dir":"Reference","previous_headings":"","what":"Validation of inputs","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"Inputs also validated make sure validity graph: Hypothesis weights hypotheses numeric. Transition weights transitions numeric. Length hypotheses dimensions transitions match. Hypothesis weights hypotheses must non-negative sum 1. Transition weights transitions: Values must non-negative. Rows must sum 1. Diagonal entries must 0. Hypothesis names hyp_names override names hypotheses transitions.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_create.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_create.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) hyp_names <- c(\"H11\", \"H12\", \"H21\", \"H22\") g <- graph_create(hypotheses, transitions, hyp_names) g #> Initial graph #>  #> --- Hypothesis weights --- #> H11: 0.5 #> H12: 0.5 #> H21: 0.0 #> H22: 0.0 #>  #> --- Transition weights --- #>      H11 H12 H21 H22 #>  H11   0   0   1   0 #>  H12   0   0   0   1 #>  H21   0   1   0   0 #>  H22   1   0   0   0  # Explicit names override names in `hypotheses` (with a warning) hypotheses <- c(h1 = 0.5, h2 = 0.5, h3 = 0, h4 = 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions, hyp_names) #> Warning: Hypothesis names specified - overriding names in #>                     `hypotheses` and `transitions` g #> Initial graph #>  #> --- Hypothesis weights --- #> H11: 0.5 #> H12: 0.5 #> H21: 0.0 #> H22: 0.0 #>  #> --- Transition weights --- #>      H11 H12 H21 H22 #>  H11   0   0   1   0 #>  H12   0   0   0   1 #>  H21   0   1   0   0 #>  H22   1   0   0   0  # Use names in `transitions` hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   H1 = c(0, 0, 1, 0),   H2 = c(0, 0, 0, 1),   H3 = c(0, 1, 0, 0),   H4 = c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions) g #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0  # Unmatched names in `hypotheses` and `transitions` (with an error) hypotheses <- c(h1 = 0.5, h2 = 0.5, h3 = 0, h4 = 0) transitions <- rbind(   H1 = c(0, 0, 1, 0),   H2 = c(0, 0, 0, 1),   H3 = c(0, 1, 0, 0),   H4 = c(1, 0, 0, 0) ) if (FALSE) { # \\dontrun{ g <- graph_create(hypotheses, transitions) } # }  # When names are not specified, hypotheses are numbered sequentially as # H1, H2, ... hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions) g #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_generate_weights.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"graphical multiple comparison procedure defines closed test procedure, tests intersection hypothesis reject individual hypothesis intersection hypotheses involving rejected. intersection hypothesis represents parameter space individual null hypotheses involved true simultaneously. closure based graph consists updated graphs (corresponding intersection hypotheses) combinations hypotheses deleted. graphical multiple comparison procedure \\(m\\) hypotheses, \\(2^{m}-1\\) updated graphs (intersection hypotheses), including initial graph (overall intersection hypothesis). weighting strategy graph consists hypothesis weights \\(2^{m}-1\\) updated graphs (intersection hypotheses). algorithm derive weighting strategy based Algorithm 1 Bretz et al. (2011).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"","code":"graph_generate_weights(graph)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"graph initial graph returned graph_create().","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"numeric matrix intersection hypotheses hypothesis weights. graphical multiple comparison procedure \\(m\\) hypotheses, number rows \\(2^{m}-1\\), corresponds intersection hypothesis. number columns \\(2\\cdot m\\). first \\(m\\) columns indicate individual hypotheses included given intersection hypothesis second half columns provide hypothesis weights individual hypothesis given intersection hypothesis.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"performance","dir":"Reference","previous_headings":"","what":"Performance","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"Generation intersection hypotheses closely related power set given set indices. number hypotheses increases, memory time usage can grow quickly (e.g., rate \\(O(2^n)\\)). also multiple ways implement Algorithm 1 Bretz et al. (2011). See vignette(\"generate-closure\") information generating intersection hypotheses comparisons different approaches calculate weighting strategies.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  graph_generate_weights(g) #>    H1 H2 H3 H4  H1  H2  H3  H4 #> 1   1  1  1  1 0.5 0.5 0.0 0.0 #> 2   1  1  1  0 0.5 0.5 0.0 0.0 #> 3   1  1  0  1 0.5 0.5 0.0 0.0 #> 4   1  1  0  0 0.5 0.5 0.0 0.0 #> 5   1  0  1  1 0.5 0.0 0.0 0.5 #> 6   1  0  1  0 1.0 0.0 0.0 0.0 #> 7   1  0  0  1 0.5 0.0 0.0 0.5 #> 8   1  0  0  0 1.0 0.0 0.0 0.0 #> 9   0  1  1  1 0.0 0.5 0.5 0.0 #> 10  0  1  1  0 0.0 0.5 0.5 0.0 #> 11  0  1  0  1 0.0 1.0 0.0 0.0 #> 12  0  1  0  0 0.0 1.0 0.0 0.0 #> 13  0  0  1  1 0.0 0.0 0.5 0.5 #> 14  0  0  1  0 0.0 0.0 1.0 0.0 #> 15  0  0  0  1 0.0 0.0 0.0 1.0"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":null,"dir":"Reference","previous_headings":"","what":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"multiple hypotheses rejected using graph_test_shortcut(), may multiple orderings sequences hypotheses rejected one one. default order graph_test_shortcut() based adjusted p-values, smallest largest. function graph_rejection_orderings() provides possible valid orders (sequences) rejections. Although order rejection affect final rejection decisions Bretz et al. (2009), different sequences offer different ways explain step--step process shortcut graphical multiple comparison procedures.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"","code":"graph_rejection_orderings(shortcut_test_result)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"shortcut_test_result graph_report object returned graph_test_shortcut().","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"modified graph_report object containing valid orderings rejections hypotheses","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  p <- c(0.018, 0.01, 0.105, 0.006) alpha <- 0.025  shortcut_testing <- graph_test_shortcut(g, p, alpha, verbose = TRUE)  # Reject H1, H2, and H4 shortcut_testing$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE  TRUE   # Default order of rejections: H2, H1, H4 shortcut_testing$details$del_seq #> [1] \"H2\" \"H1\" \"H4\"  # There is another valid sequence of rejection: H2, H4, H1 graph_rejection_orderings(shortcut_testing)$valid_orderings #> [[1]] #> H2 H1 H4  #>  2  1  4  #>  #> [[2]] #> H2 H4 H1  #>  2  4  1  #>   # Finally, intermediate updated graphs can be obtained by providing the order # of rejections into `[graph_update()]` graph_update(g, delete = c(2, 4, 1)) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>      H1  H2  H3  H4 #>  H1 0.0 0.5 0.5 0.0 #>  H2 0.5 0.0 0.0 0.5 #>  H3 0.0 1.0 0.0 0.0 #>  H4 1.0 0.0 0.0 0.0 #>  #> Updated graph after deleting hypotheses 2, 4, 1 #>  #> --- Hypothesis weights --- #> H1: NA #> H2: NA #> H3:  1 #> H4: NA #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1 NA NA NA NA #>  H2 NA NA NA NA #>  H3 NA NA  0 NA #>  H4 NA NA NA NA #>  #> Deletion sequence ($intermediate_graphs) --------------------------------------- #>  #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>     Step 1: Updated graph after removing hypothesis 2 #>  #>     --- Hypothesis weights --- #>     H1: 0.75 #>     H2:   NA #>     H3: 0.00 #>     H4: 0.25 #>  #>     --- Transition weights --- #>              H1       H2       H3       H4 #>     H1 0.000000       NA 0.666667 0.333333 #>     H2       NA       NA       NA       NA #>     H3 0.500000       NA 0.000000 0.500000 #>     H4 1.000000       NA 0.000000 0.000000 #>  #>       Step 2: Updated graph after removing hypotheses 2, 4 #>  #>       --- Hypothesis weights --- #>       H1:  1 #>       H2: NA #>       H3:  0 #>       H4: NA #>  #>       --- Transition weights --- #>          H1 H2 H3 H4 #>       H1  0 NA  1 NA #>       H2 NA NA NA NA #>       H3  1 NA  0 NA #>       H4 NA NA NA NA #>  #>         Step 3: Updated graph after removing hypotheses 2, 4, 1 #>  #>         --- Hypothesis weights --- #>         H1: NA #>         H2: NA #>         H3:  1 #>         H4: NA #>  #>         --- Transition weights --- #>            H1 H2 H3 H4 #>         H1 NA NA NA NA #>         H2 NA NA NA NA #>         H3 NA NA  0 NA #>         H4 NA NA NA NA #>  #>   Final updated graph after removing deleted hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_closure.html","id":null,"dir":"Reference","previous_headings":"","what":"Perform closed graphical multiple comparison procedures — graph_test_closure","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"Closed graphical multiple comparison procedures, graphical multiple comparison procedures based closure, generate closure based graph consisting intersection hypotheses. tests intersection hypothesis rejects individual hypothesis intersection hypotheses involving rejected. intersection hypothesis represents parameter space individual null hypotheses involved true simultaneously. graphical multiple comparison procedure $m$ hypotheses, \\(2^m-1\\) intersection hypotheses. intersection hypothesis, test type chosen determine reject intersection hypothesis. Current choices test types include Bonferroni, Simes parametric. implementation offers general framework covering Bretz et al. (2011), Lu (2016), Xi et al. (2017). See vignette(\"closed-testing\") illustration closed test procedures interpretation outputs.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_closure.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"","code":"graph_test_closure(   graph,   p,   alpha = 0.025,   test_groups = list(seq_along(graph$hypotheses)),   test_types = c(\"bonferroni\"),   test_corr = rep(list(NA), length(test_types)),   verbose = FALSE,   test_values = FALSE )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_closure.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"graph initial graph returned graph_create(). p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. alpha numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. test_groups list numeric vectors specifying hypotheses test together. Grouping needed correctly perform Simes parametric tests. test_types character vector test types apply test group. needed correctly perform Simes parametric tests. length match number elements test_groups. test_corr (Optional) list numeric correlation matrices. entry list correspond test group. test group using Bonferroni Simes tests, corresponding entry test_corr NA. test group using parametric tests, corresponding entry test_corr numeric correlation matrix specifying correlation test statistics hypotheses test group. length match number elements test_groups. verbose logical scalar specifying whether details adjusted p-value calculations included results. verbose = TRUE, adjusted p-values provided intersection hypothesis. default verbose = FALSE. test_values logical scalar specifying whether adjusted significance levels provided hypothesis. test_values = TRUE, provides equivalent way performing graphical multiple comparison procedures comparing p-value significance level. p-value hypothesis less equal significance level, hypothesis rejected. default test_values = FALSE.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_closure.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"graph_report object list 4 elements: inputs - Input parameters, list : graph - Initial graph, p - (Unadjusted raw) p-values, alpha - Overall significance level, test_groups - Groups hypotheses different types tests, test_types - Different types tests, test_corr - Correlation matrices parametric tests. outputs - Output parameters, list : adjusted_p - Adjusted p-values, rejected - Rejected hypotheses, graph - Updated graph deleting rejected hypotheses. details - Verbose outputs adjusted p-values intersection hypotheses, verbose = TRUE. test_values - Adjusted significance levels, test_values = TRUE.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_closure.html","id":"details-for-test-specification","dir":"Reference","previous_headings":"","what":"Details for test specification","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"Test specification includes three components: test_groups, test_types, test_corr. Alignment among entries components important correct implementation. two ways provide test specification. first approach \"unnamed\" approach, assumes 3 components ordered way, .e., $n$-th element test_types test_corr apply $n$-th group test_groups. second \"named\" approach uses name element component connect element test_types test_corr correct element test_groups. Consistency ensured correct implementation.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_closure.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_closure.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses # (H1 and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  p <- c(0.018, 0.01, 0.105, 0.006) alpha <- 0.025  # Closed graphical multiple comparison procedure using Bonferroni tests # Same results as `graph_test_shortcut(g, p, alpha)` graph_test_closure(g, p, alpha) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Test types #>   bonferroni: (H1, H2, H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1        0.024   TRUE #>           H2        0.020   TRUE #>           H3        0.105  FALSE #>           H4        0.024   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>   # Closed graphical multiple comparison procedure using parametric tests for # H1 and H2, and Bonferroni tests for H3 and H4 set.seed(1234) corr_list <- list(matrix(c(1, 0.5, 0.5, 1), nrow = 2), NA) graph_test_closure(   graph = g,   p = p,   alpha = alpha,   test_groups = list(1:2, 3:4),   test_types = c(\"parametric\", \"bonferroni\"),   test_corr = corr_list ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Correlation matrix:     H1  H2 #>                       H1 1.0 0.5 #>                       H2 0.5 1.0 #>  #>   Test types #>   parametric: (H1, H2) #>   bonferroni: (H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1      0.02400   TRUE #>           H2      0.01871   TRUE #>           H3      0.10500  FALSE #>           H4      0.02400   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>  # The \"named\" approach to obtain the same results # Note that \"group2\" appears before \"group1\" in `test_groups` set.seed(1234) corr_list <- list(group1 = matrix(c(1, 0.5, 0.5, 1), nrow = 2), group2 = NA) graph_test_closure(   graph = g,   p = p,   alpha = alpha,   test_groups = list(group1 = 1:2, group2 = 3:4),   test_types = c(group2 = \"bonferroni\", group1 = \"parametric\"),   test_corr = corr_list ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Correlation matrix:     H1  H2 #>                       H1 1.0 0.5 #>                       H2 0.5 1.0 #>  #>   Test types #>   parametric: (H1, H2) #>   bonferroni: (H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1      0.02400   TRUE #>           H2      0.01871   TRUE #>           H3      0.10500  FALSE #>           H4      0.02400   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>   # Closed graphical multiple comparison procedure using parametric tests for # H1 and H2, and Simes tests for H3 and H4 set.seed(1234) graph_test_closure(   graph = g,   p = p,   alpha = alpha,   test_groups = list(group1 = 1:2, group2 = 3:4),   test_types = c(group1 = \"parametric\", group2 = \"simes\"),   test_corr = corr_list ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Correlation matrix:     H1  H2 #>                       H1 1.0 0.5 #>                       H2 0.5 1.0 #>  #>   Test types #>   parametric: (H1, H2) #>        simes: (H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1      0.02400   TRUE #>           H2      0.01871   TRUE #>           H3      0.10500  FALSE #>           H4      0.02400   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_fast.html","id":null,"dir":"Reference","previous_headings":"","what":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","title":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","text":"functions performs similarly graph_test_closure() graph_test_shortcut() optimized efficiently calculating power. example, generating weights calculating adjusted weights can done . Vectorization applied possible.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_fast.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","text":"","code":"graph_test_closure_fast(p, alpha, adjusted_weights, matrix_intersections)  graph_test_shortcut_fast(p, alpha, adjusted_weights)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_fast.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","text":"p numeric vector one-sided p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. alpha numeric value one-sided overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing. Note one-sided tests supported. adjusted_weights adjusted hypothesis weights, second half columns graph_generate_weights() output, adjusted appropriate test types (Bonferroni, Simes, parametric). matrix_intersections matrix hypothesis indicators weighting strategy, first half graph_generate_weights() output.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_fast.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","text":"logical integer vector indicating whether hypothesis can rejected .","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":null,"dir":"Reference","previous_headings":"","what":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"Shortcut graphical multiple comparison procedures sequentially rejective procedure based Bretz et al. (2009). $m$ hypotheses, $m$ steps obtain rejection decisions. procedure equivalent closed graphical multiple comparison procedures using Bonferroni tests intersection hypotheses, shortcut procedures faster perform. See vignette(\"shortcut-testing\") illustration shortcut procedures interpretation outputs.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"","code":"graph_test_shortcut(   graph,   p,   alpha = 0.025,   verbose = FALSE,   test_values = FALSE )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"graph initial graph returned graph_create(). p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. alpha numeric scalar overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. verbose logical scalar specifying whether details intermediate update graphs included results. verbose = TRUE, intermediate update graphs provided deleting hypothesis, rejected. default verbose = FALSE. test_values logical scalar specifying whether adjusted significance levels provided hypothesis. test_values = TRUE, provides equivalent way performing graphical multiple comparison procedures comparing p-value significance level. p-value hypothesis less equal significance level, hypothesis rejected. order rejection based order adjusted p-values smallest largest. default test_values = FALSE.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"S3 object class graph_report list 4 elements: inputs - Input parameters, list : graph - Initial graph, *p - (Unadjusted raw) p-values, alpha - Overall significance level, test_groups - Groups hypotheses different types tests, list hypotheses graph_test_shortcut(), test_types - Different types tests, \"bonferroni\" graph_test_shortcut(). Output parameters outputs, list : adjusted_p - Adjusted p-values, rejected - Rejected hypotheses, graph - Updated graph deleting rejected hypotheses. details - Verbose outputs intermediate updated graphs, verbose = TRUE. test_values - Adjusted significance levels, test_values = TRUE.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  p <- c(0.018, 0.01, 0.105, 0.006) alpha <- 0.025 graph_test_shortcut(g, p, alpha) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0  0  1  0 #>   H2  0  0  0  1 #>   H3  0  1  0  0 #>   H4  1  0  0  0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Test types #>   bonferroni: (H1, H2, H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1        0.020   TRUE #>           H2        0.020   TRUE #>           H3        0.105  FALSE #>           H4        0.020   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_update.html","id":null,"dir":"Reference","previous_headings":"","what":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"hypothesis deleted, initial graph updated. deleted hypothesis hypothesis weight 0 transition weight 0. Remaining hypotheses updated hypothesis weights transition weights according Algorithm 1 Bretz et al. (2009).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_update.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"","code":"graph_update(graph, delete)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_update.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"graph initial graph returned graph_create(). delete logical integer vector, denoting hypotheses delete. logical vector results \"unordered mode\", means hypotheses corresponding TRUE delete deleted. sequence deletion follow sequence TRUE's delete. case, length logical vector must match number hypotheses graph. integer vector results \"ordered mode\", means delete specifies sequence hypotheses deleted indicating location deleted hypotheses, e.g., 1st, 2nd, etc. case, integer vector can length, must contain valid hypothesis numbers (greater 0, less equal number hypotheses graph).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_update.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"S3 object class updated_graph list 4 elements: initial_graph: initial graph object. updated_graph: updated graph object specified hypotheses deleted. deleted: numeric vector indicating hypotheses deleted. intermediate_graphs: using ordered mode, list intermediate updated graphs hypothesis deleted according sequence specified delete.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_update.html","id":"sequence-of-deletion","dir":"Reference","previous_headings":"","what":"Sequence of deletion","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"multiple hypotheses deleted graph, many sequences deletion initial graph updated updated graph. interest updated graph hypotheses specified delete deleted, updated graph matter sequence deletion used. property proved Bretz et al. (2009). interest intermediate updated graph hypothesis deleted according sequence specified delete, integer vector delete specified detailed outputs provided.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_update.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graph_update.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  # Delete the second and third hypotheses in the \"unordered mode\" graph_update(g, delete = c(FALSE, TRUE, TRUE, FALSE)) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 2, 3 #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2:  NA #> H3:  NA #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA NA  1 #>  H2 NA NA NA NA #>  H3 NA NA NA NA #>  H4  1 NA NA  0  # Equivalent way in the \"ordered mode\" to obtain the updated graph after # deleting the second and third hypotheses # Additional intermediate updated graphs are also provided graph_update(g, delete = 2:3) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 2, 3 #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2:  NA #> H3:  NA #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA NA  1 #>  H2 NA NA NA NA #>  H3 NA NA NA NA #>  H4  1 NA NA  0 #>  #> Deletion sequence ($intermediate_graphs) --------------------------------------- #>  #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0  0  1  0 #>   H2  0  0  0  1 #>   H3  0  1  0  0 #>   H4  1  0  0  0 #>  #>     Step 1: Updated graph after removing hypothesis 2 #>  #>     --- Hypothesis weights --- #>     H1: 0.5 #>     H2:  NA #>     H3: 0.0 #>     H4: 0.5 #>  #>     --- Transition weights --- #>        H1 H2 H3 H4 #>     H1  0 NA  1  0 #>     H2 NA NA NA NA #>     H3  0 NA  0  1 #>     H4  1 NA  0  0 #>  #>       Step 2: Updated graph after removing hypotheses 2, 3 #>  #>       --- Hypothesis weights --- #>       H1: 0.5 #>       H2:  NA #>       H3:  NA #>       H4: 0.5 #>  #>       --- Transition weights --- #>          H1 H2 H3 H4 #>       H1  0 NA NA  1 #>       H2 NA NA NA NA #>       H3 NA NA NA NA #>       H4  1 NA NA  0 #>  #>   Final updated graph after removing deleted hypotheses #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2:  NA #>   H3:  NA #>   H4: 0.5 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0 NA NA  1 #>   H2 NA NA NA NA #>   H3 NA NA NA NA #>   H4  1 NA NA  0 #>"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graphicalMCP-package.html","id":null,"dir":"Reference","previous_headings":"","what":"graphicalMCP: Graphical Multiple Comparison Procedures — graphicalMCP-package","title":"graphicalMCP: Graphical Multiple Comparison Procedures — graphicalMCP-package","text":"Multiple comparison procedures (MCPs) control familywise error rate clinical trials. Graphical MCPs include many commonly used procedures special cases; see Bretz et al. (2011) doi:10.1002/bimj.201000239 , Lu (2016) doi:10.1002/sim.6985 , Xi et al. (2017) doi:10.1002/bimj.201600233 . package low-dependency implementation graphical MCPs allow mixed types tests. also includes power simulations visualization graphical MCPs.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/graphicalMCP-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"graphicalMCP: Graphical Multiple Comparison Procedures — graphicalMCP-package","text":"Maintainer: Dong Xi dong.xi1@gilead.com Authors: Ethan Brockmann ethan.brockmann@atorusresearch.com contributors: Gilead Sciences, Inc. [copyright holder, funder]","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/input_val.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate inputs for testing and power simulations — test_input_val","title":"Validate inputs for testing and power simulations — test_input_val","text":"Validate inputs testing power simulations","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/input_val.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate inputs for testing and power simulations — test_input_val","text":"","code":"test_input_val(   graph,   p,   alpha,   test_groups = list(seq_along(graph$hypotheses)),   test_types = c(\"bonferroni\"),   test_corr,   verbose,   test_values )  power_input_val(graph, sim_n, power_marginal, test_corr, success)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/input_val.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate inputs for testing and power simulations — test_input_val","text":"graph initial graph returned graph_create(). p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. alpha numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. test_groups list numeric vectors specifying hypotheses test together. Grouping needed correctly perform Simes parametric tests. test_types character vector test types apply test group. needed correctly perform Simes parametric tests. length match number elements test_groups. test_corr (Optional) list numeric correlation matrices. entry list correspond test group. test group using Bonferroni Simes tests, corresponding entry test_corr NA. test group using parametric tests, corresponding entry test_corr numeric correlation matrix specifying correlation test statistics hypotheses test group. length match number elements test_groups. verbose logical scalar specifying whether details adjusted p-value calculations included results. verbose = TRUE, adjusted p-values provided intersection hypothesis. default verbose = FALSE. test_values logical scalar specifying whether adjusted significance levels provided hypothesis. test_values = TRUE, provides equivalent way performing graphical multiple comparison procedures comparing p-value significance level. p-value hypothesis less equal significance level, hypothesis rejected. default test_values = FALSE. sim_n integer scalar specifying number simulations. default 1e5. power_marginal numeric vector marginal power values use simulating p-values. See Details simulation process. success list user-defined functions specify success criteria. Functions must take one simulation's logical vector results input, return length-one logical vector. instance, \"success\" means rejecting hypotheses 1 2, use sim_success = list(\"1 2\" = function(x) x[1] && x[2]). list named, function body used name. Lambda functions also work starting R 4.1, e.g. sim_success = list(\\(x) x[3] || x[4]).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/input_val.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate inputs for testing and power simulations — test_input_val","text":"Returns graph invisibly","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.initial_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 plot method for class initial_graph — plot.initial_graph","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"plot initial_graph translates hypotheses vertices transitions edges create network plot. Vertices labeled hypothesis names hypothesis weights, edges labeled transition weights. See vignette(\"graph-examples\") illustration commonly used multiple comparison procedure using graphs.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"","code":"# S3 method for class 'initial_graph' plot(   x,   ...,   v_palette = c(\"#6baed6\", \"#cccccc\"),   layout = \"grid\",   nrow = NULL,   ncol = NULL,   edge_curves = NULL,   precision = 4,   eps = NULL,   background_color = \"white\",   margins = c(0, 0, 0, 0) )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"x object class initial_graph plot. ... arguments passed igraph::plot.igraph(). v_palette character vector length two specifying colors retained deleted hypotheses. extensive color customization must done vertex.color. layout igraph layout specification (See ?igraph.plotting), \"grid\", lays hypotheses left--right top--bottom. nrow ncol control grid shape. nrow integer scalar specifying number rows vertex grid. row column counts specified, vertices laid close square possible. ncol integer scalar specifying number columns vertex grid. row column counts specified, vertices laid close square possible. edge_curves named numeric vector specifying curvature specific edges. Edge pairs (two vertices share edge possible direction) detected automatically get 0.25 curvature. Adjust edges adding entry name \"vertex1|vertex2, adjust default edge pairs curvature adding entry name \"pairs\" - edge_curves = c(\"pairs\" = 0.5, \"H1|H3\" = 0.25, \"H3|H4\" = 0.75). precision integer scalar indicating number decimal places display. eps numeric scalar. transition weight eps displayed \\(\\epsilon\\), indicates edges infinitesimally small weights. See Bretz et al. (2009) details. background_color character scalar specifying background color whole plotting area. Passed directly graphics::par() (bg). margins length 4 numeric vector specifying margins plot. Defaults 0, since igraph plots tend large margins. passed directly graphics::par() (mar).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"object x class initial_graph, plotting initial graph.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"customization-of-graphs","dir":"Reference","previous_headings":"","what":"Customization of graphs","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"values igraph::plot.igraph() get defaults changed graphicalMCP. values can still changed passing arguments plot.initial_graph(). new defaults: vertex.color = \"#6baed6\", vertex.label.color = \"black\", vertex.size = 20, edge.arrow.size = 1, edge.arrow.width = 1, edge.label.color = \"black\" asp = 0. Neither graphicalMCP igraph anything overlapping edge labels. run problem, vertices practically moved enough avoid collisions edge labels, using edge curves can help. igraph puts edge labels closer tail edge edge straight, closer head edge curved. setting edge's curve small value, effectively straight edge can shifted new position.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Xi, D., Bretz, F. (2019). Symmetric graphs equally weighted tests, application Hochberg procedure. Statistics Medicine, 38(27), 5268-5282.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions) plot(g)   # A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and four secondary hypotheses (H31, H32, H41, and H42) # See Figure 6 in Xi and Bretz (2019). hypotheses <- c(0.5, 0.5, 0, 0, 0, 0) epsilon <- 1e-5 transitions <- rbind(   c(0, 0.5, 0.25, 0, 0.25, 0),   c(0.5, 0, 0, 0.25, 0, 0.25),   c(0, 0, 0, 0, 1, 0),   c(epsilon, 0, 0, 0, 0, 1 - epsilon),   c(0, epsilon, 1 - epsilon, 0, 0, 0),   c(0, 0, 0, 1, 0, 0) ) hyp_names <- c(\"H1\", \"H2\", \"H31\", \"H32\", \"H41\", \"H42\") g <- graph_create(hypotheses, transitions, hyp_names)  plot_layout <- rbind(   c(0.15, 0.5),   c(0.65, 0.5),   c(0, 0),   c(0.5, 0),   c(0.3, 0),   c(0.8, 0) )  plot(g, layout = plot_layout, eps = epsilon, edge_curves = c(pairs = .5))"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.updated_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 plot method for the class updated_graph — plot.updated_graph","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"Plotting updated graph light wrapper around plot.initial_graph(), changing default vertex color use gray deleted hypotheses.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"","code":"# S3 method for class 'updated_graph' plot(x, ...)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"x object class updated_graph plot. ... Arguments passed plot.initial_graph v_palette character vector length two specifying colors retained deleted hypotheses. extensive color customization must done vertex.color. layout igraph layout specification (See ?igraph.plotting), \"grid\", lays hypotheses left--right top--bottom. nrow ncol control grid shape. nrow integer scalar specifying number rows vertex grid. row column counts specified, vertices laid close square possible. ncol integer scalar specifying number columns vertex grid. row column counts specified, vertices laid close square possible. edge_curves named numeric vector specifying curvature specific edges. Edge pairs (two vertices share edge possible direction) detected automatically get 0.25 curvature. Adjust edges adding entry name \"vertex1|vertex2, adjust default edge pairs curvature adding entry name \"pairs\" - edge_curves = c(\"pairs\" = 0.5, \"H1|H3\" = 0.25, \"H3|H4\" = 0.75). precision integer scalar indicating number decimal places display. eps numeric scalar. transition weight eps displayed \\(\\epsilon\\), indicates edges infinitesimally small weights. See Bretz et al. (2009) details. background_color character scalar specifying background color whole plotting area. Passed directly graphics::par() (bg). margins length 4 numeric vector specifying margins plot. Defaults 0, since igraph plots tend large margins. passed directly graphics::par() (mar).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"object x class updated_graph, plotting updated graph.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  # Delete the second and third hypotheses in the \"unordered mode\" plot(   graph_update(     g,     c(FALSE, TRUE, TRUE, FALSE)   ),   layout = \"grid\" )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.graph_report.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 print method for the class graph_report — print.graph_report","title":"S3 print method for the class graph_report — print.graph_report","text":"printed graph_report displays initial graph, p-values significance levels, rejection decisions, optional detailed test results.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.graph_report.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 print method for the class graph_report — print.graph_report","text":"","code":"# S3 method for class 'graph_report' print(x, ..., precision = 4, indent = 2, rows = 10)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.graph_report.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 print method for the class graph_report — print.graph_report","text":"x object class graph_report print. ... values passed methods (currently unused) precision integer scalar indicating number decimal places display. indent integer scalar indicating many spaces indent results. rows integer scalar indicating many rows detailed test results print.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.graph_report.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 print method for the class graph_report — print.graph_report","text":"object x class graph_report, printing report conducting graphical multiple comparison procedure.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.graph_report.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 print method for the class graph_report — print.graph_report","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.graph_report.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 print method for the class graph_report — print.graph_report","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  p <- c(0.018, 0.01, 0.105, 0.006) alpha <- 0.025 graph_test_shortcut(g, p, alpha) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0  0  1  0 #>   H2  0  0  0  1 #>   H3  0  1  0  0 #>   H4  1  0  0  0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Test types #>   bonferroni: (H1, H2, H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1        0.020   TRUE #>           H2        0.020   TRUE #>           H3        0.105  FALSE #>           H4        0.020   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.initial_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 print method for the class initial_graph — print.initial_graph","title":"S3 print method for the class initial_graph — print.initial_graph","text":"printed initial_graph displays header stating \"Initial graph\", hypothesis weights, transition weights.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.initial_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 print method for the class initial_graph — print.initial_graph","text":"","code":"# S3 method for class 'initial_graph' print(x, ..., precision = 4, indent = 0)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.initial_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 print method for the class initial_graph — print.initial_graph","text":"x object class initial_graph print. ... values passed methods (currently unused). precision integer scalar indicating number decimal places display. indent integer scalar indicating many spaces indent results.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.initial_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 print method for the class initial_graph — print.initial_graph","text":"object x class initial_graph, printing initial graph.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.initial_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 print method for the class initial_graph — print.initial_graph","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.initial_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 print method for the class initial_graph — print.initial_graph","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) hyp_names <- c(\"H11\", \"H12\", \"H21\", \"H22\") g <- graph_create(hypotheses, transitions, hyp_names) g #> Initial graph #>  #> --- Hypothesis weights --- #> H11: 0.5 #> H12: 0.5 #> H21: 0.0 #> H22: 0.0 #>  #> --- Transition weights --- #>      H11 H12 H21 H22 #>  H11   0   0   1   0 #>  H12   0   0   0   1 #>  H21   0   1   0   0 #>  H22   1   0   0   0"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.power_report.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 print method for the class power_report — print.power_report","title":"S3 print method for the class power_report — print.power_report","text":"printed power_report displays initial graph, testing simulation options, power outputs, optional detailed simulations test results.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.power_report.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 print method for the class power_report — print.power_report","text":"","code":"# S3 method for class 'power_report' print(x, ..., precision = 4, indent = 2, rows = 10)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.power_report.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 print method for the class power_report — print.power_report","text":"x object class power_report print ... values passed methods (currently unused) precision integer scalar indicating number decimal places display. indent integer scalar indicating many spaces indent results. rows integer scalar indicating many rows detailed test results print.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.power_report.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 print method for the class power_report — print.power_report","text":"object x class power_report, printing report conducting power simulations based graphical multiple comparison procedure.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.power_report.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 print method for the class power_report — print.power_report","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011a). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Bretz, F., Maurer, W., Hommel, G. (2011b). Test power considerations multiple endpoint analyses using sequentially rejective graphical procedures. Statistics Medicine, 30(13), 1489-1501.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.power_report.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 print method for the class power_report — print.power_report","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011). alpha <- 0.025 hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  marginal_power <- c(0.8, 0.8, 0.7, 0.9) corr1 <- matrix(0.5, nrow = 2, ncol = 2) diag(corr1) <- 1 corr <- rbind(   cbind(corr1, 0.5 * corr1),   cbind(0.5 * corr1, corr1) ) success_fns <- list(   # Probability to reject both H1 and H2   `H1andH2` = function(x) x[1] & x[2],   # Probability to reject both (H1 and H3) or (H2 and H4)   `(H1andH3)or(H2andH4)` = function(x) (x[1] & x[3]) | (x[2] & x[4]) ) set.seed(1234) # Bonferroni tests power_output <- graph_calculate_power(   g,   alpha,   sim_corr = corr,   sim_n = 1e5,   power_marginal = marginal_power,   sim_success = success_fns )"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.updated_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 print method for the class updated_graph — print.updated_graph","title":"S3 print method for the class updated_graph — print.updated_graph","text":"printed updated_graph displays initial graph, (final) updated graph, sequence intermediate updated graphs hypotheses deleted (available).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.updated_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 print method for the class updated_graph — print.updated_graph","text":"","code":"# S3 method for class 'updated_graph' print(x, ..., precision = 6, indent = 2)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.updated_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 print method for the class updated_graph — print.updated_graph","text":"x object class updated_graph print. ... values passed methods (currently unused). precision integer scalar indicating number decimal places display. indent integer scalar indicating many spaces indent results.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.updated_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 print method for the class updated_graph — print.updated_graph","text":"object x class updated_graph, printing updated graph.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.updated_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 print method for the class updated_graph — print.updated_graph","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011a). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/print.updated_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 print method for the class updated_graph — print.updated_graph","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  # Delete the second and third hypotheses in the \"unordered mode\" graph_update(g, delete = c(FALSE, TRUE, TRUE, FALSE)) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 2, 3 #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2:  NA #> H3:  NA #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA NA  1 #>  H2 NA NA NA NA #>  H3 NA NA NA NA #>  H4  1 NA NA  0  # Equivalent way in the \"ordered mode\" to obtain the updated graph after # deleting the second and third hypotheses # Additional intermediate updated graphs are also provided graph_update(g, delete = 2:3) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 2, 3 #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2:  NA #> H3:  NA #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA NA  1 #>  H2 NA NA NA NA #>  H3 NA NA NA NA #>  H4  1 NA NA  0 #>  #> Deletion sequence ($intermediate_graphs) --------------------------------------- #>  #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0  0  1  0 #>   H2  0  0  0  1 #>   H3  0  1  0  0 #>   H4  1  0  0  0 #>  #>     Step 1: Updated graph after removing hypothesis 2 #>  #>     --- Hypothesis weights --- #>     H1: 0.5 #>     H2:  NA #>     H3: 0.0 #>     H4: 0.5 #>  #>     --- Transition weights --- #>        H1 H2 H3 H4 #>     H1  0 NA  1  0 #>     H2 NA NA NA NA #>     H3  0 NA  0  1 #>     H4  1 NA  0  0 #>  #>       Step 2: Updated graph after removing hypotheses 2, 3 #>  #>       --- Hypothesis weights --- #>       H1: 0.5 #>       H2:  NA #>       H3:  NA #>       H4: 0.5 #>  #>       --- Transition weights --- #>          H1 H2 H3 H4 #>       H1  0 NA NA  1 #>       H2 NA NA NA NA #>       H3 NA NA NA NA #>       H4  1 NA NA  0 #>  #>   Final updated graph after removing deleted hypotheses #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2:  NA #>   H3:  NA #>   H4: 0.5 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0 NA NA  1 #>   H2 NA NA NA NA #>   H3 NA NA NA NA #>   H4  1 NA NA  0 #>"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html","id":null,"dir":"Reference","previous_headings":"","what":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"intersection hypothesis can tested mixture test types including Bonferroni, parametric Simes tests. function organize outputs testing prepare graph_report.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"","code":"test_values_bonferroni(p, hypotheses, alpha, intersection = NA)  test_values_parametric(p, hypotheses, alpha, intersection = NA, test_corr)  test_values_simes(p, hypotheses, alpha, intersection = NA)"},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. hypotheses numeric vector hypothesis weights graphical multiple comparison procedure. Must vector values 0 & 1 (inclusive). length match row column lengths transitions. sum hypothesis weights exceed 1. alpha numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. intersection (optional) numeric scalar used name intersection hypothesis weighting strategy. test_corr (Optional) list numeric correlation matrices. entry list correspond test group. test group using Bonferroni Simes tests, corresponding entry test_corr NA. test group using parametric tests, corresponding entry test_corr numeric correlation matrix specifying correlation test statistics hypotheses test group. length match number elements test_groups.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"data frame rows corresponding individual hypotheses involved intersection hypothesis hypothesis weights hypotheses. following columns: Intersection - Name intersection hypothesis, Hypothesis - Name individual hypothesis, Test - Test type individual hypothesis, p - (Unadjusted raw) p-values individual hypothesis, c_value- C value parametric tests, Weight - Hypothesis weight individual hypothesis, Alpha - Overall significance level \\(\\alpha\\), Inequality_holds - Indicator show p-value less equal significance level. Bonferroni Simes tests, significance level hypothesis weight times \\(\\alpha\\). parametric tests, significance level c value times hypothesis weight times \\(\\alpha\\).","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-010","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.1.0","title":"graphicalMCP 0.1.0","text":"First release","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-011","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.1.1","title":"graphicalMCP 0.1.1","text":"Added compilation vignettes (#73) Removed duplicated columns “*” test values (#75)","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-012","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.1.2","title":"graphicalMCP 0.1.2","text":"Updated function documentation Updated references","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-020","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.0","title":"graphicalMCP 0.2.0","text":"Corrected typos Updated function documentation CRAN release","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-021","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.1","title":"graphicalMCP 0.2.1","text":"Corrected typos First CRAN release","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-022","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.2","title":"graphicalMCP 0.2.2","text":"Updated citations Resubmission first CRAN release","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-023","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.3","title":"graphicalMCP 0.2.3","text":"Included cran-comments.ms .Rbuildignore Resubmission first CRAN release","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-024","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.4","title":"graphicalMCP 0.2.4","text":"Updated documentation according issue #84 Resubmission first CRAN release","code":""},{"path":"https://gilead-biostats.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-025","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.5","title":"graphicalMCP 0.2.5","text":"Updated adjust_weights_parametric_util.Rd Resubmission first CRAN release","code":""}]
+[{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"Apache License","title":"Apache License","text":"Version 2.0, January 2004 <http://www.apache.org/licenses/>","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_1-definitions","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"1. Definitions","title":"Apache License","text":"“License” shall mean terms conditions use, reproduction, distribution defined Sections 1 9 document. “Licensor” shall mean copyright owner entity authorized copyright owner granting License. “Legal Entity” shall mean union acting entity entities control, controlled , common control entity. purposes definition, “control” means () power, direct indirect, cause direction management entity, whether contract otherwise, (ii) ownership fifty percent (50%) outstanding shares, (iii) beneficial ownership entity. “” (“”) shall mean individual Legal Entity exercising permissions granted License. “Source” form shall mean preferred form making modifications, including limited software source code, documentation source, configuration files. “Object” form shall mean form resulting mechanical transformation translation Source form, including limited compiled object code, generated documentation, conversions media types. “Work” shall mean work authorship, whether Source Object form, made available License, indicated copyright notice included attached work (example provided Appendix ). “Derivative Works” shall mean work, whether Source Object form, based (derived ) Work editorial revisions, annotations, elaborations, modifications represent, whole, original work authorship. purposes License, Derivative Works shall include works remain separable , merely link (bind name) interfaces , Work Derivative Works thereof. “Contribution” shall mean work authorship, including original version Work modifications additions Work Derivative Works thereof, intentionally submitted Licensor inclusion Work copyright owner individual Legal Entity authorized submit behalf copyright owner. purposes definition, “submitted” means form electronic, verbal, written communication sent Licensor representatives, including limited communication electronic mailing lists, source code control systems, issue tracking systems managed , behalf , Licensor purpose discussing improving Work, excluding communication conspicuously marked otherwise designated writing copyright owner “Contribution.” “Contributor” shall mean Licensor individual Legal Entity behalf Contribution received Licensor subsequently incorporated within Work.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_2-grant-of-copyright-license","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"2. Grant of Copyright License","title":"Apache License","text":"Subject terms conditions License, Contributor hereby grants perpetual, worldwide, non-exclusive, -charge, royalty-free, irrevocable copyright license reproduce, prepare Derivative Works , publicly display, publicly perform, sublicense, distribute Work Derivative Works Source Object form.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_3-grant-of-patent-license","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"3. Grant of Patent License","title":"Apache License","text":"Subject terms conditions License, Contributor hereby grants perpetual, worldwide, non-exclusive, -charge, royalty-free, irrevocable (except stated section) patent license make, made, use, offer sell, sell, import, otherwise transfer Work, license applies patent claims licensable Contributor necessarily infringed Contribution(s) alone combination Contribution(s) Work Contribution(s) submitted. institute patent litigation entity (including cross-claim counterclaim lawsuit) alleging Work Contribution incorporated within Work constitutes direct contributory patent infringement, patent licenses granted License Work shall terminate date litigation filed.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_4-redistribution","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"4. Redistribution","title":"Apache License","text":"may reproduce distribute copies Work Derivative Works thereof medium, without modifications, Source Object form, provided meet following conditions: () must give recipients Work Derivative Works copy License; (b) must cause modified files carry prominent notices stating changed files; (c) must retain, Source form Derivative Works distribute, copyright, patent, trademark, attribution notices Source form Work, excluding notices pertain part Derivative Works; (d) Work includes “NOTICE” text file part distribution, Derivative Works distribute must include readable copy attribution notices contained within NOTICE file, excluding notices pertain part Derivative Works, least one following places: within NOTICE text file distributed part Derivative Works; within Source form documentation, provided along Derivative Works; , within display generated Derivative Works, wherever third-party notices normally appear. contents NOTICE file informational purposes modify License. may add attribution notices within Derivative Works distribute, alongside addendum NOTICE text Work, provided additional attribution notices construed modifying License. may add copyright statement modifications may provide additional different license terms conditions use, reproduction, distribution modifications, Derivative Works whole, provided use, reproduction, distribution Work otherwise complies conditions stated License.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_5-submission-of-contributions","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"5. Submission of Contributions","title":"Apache License","text":"Unless explicitly state otherwise, Contribution intentionally submitted inclusion Work Licensor shall terms conditions License, without additional terms conditions. Notwithstanding , nothing herein shall supersede modify terms separate license agreement may executed Licensor regarding Contributions.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_6-trademarks","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"6. Trademarks","title":"Apache License","text":"License grant permission use trade names, trademarks, service marks, product names Licensor, except required reasonable customary use describing origin Work reproducing content NOTICE file.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_7-disclaimer-of-warranty","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"7. Disclaimer of Warranty","title":"Apache License","text":"Unless required applicable law agreed writing, Licensor provides Work (Contributor provides Contributions) “” BASIS, WITHOUT WARRANTIES CONDITIONS KIND, either express implied, including, without limitation, warranties conditions TITLE, NON-INFRINGEMENT, MERCHANTABILITY, FITNESS PARTICULAR PURPOSE. solely responsible determining appropriateness using redistributing Work assume risks associated exercise permissions License.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_8-limitation-of-liability","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"8. Limitation of Liability","title":"Apache License","text":"event legal theory, whether tort (including negligence), contract, otherwise, unless required applicable law (deliberate grossly negligent acts) agreed writing, shall Contributor liable damages, including direct, indirect, special, incidental, consequential damages character arising result License use inability use Work (including limited damages loss goodwill, work stoppage, computer failure malfunction, commercial damages losses), even Contributor advised possibility damages.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"id_9-accepting-warranty-or-additional-liability","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"9. Accepting Warranty or Additional Liability","title":"Apache License","text":"redistributing Work Derivative Works thereof, may choose offer, charge fee , acceptance support, warranty, indemnity, liability obligations /rights consistent License. However, accepting obligations, may act behalf sole responsibility, behalf Contributor, agree indemnify, defend, hold Contributor harmless liability incurred , claims asserted , Contributor reason accepting warranty additional liability. END TERMS CONDITIONS","code":""},{"path":"https://openpharma.github.io/graphicalMCP/LICENSE.html","id":"appendix-how-to-apply-the-apache-license-to-your-work","dir":"","previous_headings":"","what":"APPENDIX: How to apply the Apache License to your work","title":"Apache License","text":"apply Apache License work, attach following boilerplate notice, fields enclosed brackets [] replaced identifying information. (Don’t include brackets!) text enclosed appropriate comment syntax file format. also recommend file class name description purpose included “printed page” copyright notice easier identification within third-party archives.","code":"Copyright 2023 Gilead Sciences  Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at    http://www.apache.org/licenses/LICENSE-2.0  Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License."},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"motivating-example","dir":"Articles","previous_headings":"","what":"Motivating example","title":"Graphical multiple comparison procedures based on the closure principle","text":"Consider confirmatory clinical trial comparing test treatment (treatment) control treatment (control) disease. two doses treatment: low dose high dose. three endpoints included multiplicity adjustment strategy, primary endpoint (PE) two secondary endpoints (SE1 SE2). total, six null hypotheses: H1H_1, H3H_3 H5H_5 primary hypothesis two secondary hypotheses respectively low dose versus control; H2H_2, H4H_4 H6H_6 primary hypothesis two secondary hypotheses respectively high dose versus control. clinical considerations constrain structure multiple comparison procedures, can flexibly incorporated using graphical approaches. First, low high doses considered equally important, means rejecting primary hypothesis either dose versus control leads successful trial. Regarding secondary hypotheses, one tested corresponding primary hypothesis rejected. means H3H_3 H5H_5 tested H1H_1 rejected; H4H_4 H6H_6 tested H2H_2 rejected. addition, statistical considerations complete graph. primary hypotheses H1H_1 H2H_2 equal hypothesis weight 0.5. secondary hypotheses hypothesis weight 0. primary hypothesis rejected, weight propagate along three outgoing edges: one primary hypothesis two descendant secondary hypotheses. edge primary hypothesis transition weight 0.5; two edges descendant secondary hypotheses equal transition weight 0.25. secondary hypotheses dose-control comparison, edge transition weight 1 (close 1 allow ϵ\\epsilon edges). hypothesis weights dose-control comparison group propagated primary hypothesis dose-control comparison, hypotheses first dose-control comparison group deleted. specifications, can create following graph.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"create-a-graph","dir":"Articles","previous_headings":"Motivating example","what":"Create a graph","title":"Graphical multiple comparison procedures based on the closure principle","text":"","code":"hypotheses <- c(0.5, 0.5, 0, 0, 0, 0)  epsilon <- 1e-5 transitions <- rbind(   c(0, 0.5, 0.25, 0, 0.25, 0),   c(0.5, 0, 0, 0.25, 0, 0.25),   c(0, 0, 0, 0, 1, 0),   c(epsilon, 0, 0, 0, 0, 1 - epsilon),   c(0, epsilon, 1 - epsilon, 0, 0, 0),   c(0, 0, 0, 1, 0, 0) )  hyp_names <- c(\"H1\", \"H2\", \"H3\", \"H4\", \"H5\", \"H6\") g <- graph_create(hypotheses, transitions, hyp_names)  plot_layout <- rbind(   c(0.15, 0.5),   c(0.65, 0.5),   c(0, 0),   c(0.5, 0),   c(0.3, 0),   c(0.8, 0) )  plot(   g,   layout = plot_layout,   eps = epsilon,   edge_curves = c(pairs = 0.8),   vertex.size = 35 )"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"bonferroni-tests","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle","what":"Bonferroni tests","title":"Graphical multiple comparison procedures based on the closure principle","text":"Given set p-values H1,…,H6H_1, \\ldots, H_6, graphical multiple comparison procedure can performed control family-wise error rate (FWER) significance level alpha. one-sided p-values, alpha often set 0.025 (default). First, perform Bonferroni-based procedure using closure principle (Bretz et al. 2009). running procedure, none hypotheses rejected. results identical using graph_test_shortcut().","code":"p_values <- c(0.015, 0.013, 0.01, 0.007, 0.1, 0.0124) test_results <- graph_test_closure(   g,   p = p_values,   alpha = 0.025,   verbose = TRUE,   test_values = TRUE )  test_results$outputs$adjusted_p #>    H1    H2    H3    H4    H5    H6  #> 0.026 0.026 0.028 0.028 0.100 0.028  test_results$outputs$rejected #>    H1    H2    H3    H4    H5    H6  #> FALSE FALSE FALSE FALSE FALSE FALSE # Same testing results as # 'graph_test_shortcut(g, p = p_values, alpha = 0.025)$outputs$rejected'"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"obtain-the-closure","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Bonferroni tests","what":"Obtain the closure","title":"Graphical multiple comparison procedures based on the closure principle","text":"investigate closure every intersection hypothesis rejected, one obtain detailed output specifying verbose = TRUE. hypotheses tested using Bonferroni tests, adjusted p-value every intersection hypothesis adjusted p-value group 1 (meaning hypotheses group Bonferroni tests). intersection hypothesis rejected adjusted p-value less equal alpha. Adjusted p-values initially calculated groups hypotheses. case one group, includes hypotheses, can . adjusted p-value intersection hypothesis minimum across groups within intersection. Finally, adjusted p-value individual hypothesis whole procedure equal maximum adjusted p-values across intersections involving hypothesis.","code":"test_results_verbose <-   graph_test_closure(     g,     p = p_values,     alpha = 0.025,     verbose = TRUE   )  head(test_results_verbose$details$results) #>   Intersection  H1  H2 H3 H4 H5 H6 adj_p_grp1 adj_p_inter reject_intersection #> 1       111111 0.5 0.5  0  0  0  0      0.026       0.026               FALSE #> 2       111110 0.5 0.5  0  0  0 NA      0.026       0.026               FALSE #> 3       111101 0.5 0.5  0  0 NA  0      0.026       0.026               FALSE #> 4       111100 0.5 0.5  0  0 NA NA      0.026       0.026               FALSE #> 5       111011 0.5 0.5  0 NA  0  0      0.026       0.026               FALSE #> 6       111010 0.5 0.5  0 NA  0 NA      0.026       0.026               FALSE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"obtain-adjusted-significance-levels","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Bonferroni tests","what":"Obtain adjusted significance levels","title":"Graphical multiple comparison procedures based on the closure principle","text":"equivalent way obtain rejections via adjusting significance levels. hypothesis rejected p-value less equal adjusted significance level. One can obtain adjusted significance levels every hypothesis every intersection hypothesis closure specifying test_values = TRUE. hypothesis rejected closed testing procedure intersection hypotheses involving rejected. intersection hypothesis rejected null hypotheses within rejected.","code":"test_results_test_values <-   graph_test_closure(     g,     test_types = \"b\",     p = p_values,     alpha = 0.025,     test_values = TRUE   )  head(test_results_test_values$test_values$results) #>   Intersection Hypothesis       Test      p Weight Alpha Inequality_holds #> 1       111111         H1 bonferroni 0.0150    0.5 0.025            FALSE #> 2       111111         H2 bonferroni 0.0130    0.5 0.025            FALSE #> 3       111111         H3 bonferroni 0.0100    0.0 0.025            FALSE #> 4       111111         H4 bonferroni 0.0070    0.0 0.025            FALSE #> 5       111111         H5 bonferroni 0.1000    0.0 0.025            FALSE #> 6       111111         H6 bonferroni 0.0124    0.0 0.025            FALSE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"mixed-procedures-for-graphical-approaches","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle","what":"Mixed procedures for graphical approaches","title":"Graphical multiple comparison procedures based on the closure principle","text":"framework graphicalMCP allows mixture tests improve performance Bonferroni-based graphical approaches. can group hypotheses multiple subgroups perform separate test every subgroup. Currently, graphicalMCP supports Bonferroni, parametric Simes tests. connect results different subgroups hypotheses, Bonferroni tests used. , show two examples. first example applies parametric tests primary hypotheses (Xi et al. 2017), second example applies Simes tests two subgroups secondary hypotheses addition parametric tests primary hypotheses.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"parametric-tests-for-primary-hypotheses","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Mixed procedures for graphical approaches","what":"Parametric tests for primary hypotheses","title":"Graphical multiple comparison procedures based on the closure principle","text":"example, assume test statistics primary hypotheses follow asymptotic bivariate normal distribution. null hypotheses H1H_1 H2H_2, mean distribution 0. correlation test statistics H1H_1 H2H_2 can calculated function sample size. Assume sample size control, low high doses n0n_0, n1n_1 n2n_2, respectively. correlation test statistics H1H_1 H2H_2 ρ12=(n1n1+n0)1/2(n2n2+n0)1/2\\rho_{12}=\\left(\\frac{n_1}{n_1+n_0}\\right)^{1/2}\\left(\\frac{n_2}{n_2+n_0}\\right)^{1/2}. equal randomization, correlation 0.5. intersection hypothesis H1∩H2∩H3∩H4∩H5∩H6H_1\\cap H_2\\cap H_3\\cap H_4\\cap H_5\\cap H_6, hypothesis weights 0.5, 0.5, 0, 0, 0, 0, respectively H1,…,H6H_1,\\ldots, H_6. Assume one-sided p-values hypotheses p1,…,p6p_1,\\ldots,p_6, respectively. intersection hypothesis rejected Bonferroni test p1≤0.5αp_1\\leq 0.5\\alpha p2≤0.5αp_2\\leq 0.5\\alpha. Alternatively, parametric test utilizes correlation test statistics t1=Φ−1(1−p1)t_1=\\Phi^{-1}(1 - p_1) t2=Φ−1(1−p2)t_2=\\Phi^{-1}(1 - p_2). intersection hypothesis can rejected p1≤c×0.5αp_1\\leq c\\times 0.5\\alpha p2≤c×0.5αp_2\\leq c\\times 0.5\\alpha, cc value adjustment due correlation t1t_1 t2t_2. specifically, cc can solved solution Pr{(p1≤c×0.5α)∪(p2≤c×0.5α)}=αPr\\{(p_1\\leq c\\times 0.5\\alpha)\\cup (p_2\\leq c\\times 0.5\\alpha)\\}=\\alpha. given correlation ρ12\\rho_{12}, cc value can solved using uniroot function mvtnorm package. example, ρ12=0.5\\rho_{12}=0.5, cc value 1.078. can obtain adjusted significance level H1H_1 H2H_2 c×0.5αc\\times 0.5\\alpha. Alternatively, can calculate adjusted p-value H1∩H2∩H3∩H4∩H5∩H6H_1\\cap H_2\\cap H_3\\cap H_4\\cap H_5\\cap H_6 Pr{(P1≤min{p1,p2})∪(P2≤min{p1,p2})}Pr\\{(P_1\\leq \\min{\\{p_1, p_2\\}})\\cup (P_2\\leq \\min{\\{p_1, p_2\\}})\\}. implement procedure, need create two subgroups: one H1H_1 H2H_2, one rest hypotheses. first subgroup hypotheses, apply parametric tests; second subgroup (subsets), apply Bonferroni tests. Three additional inputs needed: specify grouping information test_groups, identify types tests every subgroup test_types, provide correlation matrix parametric tests test_corr. Assume correlation 0.5 test statistics primary hypotheses. procedure rejects H1H_1 H2H_2, others. Compared Bonferroni-based graphical approach didn’t rejected hypothesis, illustrates power improvement using parametric tests Bonferroni tests.","code":"corr_12 <- matrix(0.5, nrow = 2, ncol = 2) diag(corr_12) <- 1  test_results_parametric <-   graph_test_closure(     g,     p = p_values,     alpha = 0.025,     test_groups = list(c(1, 2), 3:6),     test_types = c(\"parametric\", \"bonferroni\"),     test_corr = list(corr_12, NA),     test_values = TRUE   )  test_results_parametric$outputs$adjusted_p #>         H1         H2         H3         H4         H5         H6  #> 0.02413846 0.02413846 0.02800000 0.02800000 0.10000000 0.02800000 test_results_parametric$outputs$rejected #>    H1    H2    H3    H4    H5    H6  #>  TRUE  TRUE FALSE FALSE FALSE FALSE  head(test_results_parametric$test_values$results) #>   Intersection Hypothesis       Test      p      c_value Weight Alpha #> 1       111111         H1 parametric 0.0150 1.0782936582    0.5 0.025 #> 2       111111         H2 parametric 0.0130 1.0782936582    0.5 0.025 #> 3       111111         H3 bonferroni 0.0100                 0.0 0.025 #> 4       111111         H4 bonferroni 0.0070                 0.0 0.025 #> 5       111111         H5 bonferroni 0.1000                 0.0 0.025 #> 6       111111         H6 bonferroni 0.0124                 0.0 0.025 #>   Inequality_holds #> 1            FALSE #> 2             TRUE #> 3            FALSE #> 4            FALSE #> 5            FALSE #> 6            FALSE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"parametric-tests-for-primary-hypotheses-and-simes-tests-for-secondary-hypotheses","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Mixed procedures for graphical approaches","what":"Parametric tests for primary hypotheses and Simes tests for secondary hypotheses","title":"Graphical multiple comparison procedures based on the closure principle","text":"addition using parametric tests primary hypotheses, ways improve Bonferroni-based graphical approaches. One way apply Simes tests secondary hypotheses(Bretz et al. 2011; Lu 2016). Simes tests improve Bonferroni tests may reject intersection hypothesis p-values relatively small, even ’re larger adjusted significance levels Bonferroni tests. intersection hypothesis H3∩H5H_3\\cap H_5, hypothesis weights 0.5 0.5, respectively H3H_3 H5H_5. intersection hypothesis rejected Bonferroni test p3≤0.5αp_3\\leq 0.5\\alpha p5≤0.5αp_5\\leq 0.5\\alpha. addition conditions, Simes test can also reject intersection hypothesis p3p_3 p5p_5 less equal α\\alpha. order control Type error Simes test, distributional requirement needed, called MTP2MTP_2(Sarkar 1998). case, means correlation test statistics H3H_3 H5H_5 non-negative. illustrate possibility using mixed tests example, keep parametric tests primary hypotheses apply Simes tests secondary hypotheses. two sets secondary hypotheses: H3H_3 H5H_5 secondary hypotheses low dose versus control, H4H_4 H6H_6 secondary hypotheses high dose versus control. believed correlation test statistics H3H_3 H5H_5 non-negative case H4H_4 H6H_6. Thus one can apply Simes tests H3H_3 H5H_5, separately H4H_4 H6H_6. Note different applying Simes tests H3…,H6H_3\\ldots,H_6 requires stronger MTP2MTP_2 condition. implement procedure, create three subgroups: one H1H_1 H2H_2, one H3H_3 H5H_5, one H4H_4 H6H_6. first subgroup hypotheses, apply parametric tests; second third subgroups, apply separate Simes tests. Assume correlation 0.5 test statistics primary hypotheses. procedure rejects H1H_1, H2H_2, H4H_4, H6H_6, H3H_3. Compared results using parametric tests primary hypotheses (Bonferroni tests secondary hypotheses), H3H_3, H4H_4 H6H_6 additional hypotheses rejected using Simes tests, showing power improvement using Simes tests.","code":"test_results_parametric_simes <-   graph_test_closure(     g,     p = p_values, alpha = 0.025,     test_groups = list(c(1, 2), c(3, 5), c(4, 6)),     test_types = c(\"parametric\", \"simes\", \"simes\"),     test_corr = list(corr_12, NA, NA),     test_values = TRUE   )  test_results_parametric_simes$outputs$adjusted_p #>         H1         H2         H3         H4         H5         H6  #> 0.02413846 0.02413846 0.02480008 0.02480000 0.10000000 0.02480008 test_results_parametric_simes$outputs$rejected #>    H1    H2    H3    H4    H5    H6  #>  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  head(test_results_parametric_simes$test_values$results) #>   Intersection Hypothesis       Test      p      c_value Weight Alpha #> 1       111111         H1 parametric 0.0150 1.0782936582    0.5 0.025 #> 2       111111         H2 parametric 0.0130 1.0782936582    0.5 0.025 #> 3       111111         H3      simes 0.0100                 0.0 0.025 #> 4       111111         H5      simes 0.1000                 0.0 0.025 #> 5       111111         H4      simes 0.0070                 0.0 0.025 #> 6       111111         H6      simes 0.0124                 0.0 0.025 #>   Inequality_holds #> 1            FALSE #> 2             TRUE #> 3            FALSE #> 4            FALSE #> 5            FALSE #> 6            FALSE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"power-calculation","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle","what":"Power calculation","title":"Graphical multiple comparison procedures based on the closure principle","text":"Given graph, trial team often interested power trial. single null hypothesis, power probability reject null hypothesis significance level alpha alternative hypothesis true (.e. true positive). multiple null hypotheses, multiple version power. example, power reject least one hypothesis power reject hypotheses, given alternative hypotheses true. graphical multiple comparison procedures, also important understand power reject hypothesis, given multiplicity adjustment. Sometimes, team may want customize definitions power define success. Thus power calculation important aspect trial design.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"input-marginal-power-for-primary-hypotheses","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"Input: Marginal power for primary hypotheses","title":"Graphical multiple comparison procedures based on the closure principle","text":"Assume primary endpoint occurrence unfavorable clinical event. evaluate treatment effect, proportion patients event calculated lower better. Assume proportions 0.181 low high doses, 0.3 control. Using equal randomization among three treatment groups, clinical trial team chooses total sample size 600 200 per group. leads marginal power 80% H1H_1 H2H_2, respectively, using two-sample test difference proportions unpooled variance one-sided significance level 0.025. calculation, use marginal power combine information treatment effect, nuisance parameter, sample sizes hypothesis. Note significance level used marginal power alpha used power calculation significance level FWER control. addition, marginal power one--one relationship noncentrality parameter, illustrated .","code":"alpha <- 0.025 prop <- c(0.3, 0.181, 0.181) sample_size <- rep(200, 3)  unpooled_variance <-   prop[-1] * (1 - prop[-1]) / sample_size[-1] +   prop[1] * (1 - prop[1]) / sample_size[1]  noncentrality_parameter_primary <-   -(prop[-1] - prop[1]) / sqrt(unpooled_variance)  marginal_power_primary <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_primary,   sd = 1,   lower.tail = FALSE )  names(marginal_power_primary) <- c(\"H1\", \"H2\") marginal_power_primary #>        H1        H2  #> 0.8028315 0.8028315"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"input-marginal-power-for-secondary-hypotheses","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"Input: Marginal power for secondary hypotheses","title":"Graphical multiple comparison procedures based on the closure principle","text":"Assume secondary endpoint (SE1) change total medication score baseline, continuous outcome. Also assume secondary endpoint (SE2) change another medication score baseline, continuous outcome contains fewer categories compared SE1. evaluate treatment effect, mean change calculated reduction better. Assume mean change baseline SE1 reduction 7.5 8.25, respectively low high doses, 5 control. Also assume mean change baseline SE2 reduction 8 9, respectively low high doses, 6 control. assume known common standard deviation 10. Given sample size 200 per treatment group, marginal power 71% 90% H3H_3 H4H_4, respectively 52% 85% H5H_5 H6H_6, respectively using two-sample zz-test difference means one-sided significance level 0.025.","code":"mean_change_se1 <- c(5, 7.5, 8.25) sd <- rep(10, 3) variance <- sd[-1]^2 / sample_size[-1] + sd[1]^2 / sample_size[1]  noncentrality_parameter_se1 <-   (mean_change_se1[-1] - mean_change_se1[1]) /     sqrt(variance)  marginal_power_se1 <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_se1,   sd = 1,   lower.tail = FALSE )  names(marginal_power_se1) <- c(\"H3\", \"H4\") marginal_power_se1 #>        H3        H4  #> 0.7054139 0.9014809  mean_change_se2 <- c(6, 8, 9)  noncentrality_parameter_se2 <-   (mean_change_se2[-1] - mean_change_se2[1]) /     sqrt(variance)  marginal_power_se2 <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_se2,   sd = 1,   lower.tail = FALSE )  names(marginal_power_se2) <- c(\"H5\", \"H6\") marginal_power_se2 #>        H5        H6  #> 0.5159678 0.8508384"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"input-correlation-structure-to-simulate-test-statistics","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"Input: Correlation structure to simulate test statistics","title":"Graphical multiple comparison procedures based on the closure principle","text":"addition marginal power, also need make assumptions joint distribution test statistics. example, assume follow multivariate normal distribution means ’re defined noncentrality parameters correlation matrix RR. obtain correlations, helpful understand two types correlations example. correlation two dose-control comparisons endpoint correlation endpoints. former correlation can calculated function sample size. example, correlation test statistics H1H_1 H2H_2 ρ12=(n1n1+n0)1/2(n2n3+n0)1/2\\rho_{12}=\\left(\\frac{n_1}{n_1+n_0}\\right)^{1/2}\\left(\\frac{n_2}{n_3+n_0}\\right)^{1/2}. equal randomization, correlation 0.5. correlation test statistics H3H_3 H4H_4 H5H_5 H6H_6 . hand, correlation endpoints dose-control comparison often estimated based prior knowledge previous trials. Without information, assume ρ13=ρ15=ρ24=ρ26=ρ35=ρ46=0.5\\rho_{13}=\\rho_{15}=\\rho_{24}=\\rho_{26}=\\rho_{35}=\\rho_{46}=0.5. practice, one set correlation parameter try multiple values assess sensitivity assumption. Regarding correlation test statistics H1H_1 H4(H6)H_4 (H_6) H2H_2 H3(H5)H_3 (H_5), even difficult estimate. use simple product rule, means correlation product correlations two previously assumed correlations. example, ρ14=ρ12*ρ24\\rho_{14}=\\rho_{12}*\\rho_{24} ρ23=ρ12*ρ13\\rho_{23}=\\rho_{12}*\\rho_{13}. practice, assumptions may made tested, instead using product rule.","code":"corr <- matrix(0, nrow = 6, ncol = 6)  corr[1, 2] <-   corr[3, 4] <-   corr[5, 6] <-   sqrt(     sample_size[2] / sum(sample_size[1:2]) *       sample_size[3] / sum(sample_size[c(1, 3)])   )  rho <- 0.5  corr[1, 3] <-   corr[1, 5] <-   corr[2, 4] <-   corr[2, 6] <-   corr[3, 5] <-   corr[4, 6] <-   rho  corr[1, 4] <- corr[1, 6] <- corr[2, 3] <- corr[2, 5] <- corr[1, 2] * rho  corr[3, 6] <- corr[1, 3] * corr[1, 6] corr[4, 5] <- corr[1, 4] * corr[1, 6]  corr <- corr + t(corr) diag(corr) <- 1 colnames(corr) <- hyp_names rownames(corr) <- hyp_names corr #>      H1   H2    H3     H4     H5    H6 #> H1 1.00 0.50 0.500 0.2500 0.5000 0.250 #> H2 0.50 1.00 0.250 0.5000 0.2500 0.500 #> H3 0.50 0.25 1.000 0.5000 0.5000 0.125 #> H4 0.25 0.50 0.500 1.0000 0.0625 0.500 #> H5 0.50 0.25 0.500 0.0625 1.0000 0.500 #> H6 0.25 0.50 0.125 0.5000 0.5000 1.000"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"user-defined-success-criteria","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"User-defined success criteria","title":"Graphical multiple comparison procedures based on the closure principle","text":"mentioned earlier, multiple versions “power” multiple hypotheses. Commonly used “power” definitions include: - Local power: probability hypothesis rejected (multiplicity adjustment) - Expected . rejections: expected number rejections - Power reject 1 : probability reject least one hypothesis - Power reject : probability reject hypotheses default outputs graph_calculate_power function. addition, user customize success criteria define versions “power”.","code":"success_fns <- list(   # Probability to reject H1   H1 = function(x) x[1],    # Expected number of rejections   `Expected no. of rejections` =     function(x) x[1] + x[2] + x[3] + x[4] + x[5] + x[6],    # Probability to reject at least one hypothesis   `AtLeast1` = function(x) x[1] | x[2] | x[3] | x[4] | x[5] | x[6],    # Probability to reject all hypotheses   `All` = function(x) x[1] & x[2] & x[3] & x[4] & x[5] & x[6],    # Probability to reject both H1 and H2   `H1andH2` = function(x) x[1] & x[2],    # Probability to reject all hypotheses for the low dose or the high dose   `(H1andH3andH5)or(H2andH4andH6)` <-     function(x) (x[1] & x[3] & x[5]) | (x[2] & x[4] & x[6]) )"},{"path":"https://openpharma.github.io/graphicalMCP/articles/closed-testing.html","id":"output-calculate-power","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure based on the closure principle > Power calculation","what":"Output: Calculate power","title":"Graphical multiple comparison procedures based on the closure principle","text":"Given inputs, can calculate power via simulation graphical multiple comparison procedure one-sided significance level alpha = 0.025 using sim_n = 1e5 simulations random seed 1234. three procedures compare: Bonferroni-based procedure, procedure using parametric tests primary hypotheses, procedure using parametric tests primary hypotheses Simes tests two sets secondary hypotheses separately. local power hypotheses H1,…,H6H_1, \\ldots, H_6 - 0.760, 0.752, 0.510, 0.665, 0.391, 0.625, respectively using Bonferroni-based procedure, - 0.764, 0.756, 0.511, 0.668, 0.392, 0.628, respectively using procedure using parametric tests primary hypotheses, - 0.764, 0.757, 0.521, 0.673, 0.402, 0.633, respectively using procedure using parametric tests primary hypotheses Simes tests two sets secondary hypotheses separately. Note local power improved hypotheses parametric tests Simes tests applied Bonferroni-based procedure. see detailed outputs simulated p-values rejection decisions hypotheses, can specify verbose = TRUE. produce lot outputs. allow flexible printing functions, user can change following: - indented space default setting indent = 2 - precision numeric values (.e., number decimal places) default setting precision = 6","code":"set.seed(1234) power_bonferroni <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(     marginal_power_primary,     marginal_power_se1,     marginal_power_se2   ),   sim_success = success_fns )  round(power_bonferroni$power$power_local, 3) #>    H1    H2    H3    H4    H5    H6  #> 0.760 0.752 0.510 0.665 0.391 0.625  set.seed(1234) power_parametric <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(     marginal_power_primary,     marginal_power_se1,     marginal_power_se2   ),   test_groups = list(c(1, 2), 3:6),   test_types = c(\"parametric\", \"bonferroni\"),   test_corr = list(corr_12, NA),   sim_success = success_fns )  round(power_parametric$power$power_local, 3) #>    H1    H2    H3    H4    H5    H6  #> 0.764 0.756 0.511 0.668 0.392 0.628  set.seed(1234) power_parametric_simes <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(     marginal_power_primary,     marginal_power_se1,     marginal_power_se2   ),   test_groups = list(c(1, 2), c(3, 5), c(4, 6)),   test_types = c(\"parametric\", \"simes\", \"simes\"),   test_corr = list(corr_12, NA, NA),   sim_success = success_fns )  round(power_parametric_simes$power$power_local, 3) #>    H1    H2    H3    H4    H5    H6  #> 0.764 0.757 0.521 0.673 0.402 0.633 set.seed(1234) power_verbose_output_parametric_simes <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(     marginal_power_primary,     marginal_power_se1,     marginal_power_se2   ),   test_groups = list(c(1, 2), c(3, 5), c(4, 6)),   test_types = c(\"parametric\", \"simes\", \"simes\"),   test_corr = list(corr_12, NA, NA),   sim_success = success_fns,   verbose = TRUE )  head(power_verbose_output_parametric_simes$details$p_sim, 10) #>                 H1           H2           H3           H4           H5 #>  [1,] 0.0236514114 6.962444e-03 3.835101e-03 0.0615622415 0.0034034237 #>  [2,] 0.0367030430 4.681135e-02 6.857853e-02 0.0284812435 0.1496042440 #>  [3,] 0.0157541925 6.543826e-03 1.152738e-03 0.0007655046 0.0836186744 #>  [4,] 0.0053369856 8.699959e-07 9.952719e-03 0.0002429371 0.0369937655 #>  [5,] 0.0342665326 1.788794e-01 6.202961e-03 0.0305855529 0.0461642736 #>  [6,] 0.0011139852 1.783703e-02 6.083855e-02 0.0087065723 0.3865009844 #>  [7,] 0.2540774514 2.101193e-01 2.616673e-02 0.0277425681 0.0092489689 #>  [8,] 0.0908135583 4.433230e-02 1.903718e-01 0.0418782572 0.3996511810 #>  [9,] 0.0739568465 4.728371e-02 3.778643e-01 0.0296172396 0.4446759145 #> [10,] 0.0003353917 1.048743e-03 1.246528e-05 0.0032298980 0.0001601294 #>                 H6 #>  [1,] 0.0018417304 #>  [2,] 0.0552141940 #>  [3,] 0.0255279965 #>  [4,] 0.0001345536 #>  [5,] 0.0666051161 #>  [6,] 0.0867387423 #>  [7,] 0.0297658510 #>  [8,] 0.1097032475 #>  [9,] 0.0620564532 #> [10,] 0.0114581872  print(power_verbose_output_parametric_simes,   indent = 4,   precision = 6 ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>     Initial graph #>  #>     --- Hypothesis weights --- #>     H1: 0.5 #>     H2: 0.5 #>     H3: 0.0 #>     H4: 0.0 #>     H5: 0.0 #>     H6: 0.0 #>  #>     --- Transition weights --- #>             H1      H2      H3      H4      H5      H6 #>     H1 0.00000 0.50000 0.25000 0.00000 0.25000 0.00000 #>     H2 0.50000 0.00000 0.00000 0.25000 0.00000 0.25000 #>     H3 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 #>     H4 0.00001 0.00000 0.00000 0.00000 0.00000 0.99999 #>     H5 0.00000 0.00001 0.99999 0.00000 0.00000 0.00000 #>     H6 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 #>  #>     Alpha = 0.025 #>  #>     Parametric testing correlation:     H1  H2 #>                                     H1 1.0 0.5 #>                                     H2 0.5 1.0 #>  #>     Test types #>     parametric: (H1, H2) #>          simes: (H3, H5) #>          simes: (H4, H6) #>  #> Simulation parameters ($inputs) ------------------------------------------------ #>     Testing 100,000 simulations with multivariate normal params: #>  #>                           H1       H2       H3       H4       H5       H6 #>     Marginal power: 0.802831 0.802831 0.705414 0.901481 0.515968 0.850838 #>  #>     Correlation:        H1     H2     H3     H4     H5     H6 #>                  H1 1.0000 0.5000 0.5000 0.2500 0.5000 0.2500 #>                  H2 0.5000 1.0000 0.2500 0.5000 0.2500 0.5000 #>                  H3 0.5000 0.2500 1.0000 0.5000 0.5000 0.1250 #>                  H4 0.2500 0.5000 0.5000 1.0000 0.0625 0.5000 #>                  H5 0.5000 0.2500 0.5000 0.0625 1.0000 0.5000 #>                  H6 0.2500 0.5000 0.1250 0.5000 0.5000 1.0000 #>  #> Power calculation ($power) ----------------------------------------------------- #>                                      H1      H2      H3      H4      H5      H6 #>                    Local power: 0.76437 0.75656 0.52086 0.67302 0.40234 0.63292 #>  #>     Expected no. of rejections: 3.75007 #>      Power to reject 1 or more: 0.86277 #>            Power to reject all: 0.32537 #>  #>                Success measure   Power #>                             H1 0.76437 #>     Expected no. of rejections 3.75007 #>                       AtLeast1 0.86277 #>                            All 0.32537 #>                        H1andH2 0.65816 #>                                0.63324 #>  #> Simulation details ($details) -------------------------------------------------- #>         p_sim_H1    p_sim_H2    p_sim_H3    p_sim_H4    p_sim_H5    p_sim_H6 rej_H1 #>      2.36514e-02 6.96244e-03 3.83510e-03 6.15622e-02 3.40342e-03 1.84173e-03  FALSE #>      3.67030e-02 4.68113e-02 6.85785e-02 2.84812e-02 1.49604e-01 5.52142e-02  FALSE #>      1.57542e-02 6.54383e-03 1.15274e-03 7.65505e-04 8.36187e-02 2.55280e-02   TRUE #>      5.33699e-03 8.69996e-07 9.95272e-03 2.42937e-04 3.69938e-02 1.34554e-04   TRUE #>      3.42665e-02 1.78879e-01 6.20296e-03 3.05856e-02 4.61643e-02 6.66051e-02  FALSE #>      1.11399e-03 1.78370e-02 6.08385e-02 8.70657e-03 3.86501e-01 8.67387e-02   TRUE #>      2.54077e-01 2.10119e-01 2.61667e-02 2.77426e-02 9.24897e-03 2.97659e-02  FALSE #>      9.08136e-02 4.43323e-02 1.90372e-01 4.18783e-02 3.99651e-01 1.09703e-01  FALSE #>      7.39568e-02 4.72837e-02 3.77864e-01 2.96172e-02 4.44676e-01 6.20565e-02  FALSE #>      3.35392e-04 1.04874e-03 1.24653e-05 3.22990e-03 1.60129e-04 1.14582e-02   TRUE #>      rej_H2 rej_H3 rej_H4 rej_H5 rej_H6 #>        TRUE  FALSE  FALSE  FALSE   TRUE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>        TRUE   TRUE   TRUE  FALSE  FALSE #>        TRUE   TRUE   TRUE  FALSE   TRUE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>        TRUE  FALSE  FALSE  FALSE  FALSE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>       FALSE  FALSE  FALSE  FALSE  FALSE #>        TRUE   TRUE   TRUE   TRUE   TRUE #>     ... (Use `print(x, rows = <nn>)` for more)"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Comparisons with other packages","text":"two R packages cover graphical multiple comparison procedures (MCPs): gMCP (Rohmeyer Klinglmueller 2024) lrstat (Lu 2023). development graphicalMCP benefited two packages. provide comparisons graphicalMCP packages respect key functions.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"list-of-comparisons","dir":"Articles","previous_headings":"","what":"List of comparisons","title":"Comparisons with other packages","text":"graphicalMCP::graph_generate_weights() gMCP::generateWeights() graphicalMCP::graph_test_shortcut() gMCP::gMCP() graphicalMCP::graph_calculate_power() gMCP::calcPower() graphicalMCP::graph_test_closure() gMCP::gMCP() graphicalMCP::graph_calculate_power() gMCP::calcPower() graphicalMCP::graph_test_closure() gMCP::gMCP() graphicalMCP::graph_calculate_power() gMCP::calcPower()","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"comparisons-of-weighting-strategies","dir":"Articles","previous_headings":"","what":"Comparisons of weighting strategies","title":"Comparisons with other packages","text":"random graph five hypotheses generated used comparison. Weighting strategies following two functions compared: graphicalMCP::graph_generate_weights() gMCP::generateWeights(). process repeated 1000 times. Weighting strategies matched 1000 cases.","code":"set.seed(1234) identical <- NULL for (i in 1:1000) {   graph <- random_graph(5)   graphicalmcp_weights <- graphicalMCP::graph_generate_weights(graph)   dimnames(graphicalmcp_weights) <- list(NULL, NULL)   gmcp_weights <-     gMCP::generateWeights(graph$transitions, graph$hypotheses)   gmcp_weights <- gmcp_weights[nrow(gmcp_weights):1, ] # Reorder rows   identical <- c(     identical,     all.equal(gmcp_weights, graphicalmcp_weights, tolerance = 1e-7)   ) } all(identical) #> [1] TRUE"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"adjusted-p-values-for-testing","dir":"Articles","previous_headings":"Comparisons of sequentially rejective procedures based on Bonferroni tests","what":"Adjusted p-values for testing","title":"Comparisons with other packages","text":"random graph five hypotheses generated used comparison. set p-values randomly generated used graphical MCP. Adjusted p-values calculated compared using following functions: graphicalMCP::graph_test_shortcut() gMCP::gMCP(). process repeated 10000 times. Adjusted p-values matched 10000 cases.","code":"set.seed(1234) alpha <- 0.025 identical <- NULL for (i in 1:10000) {   graph <- random_graph(5)   p <- runif(5, 0, alpha)   graphicalmcp_test_shortcut <-     graph_test_shortcut(graph, p, alpha = alpha)$outputs$adjusted_p   gmcp_test_shortcut <-     gMCP(as_graphMCP(graph), p, alpha = alpha)@adjPValues   identical <- c(     identical,     all.equal(graphicalmcp_test_shortcut, gmcp_test_shortcut, tolerance = 1e-7)   ) } all(identical) #> [1] TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"power-simulations","dir":"Articles","previous_headings":"Comparisons of sequentially rejective procedures based on Bonferroni tests","what":"Power simulations","title":"Comparisons with other packages","text":"random graph five hypotheses generated used comparison. set marginal power (without multiplicity adjustment) randomly generated. Local power (multiplicity adjustment) calculated compared using following functions: graphicalMCP::graph_calculate_power() gMCP::calcPower(). Since different simulation methods used, results slightly different. maximum absolute difference local power 0.0051 (0.51%) among 1000 cases, relatively small.","code":"set.seed(1234) alpha <- 0.025 sim_corr <- matrix(.5, 5, 5) diag(sim_corr) <- 1 graphicalmcp_power <- NULL gmcp_power <- NULL for (i in 1:1000) {   graph <- random_graph(5)   marginal_power <- runif(5, 0.5, 0.9)   noncentrality_parameter <-     qnorm(1 - 0.025, lower.tail = TRUE) -     qnorm(1 - marginal_power, lower.tail = TRUE)    set.seed(1234 + i - 1)   graphicalmcp_power <- rbind(     graphicalmcp_power,     graph_calculate_power(       graph,       alpha = alpha,       power_marginal = marginal_power,       sim_corr = sim_corr,       sim_n = 2^17     )$power$power_local   )    set.seed(1234 + i - 1)   gmcp_power <- rbind(     gmcp_power,     calcPower(       graph$hypotheses,       alpha = alpha,       graph$transitions,       mean = noncentrality_parameter,       corr.sim = sim_corr,       n.sim = 2^17     )$LocalPower   ) }  diff <- data.frame(   rbind(graphicalmcp_power, gmcp_power),   procedure = rep(c(\"graphicalMCP\", \"gMCP\"), each = nrow(graphicalmcp_power)) )  write.csv(   diff,   here::here(\"vignettes/cache/comparisons_power_shortcut.csv\"),   row.names = FALSE )  diff <- read.csv(here::here(\"vignettes/cache/comparisons_power_shortcut.csv\")) graphicalmcp_power <- subset(diff, procedure == \"graphicalMCP\") gmcp_power <- subset(diff, procedure == \"gMCP\") round(   max(     abs(       graphicalmcp_power[, -ncol(graphicalmcp_power)] -         gmcp_power[, -ncol(gmcp_power)]     )   ),   4 ) # Maximum difference in local power among 1000 cases"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"adjusted-p-values-for-testing-1","dir":"Articles","previous_headings":"Comparisons of closed test procedures with parametric tests","what":"Adjusted p-values for testing","title":"Comparisons with other packages","text":"successive graph two primary two secondary hypotheses generated used comparison. set p-values randomly generated used graphical MCP. Adjusted p-values calculated compared using following functions: graphicalMCP::graph_test_closure() gMCP::gMCP(). Parametric tests used two primary hypotheses. process repeated 10000 times. Adjusted p-values matched 10000 cases.","code":"hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0.5, 0.5, 0),   c(0.5, 0, 0, 0.5),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) graph <- graph_create(hypotheses, transitions)  set.seed(1234) alpha <- 0.025 identical <- NULL test_corr <- rbind(   c(1, 0.5, NA, NA),   c(0.5, 1, NA, NA),   c(NA, NA, 1, NA),   c(NA, NA, NA, 1) ) for (i in 1:10000) {   p <- runif(4, 0, alpha)   graphicalmcp_test_parametric <- graph_test_closure(     graph,     p,     alpha = alpha,     test_groups = list(1:2, 3:4),     test_types = c(\"parametric\", \"bonferroni\"),     test_corr = list(test_corr[1:2, 1:2], NA)   )$outputs$adjusted_p   gmcp_test_parametric <- gMCP(     as_graphMCP(graph),     p,     alpha = 0.025,     correlation = test_corr   )@adjPValues   identical <- c(     identical,     all.equal(graphicalmcp_test_parametric, gmcp_test_parametric, tolerance = 1e-7)   ) } all(identical) #> [1] TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"power-simulations-1","dir":"Articles","previous_headings":"Comparisons of closed test procedures with parametric tests","what":"Power simulations","title":"Comparisons with other packages","text":"successive graph two primary two secondary hypotheses generated used comparison. set marginal power (without multiplicity adjustment) randomly generated. Local power (multiplicity adjustment) calculated compared using following functions: graphicalMCP::graph_calculate_power() gMCP::calcPower(). Parametric tests used two primary hypotheses. process repeated 100 times. Since different simulation methods used, results slightly different. maximum absolute difference local power 0.0142 (1.42%) among 100 cases, small.","code":"hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0.5, 0.5, 0),   c(0.5, 0, 0, 0.5),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) graph <- graph_create(hypotheses, transitions) test_corr <- rbind(   c(1, 0.5, NA, NA),   c(0.5, 1, NA, NA),   c(NA, NA, 1, NA),   c(NA, NA, NA, 1) ) sim_corr <- matrix(0.5, 4, 4) diag(sim_corr) <- 1 set.seed(1234) alpha <- 0.025 graphicalmcp_power_parametric <- NULL gmcp_power_parametric <- NULL for (i in 1:100) {   marginal_power <- runif(4, 0.5, 0.9)   noncentrality_parameter <-     qnorm(1 - 0.025, lower.tail = TRUE) -     qnorm(1 - marginal_power, lower.tail = TRUE)    set.seed(1234 + i - 1)   graphicalmcp_power_parametric <- rbind(     graphicalmcp_power_parametric,     graph_calculate_power(       graph,       alpha = alpha,       test_groups = list(1:2, 3:4),       test_types = c(\"parametric\", \"bonferroni\"),       test_corr = list(test_corr[1:2, 1:2], NA),       power_marginal = marginal_power,       sim_corr = sim_corr,       sim_n = 2^14     )$power$power_local   )    set.seed(1234 + i - 1)   gmcp_power_parametric <- rbind(     gmcp_power_parametric,     calcPower(       graph$hypotheses,       alpha = alpha,       graph$transitions,       corr.test = test_corr,       mean = noncentrality_parameter,       corr.sim = sim_corr,       n.sim = 2^14     )$LocalPower   ) }  diff <- data.frame(   rbind(graphicalmcp_power_parametric, gmcp_power_parametric),   procedure = rep(c(\"graphicalMCP\", \"gMCP\"), each = nrow(gmcp_power_parametric)) )  write.csv(   diff,   here::here(\"vignettes/cache/comparisons_power_parametric.csv\"),   row.names = FALSE )  diff <- read.csv(here::here(\"vignettes/cache/comparisons_power_parametric.csv\")) graphicalmcp_power <- subset(diff, procedure == \"graphicalMCP\") gmcp_power <- subset(diff, procedure == \"gMCP\") round(   max(     abs(       graphicalmcp_power_parametric[, -ncol(graphicalmcp_power_parametric)] -         gmcp_power_parametric[, -ncol(gmcp_power)]     )   ),   4 ) # Maximum difference in local power among 100 cases"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"adjusted-p-values-for-testing-2","dir":"Articles","previous_headings":"Comparisons of closed test procedures with Simes tests","what":"Adjusted p-values for testing","title":"Comparisons with other packages","text":"successive graph two primary two secondary hypotheses generated used comparison. set p-values randomly generated used graphical MCP. Adjusted p-values calculated compared using following functions: graphicalMCP::graph_test_closure() lrstat::fadjpsim(). Simes tests used two primary hypotheses. process repeated 10000 times. Adjusted p-values matched 10000 cases.","code":"hypotheses <- c(0.5, 0.5, 0, 0) eps <- 0.0001 transitions <- rbind(   c(0, 1 - eps, eps, 0),   c(1 - eps, 0, 0, eps),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) graph <- graph_create(hypotheses, transitions)  set.seed(1234) alpha <- 0.025 identical <- NULL family <- rbind(   c(1, 1, 0, 0),   c(0, 0, 1, 0),   c(0, 0, 0, 1) ) for (i in 1:10000) {   p <- runif(4, 0, alpha)   graphicalmcp_test_simes <- graph_test_closure(     graph,     p,     alpha = alpha,     test_groups = list(1:2, 3:4),     test_types = c(\"simes\", \"bonferroni\")   )$outputs$adjusted_p   names(graphicalmcp_test_simes) <- NULL   lrstat_test_simes <-     fadjpsim(       fwgtmat(graph$hypotheses, graph$transitions),       p,       family     )    identical <- c(     identical,     all.equal(graphicalmcp_test_simes, lrstat_test_simes, tolerance = 1e-7)   ) } all(identical) #> [1] TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/comparisons.html","id":"power-simulations-2","dir":"Articles","previous_headings":"Comparisons of closed test procedures with Simes tests","what":"Power simulations","title":"Comparisons with other packages","text":"Power simulations available lrstat. Thus comparison done compare graphicalMCP::graph_calculate_power() manual repetition lrstat::fadjpsim() many sets marginal power. process comparison adjusted p-values, thus omitted.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"motivating-example","dir":"Articles","previous_headings":"","what":"Motivating example","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"Consider simple successive graph four hypotheses. two primary hypotheses H1H_1 H2H_2 two secondary hypotheses H3H_3 H4H_4. Initially, hypothesis weights split equally H1H_1 H2H_2 0.5. Hypotheses H3H_3 H4H_4 receive 0 hypothesis weights H3(H4)H_3 (H_4) tested H1(H2)H_1 (H_2) rejected. Thus edge H1(H2)H_1 (H_2) H3(H4)H_3 (H_4) transition weight 1. H1H_1 H3H_3 rejected, hypothesis weights propagated H2H_2; similarly, H2H_2 H4H_4 rejected, hypothesis weights propagated H1H_1. Thus edge H3(H4)H_3 (H_4) H2(H1)H_2 (H_1) transition weight 1. graphical multiple comparison procedure illustrated .","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"generating-the-closure","dir":"Articles","previous_headings":"","what":"Generating the closure","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"closure multiple comparison procedure collection intersection hypotheses H1∩H2∩H3∩H4H_1\\cap H_2\\cap H_3\\cap H_4, H1∩H2∩H3H_1\\cap H_2\\cap H_3, H1∩H2∩H4H_1\\cap H_2\\cap H_4, H1∩H3∩H4H_1\\cap H_3\\cap H_4, H2∩H3∩H4…,H1,H2,H3H_2\\cap H_3\\cap H_4\\ \\ldots, H_1, H_2, H_3, H4H_4. words, intersection hypotheses consist intersections based non-empty subsets {1,2,3,4}\\{1, 2, 3, 4\\}, e.g., {1,2,3}\\{1, 2, 3\\}, {1,2,4}\\{1, 2, 4\\}, {1,3,4}\\{1, 3, 4\\}, {2,3,4}\\{2, 3, 4\\}, …\\ldots. Thus 24−12^4-1 intersection hypotheses. equivalent way generate intersection hypotheses use binary representation. example, intersection hypothesis H1∩H2∩H3∩H4H_1\\cap H_2\\cap H_3\\cap H_4 corresponds (1,1,1,1)(1, 1, 1, 1) H1∩H2∩H3H_1\\cap H_2\\cap H_3 corresponds (1,1,1,0)(1, 1, 1, 0). closure can indexed power set {1,2,3,4}\\{1, 2, 3, 4\\} . general, one can use rev(expand.grid(rep(list(1:0), m))) general closure, mm number hypotheses.","code":"#>    H1 H2 H3 H4 #> 1   1  1  1  1 #> 2   1  1  1  0 #> 3   1  1  0  1 #> 4   1  1  0  0 #> 5   1  0  1  1 #> 6   1  0  1  0 #> 7   1  0  0  1 #> 8   1  0  0  0 #> 9   0  1  1  1 #> 10  0  1  1  0 #> 11  0  1  0  1 #> 12  0  1  0  0 #> 13  0  0  1  1 #> 14  0  0  1  0 #> 15  0  0  0  1"},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"calculating-the-weighting-strategy","dir":"Articles","previous_headings":"Generating the closure","what":"Calculating the weighting strategy","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"Given closure, one can calculate hypothesis weight associated every hypothesis every intersection hypothesis using Algorithm 1 (Bretz et al. 2011). whole collection hypothesis weights called weighting strategy. example, hypothesis weights (0.5,0.5,0,0)(0.5, 0.5, 0, 0) intersection hypothesis H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4. hypothesis weights intersection hypothesis H1∩H2∩H3H_1\\cap H_2 \\cap H_3 (0.5,0.5,0,0)(0.5, 0.5, 0, 0), can calculated removing H4H_4 initial graph applying Algorithm 1 (Bretz et al. 2011). algorithm calculates hypothesis weights step--step fashion. example, intersection hypothesis H1∩H2H_1\\cap H_2, can start H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 calculates hypothesis weights H1∩H2∩H3H_1\\cap H_2 \\cap H_3 removing H4H_4 calculates hypothesis weights H1∩H2H_1\\cap H_2 removing H3H_3; can also start H1∩H2∩H3H_1\\cap H_2 \\cap H_3 (assuming hypotheses weights stored) calculates hypothesis weights H1∩H2H_1\\cap H_2 removing H3H_3. Therefore, two strategies calculate weighting strategy.","code":"#>      H1   H2   H3   H4 #> 1  0.50 0.50 0.00 0.00 #> 2  0.50 0.50 0.00 0.00 #> 3  0.50 0.50 0.00 0.00 #> 4  0.50 0.50 0.00 0.00 #> 5  0.75 0.00 0.00 0.25 #> 6  1.00 0.00 0.00 0.00 #> 7  0.75 0.00 0.00 0.25 #> 8  1.00 0.00 0.00 0.00 #> 9  0.00 0.75 0.25 0.00 #> 10 0.00 0.75 0.25 0.00 #> 11 0.00 1.00 0.00 0.00 #> 12 0.00 1.00 0.00 0.00 #> 13 0.00 0.00 0.50 0.50 #> 14 0.00 0.00 1.00 0.00 #> 15 0.00 0.00 0.00 1.00"},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"approach-1-simple-approach","dir":"Articles","previous_headings":"Generating the closure > Calculating the weighting strategy","what":"Approach 1: Simple approach","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"first strategy utilizes initial graph starting point calculates hypothesis weights intersection hypotheses. example, calculate hypothesis weights H1∩H2H_1\\cap H_2, start intersection hypothesis H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 sequentially remove H4H_4 H3H_3 (order). approach simple implement since hypothesis weights H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 determined initial graph always available. approach similar one implemented gMCP R package. drawback use information reduce number calculations. example, possible hypothesis weights H1∩H2∩H3H_1\\cap H_2 \\cap H_3 calculated calculating H1∩H2H_1\\cap H_2. Using information H1∩H2∩H3H_1\\cap H_2 \\cap H_3 need one-step calculation, compared two-step calculation using H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"approach-2-parent-child-approach","dir":"Articles","previous_headings":"Generating the closure > Calculating the weighting strategy","what":"Approach 2: Parent-child approach","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"approach tries avoid drawback Approach 1 saving intermediate graphs. performs one-step calculation save time. general, intersection hypothesis parent intersection hypothesis, involves hypotheses involved first intersection one extra hypothesis. example, second row matrix_intersections H1∩H2∩H3H_1\\cap H_2 \\cap H_3 parent intersection H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 first row; third row matrix_intersections H1∩H2∩H4H_1\\cap H_2 \\cap H_4 parent intersection H1∩H2∩H3∩H4H_1\\cap H_2 \\cap H_3\\cap H_4 first row. Thus can identify parent intersection hypothesis row matrix_intersections (except row 1) row number 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7. Given sequence parent hypotheses, simple obtain hypothesis weights intersection hypothesis based parent intersection hypothesis via one-step calculation. interest understand pattern obtain efficiently. First, bottom half (rows 9 - 15) top half (rows 1 - 7), row’s parent bottom half corresponding row top half, eight rows , difference flipping H1H_1 1 top half 0 bottom half. example, row 15’s parent row 15 - 8 = 7. Using observation, can determine parent hypotheses rows 9 15 1, 2, 3, 4, 5, 6, 7. similar pattern can observed rows 5 8. parent hypotheses rows 1, 2, 3, 4, respectively, flipping H2H_2 1 0. rows 3 - 4, parent hypotheses rows 1, 2, respectively, flipping H3H_3 1 0. Lastly row 2, parent hypothesis row 1. row number parent hypothesis can efficiently generated running .call(c, lapply(2^(seq_len(m) - 1), seq_len))[-2^m, ], mm number hypotheses.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"comparing-different-approaches-to-calculating-weighting-strategies","dir":"Articles","previous_headings":"Generating the closure","what":"Comparing different approaches to calculating weighting strategies","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"benchmark existing approaches calculating weighting strategies, compare following approaches: gMCP::generateWeights() (Rohmeyer Klinglmueller 2024), lrstat::fwgtmat() (Lu 2016), Approach 1 (graphicalMCP simple) Approach 2 (graphicalMCP parent-child). Random graphs generated numbers hypotheses 4, 8, 12, 16. Computing time (median log-10 milliseconds) plotted . can see gMCP::generateWeights() slowest lrstat::fwgtmat() fastest. Approach 2 (graphicalMCP parent-child) faster Approach 1 (graphicalMCP simple). Note lrstat::fwgtmat() implements calculation using C++, known faster R. less stable approaches, e.g., giving errors often others. Given computing time R-based approaches acceptable, adding Rcpp dependency considered graphicalMCP. considerations, implement Approach 2 graphicalMCP::graph_generate_weights().","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"conventional-approach-for-power-simulations","dir":"Articles","previous_headings":"Improving power simulations using parent-child relationships","what":"Conventional approach for power simulations","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"conventional approach power simulations repeat following process many times, e.g., 100,000 times. Simulate set p-values Determine hypothesis can rejected Remove rejected hypothesis update graph Repeat hypotheses can rejected Note step update graph may repeat many replications, may repetitive. mm hypotheses, 2m−12^m-1 graphs depending hypotheses rejected. graphs correspond closure weighting strategy. Thus idea avoid redundant updating graphs utilize weighting strategy.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"power-simulations-using-parent-child-relationships","dir":"Articles","previous_headings":"Improving power simulations using parent-child relationships","what":"Power simulations using parent-child relationships","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"key allow approach efficiently identify row weighting strategy, given hypotheses rejected. Remembering pattern found Approach 2, bottom half (rows 9 - 15) matrix_intersections top half (rows 1 - 7), except flipping H1H_1 1 0. means H1H_1 rejected (1 H1H_1 matrix_intersections), row number index top half. example, assume H2H_2 H4H_4 rejected index matrix_intersections (1,0,1,0)(1, 0, 1, 0). Since H1H_1 1, corresponding row top half (rows 1- 7). H2H_2 0 thus corresponding row bottom half within top half (rows 5 - 7). Since H3H_3 1 thus corresponding row top half (rows 5 - 6). H4H_4 0 thus corresponding row 6. useful way calculate row number index XXXX 2^m - sum(XXXX * 2^(m:1 - 1)). example XXXX=1010, row number (1 - 1) * 8 + (1 - 0) * 4 + (1 - 1) * 2 + (1 - 0) * 1 + 1 = 16 - 10 = 6. way efficiently identifying rows weighting_strategy, power simulations implemented follows: Obtain weighting strategy (simulations) Simulate set p-values Determine hypothesis can rejected Remove rejected hypothesis identify row weighting strategy Repeat hypotheses can rejected small modification Step 3b makes approach much faster conventional approach power simulations.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/generate-closure.html","id":"comparing-different-approaches-to-power-simulations","dir":"Articles","previous_headings":"Improving power simulations using parent-child relationships","what":"Comparing different approaches to power simulations","title":"Rationales to generate the closure and the weighting strategy of a graph","text":"benchmark existing approaches calculating weighting strategies, compare following approaches: gMCP::calcPower(), Approach 1 (graphicalMCP conventional), Approach 2 (graphicalMCP parent-child). Holm fixed sequence procedures considered numbers hypotheses 4, 8, 12, 16. Computing time (median log-10 seconds) plotted . can see gMCP::calcPower() fastest Approach 1 (graphicalMCP conventional) lowest. Note gMCP::calcPower() implements simulation using C, known faster R easy extend situations. Given computing time Approach 2 (graphicalMCP parent-child) acceptable, implement graphicalMCP::graph_calculate_power().","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"confirmatory clinical trials, regulatory guidelines mandate strong control family-wise error rate prespecified level α\\alpha. Many multiple comparison procedures (MCPs) proposed purpose. graphical approaches general framework include many common MCPs special cases. vignette, illustrate use graphicalMCP perform common MCPs. test mm hypotheses using graphical MCP, hypothesis HiH_i receives weight 0≤wi≤10\\leq w_i\\leq 1 (called hypothesis weight), ∑=1mwi≤1\\sum_{=1}^{m}w_i\\leq 1. HiH_i HjH_j, directed weighted edge 0≤gij≤10\\leq g_{ij}\\leq 1, means HiH_i rejected, hypothesis weight propagated (transferred) HjH_j gijg_{ij} determines much propagation. also require ∑j=1mgij≤1\\sum_{j=1}^{m}g_{ij}\\leq 1 gii=0g_{ii}=0.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"weighted-bonferroni-test","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Weighted Bonferroni test","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"weighted Bonferroni test splits α\\alpha among hypotheses testing every hypothesis significance level wiαw_i\\alpha. Thus rejects hypothesis p-value less equal significance level. wi=wjw_i=w_j ,ji,j, means equal split test Bonferroni test. propagation pair hypothesis.","code":"set.seed(1234) alpha <- 0.025 m <- 3 bonferroni_graph <- bonferroni(rep(1 / m, m)) # transitions <- matrix(0, m, m) # bonferroni_graph <- graph_create(rep(1 / m, m), transitions)  plot(   bonferroni_graph,   layout = igraph::layout_in_circle(     as_igraph(bonferroni_graph),     order = c(2, 1, 3)   ),   vertex.size = 70 ) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     bonferroni_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3  #>  TRUE FALSE FALSE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"holm-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Holm Procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Holm (Bonferroni-Holm) procedures improve Bonferroni tests allowing propagation (Holm 1979). words, transition weights hypotheses may zero. uniformly powerful Bonferroni tests.","code":"set.seed(1234) alpha <- 0.025 m <- 3 holm_graph <- bonferroni_holm(rep(1 / m, m)) # transitions <- matrix(1 / (m - 1), m, m) # diag(transitions) <- 0 # holm_graph <- graph_create(rep(1 / m, m), transitions)  plot(holm_graph,   layout = igraph::layout_in_circle(     as_igraph(holm_graph),     order = c(2, 1, 3)   ),   vertex.size = 70 ) p_values <- runif(m, 0, alpha)  test_results <- graph_test_shortcut(holm_graph, p = p_values, alpha = alpha)  test_results$outputs$rejected #>    H1    H2    H3  #>  TRUE FALSE FALSE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"fixed-sequence-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Fixed sequence procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Fixed sequence (hierarchical) procedures pre-specify order testing [Maurer, Hothorn, Lehmacher (1995);westfall-2001-optimally]. example, procedure test H1H_1 first. rejected, test H2H_2; otherwise testing stops. H2H_2 rejected, test H3H_3; otherwise testing stops. hypothesis, tested full α\\alpha level, can tested.","code":"set.seed(1234) alpha <- 0.025 m <- 3 fixed_sequence_graph <- fixed_sequence(m) # transitions <- rbind( #   c(0, 1, 0), #   c(0, 0, 1), #   c(0, 0, 0) # ) # fixed_sequence_graph <- graph_create(c(1, 0, 0), transitions)  plot(fixed_sequence_graph, nrow = 1, asp = 0.05, vertex.size = 40) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     fixed_sequence_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"fallback-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Fallback procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Fallback procedures one-way propagation (like fixed sequence procedures) allow hypotheses tested different significance levels (Wiens 2003).  can improved allow propagation later hypotheses earlier hypotheses, possible later hypothesis rejected earlier hypothesis can rejected. two versions improvement: fallback_improved_1 due (Wiens Dmitrienko 2005) fallback_improved_2 due (Bretz et al. 2009) respectively.","code":"set.seed(1234) alpha <- 0.025 m <- 3 fallback_graph <- fallback(rep(1 / 3, 3)) # transitions <- rbind( #   c(0, 1, 0), #   c(0, 0, 1), #   c(0, 0, 0) # ) # fallback_graph <- graph_create(rep(1 / 3, 3), transitions)  plot(fallback_graph, nrow = 1, asp = 0.05, vertex.size = 40) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     fallback_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE set.seed(1234) alpha <- 0.025 m <- 3 fallback_improved_1_graph <- fallback_improved_1(rep(1 / 3, 3)) # hypotheses <- rep(1 / 3, 3) # transitions <- rbind( #   c(0, 1, 0), #   c(0, 0, 1), #   c(hypotheses[seq_len(m - 1)] / sum(hypotheses[seq_len(m - 1)]), 0) # ) # fallback_improved_1_graph <- graph_create(rep(1 / 3, 3), transitions)  plot(   fallback_improved_1_graph,   nrow = 1,   asp = 0.05,   vertex.size = 40,   edge_curves = c(\"pairs\" = 7, \"H3|H1\" = -10) ) epsilon <- 0.0001 fallback_improved_2_graph <- fallback_improved_2(rep(1 / 3, 3), epsilon) # hypotheses <- rep(1 / 3, 3) # transitions <- rbind( #   c(0, 1, 0), #   c(1 - epsilon, 0, epsilon), #   c(1, 0, 0) # ) # fallback_improved_2_graph <- graph_create(rep(1 / 3, 3), transitions)  plot(   fallback_improved_2_graph,   nrow = 1,   asp = 0.05,   eps = 0.0001,   edge_curves = c(\"pairs\" = 7, \"H3|H1\" = -10),   vertex.size = 40 ) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     fallback_improved_2_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"serial-gatekeeping-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Serial gatekeeping procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Serial gatekeeping procedures involve ordered multiple families hypotheses, hypotheses family hypotheses must rejected proceeding test sequence. example considers primary family consisting two hypotheses H1H_1 H2H_2 secondary family consisting single hypothesis H3H_3. primary family, Holm procedure applied. H1H_1 H2H_2 rejected, H3H_3 can tested level α\\alpha; otherwise H3H_3 rejected. allow conditional propagation H3H_3, ε\\varepsilon edge used H2H_2 H3H_3. small transition weight H2H_2 propagates hypothesis weight H1H_1 (already rejected) retains small (non-zero) weight H3H_3 H1H_1 rejected, hypothesis weight H2H_2 propagated H3H_3. ε\\varepsilon assigned 0.0001 practice, value adjusted much smaller smallest p-value observed.","code":"set.seed(1234) alpha <- 0.025 m <- 3 epsilon <- 0.0001  transitions <- rbind(   c(0, 1, 0),   c(1 - epsilon, 0, epsilon),   c(0, 0, 0) )  serial_gatekeeping_graph <- graph_create(c(0.5, 0.5, 0), transitions)  plot(   serial_gatekeeping_graph,   nrow = 1,   asp = 0.05,   eps = 0.0001,   edge_curves = c(\"pairs\" = 7, \"H3|H1\" = -10),   vertex.size = 40 ) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     serial_gatekeeping_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"parallel-gatekeeping-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Parallel gatekeeping procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Parallel gatekeeping procedures also involve multiple ordered families hypotheses, null hypotheses family hypotheses must rejected proceeding test sequence (Dmitrienko, Offen, Westfall 2003). example considers primary family consisting two hypotheses H1H_1 H2H_2 secondary family consisting two hypotheses H3H_3 H4H_4. primary family, Bonferroni test applied. H1H_1 H2H_2 rejected, H3H_3 H4H_4 can tested level α/2\\alpha/2 using Holm procedure; H1H_1 H2H_2 rejected, H3H_3 H4H_4 can tested level α\\alpha using Holm procedure; otherwise H3H_3 H4H_4 rejected.  parallel gatekeeping procedure can improved adding ε\\varepsilon edges secondary hypotheses primary hypotheses, possible secondary hypotheses rejected still remaining primary hypothesis rejected (Bretz et al. 2009).","code":"set.seed(1234) alpha <- 0.025 m <- 4  transitions <- rbind(   c(0, 0, 0.5, 0.5),   c(0, 0, 0.5, 0.5),   c(0, 0, 0, 1),   c(0, 0, 1, 0) )  parallel_gatekeeping_graph <- graph_create(c(0.5, 0.5, 0, 0), transitions)  plot(parallel_gatekeeping_graph, vertex.size = 70) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     parallel_gatekeeping_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE FALSE FALSE FALSE set.seed(1234) alpha <- 0.025 m <- 4 epsilon <- 0.0001  transitions <- rbind(   c(0, 0, 0.5, 0.5),   c(0, 0, 0.5, 0.5),   c(epsilon, 0, 0, 1 - epsilon),   c(0, epsilon, 1 - epsilon, 0) )  parallel_gatekeeping_improved_graph <-   graph_create(c(0.5, 0.5, 0, 0), transitions)  plot(parallel_gatekeeping_improved_graph, eps = 0.0001, vertex.size = 70) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     parallel_gatekeeping_improved_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE FALSE FALSE FALSE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"successive-procedure","dir":"Articles","previous_headings":"Bonferroni-based procedures","what":"Successive procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Successive procedures incorporate successive relationships hypotheses. example, secondary hypothesis tested primary hypothesis rejected. similar using fixed sequence procedure component graph. example considers two primary hypotheses H1H_1 H2H_2 two secondary hypotheses H3H_3 H4H_4. Primary hypotheses H1H_1 H2H_2 receive equal hypothesis weight 0.5; secondary hypotheses H3H_3 H4H_4 receive hypothesis weight 0. secondary hypothesis H3(H4)H_3 (H_4) can tested corresponding primary hypothesis H1(H2)H_1 (H_2) rejected. represents successive relationships H1H_1 H3H_3, H2H_2 H4H_4, respectively (Maurer, Glimm, Bretz 2011). H1H_1 H3H_3 rejected, hypothesis weights propagated H2H_2 H4H_4, vice versa.  graph generalized allow propagation primary hypotheses (Maurer, Glimm, Bretz 2011). general successive graph illustrate variable determine propagation H1H_1 H2H_2.","code":"set.seed(1234) alpha <- 0.025 m <- 4 simple_successive_graph <- simple_successive_1() # transitions <- rbind( #   c(0, 0, 1, 0), #   c(0, 0, 0, 1), #   c(0, 1, 0, 0), #   c(1, 0, 0, 0) # ) # simple_successive_graph <- graph_create(c(0.5, 0.5, 0, 0), transitions)  plot(simple_successive_graph, layout = \"grid\", nrow = 2, vertex.size = 70) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     simple_successive_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE FALSE FALSE FALSE set.seed(1234) alpha <- 0.025 m <- 4  successive_var <- simple_successive_var <- function(gamma) {   graph_create(     c(0.5, 0.5, 0, 0),     rbind(       c(0, gamma, 1 - gamma, 0),       c(gamma, 0, 0, 1 - gamma),       c(0, 1, 0, 0),       c(1, 0, 0, 0)     )   ) }  successive_var_graph <- successive_var(0.5) plot(successive_var_graph, layout = \"grid\", nrow = 2, vertex.size = 70) p_values <- runif(m, 0, alpha)  test_results <-   graph_test_shortcut(     successive_var_graph,     p = p_values,     alpha = alpha   )  test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE FALSE"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"hommel-procedure","dir":"Articles","previous_headings":"Simes-based procedures","what":"Hommel procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Hommel procedure (Hommel 1988) closed test procedure uses Simes tests every intersection hypothesis. According Xi Bretz (2019), graph Hommel procedures graph Holm procedures. Thus perform Hommel procedure, just need specify test_type simes.","code":"set.seed(1234) alpha <- 0.025 m <- 3 hommel_graph <- bonferroni_holm(rep(1 / m, m))  plot(   hommel_graph,   layout = igraph::layout_in_circle(     as_igraph(hommel_graph),     order = c(2, 1, 3)   ),   vertex.size = 70 ) p_values <- runif(m, 0, alpha)  test_results <- graph_test_closure(   hommel_graph,   p = p_values,   alpha = alpha,   test_types = \"simes\" )  test_results$outputs$rejected #>   H1   H2   H3  #> TRUE TRUE TRUE"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/graph-examples.html","id":"dunnett-procedure","dir":"Articles","previous_headings":"Parametric procedures","what":"Dunnett procedure","title":"Common multiple comparison procedures illustrated using graphicalMCP","text":"Step-Dunnett procedures closed test procedure improvement Holm procedures incorporating correlation structure test statistics (Dunnett Tamhane 1991). Thus graph Holm procedures. Assume equi-correlated case, correlation pair test statistics , e.g., 0.5. can perform step-Dunnett procedure specifying test_type parametric providing correlation matrix.","code":"set.seed(1234) alpha <- 0.025 m <- 3 dunnett_graph <- bonferroni_holm(rep(1 / m, m))  plot(   dunnett_graph,   layout = igraph::layout_in_circle(     as_igraph(dunnett_graph),     order = c(2, 1, 3)   ),   vertex.size = 70 ) p_values <- runif(m, 0, alpha) corr <- matrix(0.5, m, m) diag(corr) <- 1  test_results <- graph_test_closure(   dunnett_graph,   p = p_values, alpha = alpha,   test_types = \"parametric\",   test_corr = list(corr) )  test_results$outputs$rejected #>    H1    H2    H3  #>  TRUE FALSE FALSE"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/graphicalMCP.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Get started","text":"Graphical approaches multiple comparison procedures (MCPs) general framework control familywise error rate strongly pre-specified significance level 0<α<10<\\alpha<1. approach includes many commonly used MCPs special cases transparent visualizing MCPs better communications. graphicalMCP designed design analyze graphical MCPs flexible, informative efficient way.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/graphicalMCP.html","id":"initial-graph","dir":"Articles","previous_headings":"Basic usage","what":"Initial graph","title":"Get started","text":"base object graphicalMCP initial_graph, consists vector hypothesis weights matrix transition weights (Bretz et al. 2009). object can created via graph_create(). graphical representation, hypotheses denoted nodes (vertices) associated hypothesis weights. directed edge hypothesis another indicates direction propagation hypothesis weight origin hypothesis end hypothesis. edge weighted transition weight indicating proportion propagation.","code":"library(graphicalMCP) # A graph of two primary hypotheses (H1 and H2) and two secondary hypotheses (H3 and H4) hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) hyp_names <- c(\"H1\", \"H2\", \"H3\", \"H4\") example_graph <- graph_create(hypotheses, transitions, hyp_names) example_graph #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 plot(example_graph, vertex.size = 60)"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graphicalMCP.html","id":"update-graph","dir":"Articles","previous_headings":"Basic usage","what":"Update graph","title":"Get started","text":"hypothesis removed graph, hypothesis transition weights remaining hypotheses updated according Algorithm 1 Bretz et al. (2011). example, assume hypotheses H1, H2 H4 removed graph. updated graph removing three hypotheses .","code":"updated_example <- graph_update(   example_graph,   delete = c(TRUE, TRUE, FALSE, TRUE) )  updated_example #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 1, 2, 4 #>  #> --- Hypothesis weights --- #> H1: NA #> H2: NA #> H3:  1 #> H4: NA #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1 NA NA NA NA #>  H2 NA NA NA NA #>  H3 NA NA  0 NA #>  H4 NA NA NA NA plot(updated_example, vertex.size = 60)"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graphicalMCP.html","id":"perform-graphical-mcps","dir":"Articles","previous_headings":"","what":"Perform graphical MCPs","title":"Get started","text":"Given set p-values hypotheses, graphical MCPs can performed using graph_test_shortcut() determine hypotheses can rejected significance level alpha. Assume p-values 0.01, 0.005, 0.03, 0.01 hypotheses H1-H4. one-sided significance level alpha = 0.025, rejected hypotheses H1, H2, H4. details shortcut testing can found vignette(\"shortcut-testing\"). similar testing procedure can performed using closure principle. allow tests intersection hypotheses, e.g., Simes, parametric mixture . test type Bonferroni, resulting closed procedure equivalent shortcut procedure . Additional details closed testing can found vignette(\"closed-testing\").","code":"test_results <- graph_test_shortcut(   example_graph,   p = c(0.01, 0.005, 0.03, 0.01),   alpha = 0.025 ) test_results$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE  TRUE test_results_closed <- graph_test_closure(   example_graph,   p = c(0.01, 0.005, 0.03, 0.01),   alpha = 0.025,   test_types = \"bonferroni\",   test_groups = list(1:4) ) test_results_closed$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE  TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/graphicalMCP.html","id":"power-simulations","dir":"Articles","previous_headings":"","what":"Power simulations","title":"Get started","text":"multiplicity adjustment, graphical MCPs, “power” reject hypothesis affected, compared marginal power. latter power rejected hypothesis significance level alpha without multiplicity adjustment. marginal power usually obtained pieces statistical software. graph_calculate_power() performs power simulations assess power adjusting graphical MCP (Bretz, Maurer, Hommel 2011). Assume marginal power reject H1-H4 90%, 90%, 80%, 80% test statistics independent . local power multiplicity adjustment 87.7%, 87.7%, 67.2%, 67.2% respectively H1-H4. Additional details power simulations can found vignette(\"shortcut-testing\") vignette(\"closed-testing\").","code":"set.seed(1234) power_results <- graph_calculate_power(   example_graph,   sim_n = 1e6,   power_marginal = c(0.9, 0.9, 0.8, 0.8) ) power_results$power$power_local #>       H1       H2       H3       H4  #> 0.875760 0.876295 0.670470 0.671431"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"motivating-example","dir":"Articles","previous_headings":"","what":"Motivating example","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Consider confirmatory clinical trial comparing test treatment (treatment) control treatment (control) disease. two doses treatment: low dose high dose. two endpoints included multiplicity adjustment strategy, primary endpoint (PE) secondary endpoint (SE). total, four null hypotheses: H1H_1 H3H_3 primary secondary hypotheses respectively low dose versus control; H2H_2 H4H_4 primary secondary hypotheses respectively high dose versus control. clinical considerations constrain structure multiple comparison procedures, can flexibly incorporated using graphical approaches. First, low high doses considered equally important, means rejecting primary hypothesis either dose versus control leads successful trial. Regarding secondary hypotheses, one tested corresponding primary hypothesis rejected. means H3H_3 tested H1H_1 rejected; H4H_4 tested H2H_2 rejected. addition, statistical considerations complete graph. primary hypotheses H1H_1 H2H_2 equal hypothesis weight 0.5. secondary hypotheses hypothesis weight 0. primary hypothesis rejected, weight propagated along two outgoing edges: One primary hypothesis one descendant secondary hypothesis. two edges equal transition weight 0.5. primary secondary hypotheses rejected dose-control comparison, hypothesis weights propagated primary hypothesis dose-control comparison. specifications, can create following graph.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"create-the-graph","dir":"Articles","previous_headings":"","what":"Create the graph","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"","code":"hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0.5, 0.5, 0),   c(0.5, 0, 0, 0.5),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) hyp_names <- c(\"H1\", \"H2\", \"H3\", \"H4\")  g <- graph_create(hypotheses, transitions, hyp_names)  plot(g, vertex.size = 60)"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"adjusted-p-values-and-rejections","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure","what":"Adjusted p-values and rejections","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Given set p-values H1,…,H4H_1, \\ldots, H_4, graphical multiple comparison procedure can performed control familywise error rate (FWER) significance level alpha. graph_test_shortcut function agnostic one-sided two-sided tests. one-sided p-values, alpha often set 0.025 (default); two-sided p-values, alpha often set 0.05. consider one-sided tests . hypothesis rejected adjusted p-value less equal alpha. running procedure, hypotheses H1H_1, H2H_2, H4H_4 rejected adjusted p-value calculated.","code":"p_values <- c(0.018, 0.01, 0.105, 0.006) test_results <- graph_test_shortcut(g, p = p_values, alpha = 0.025)  test_results$outputs$adjusted_p # Adjusted p-values #>    H1    H2    H3    H4  #> 0.024 0.020 0.105 0.024 test_results$outputs$rejected # Rejections #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE  TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"obtain-final-and-intermediate-graphs-after-rejections","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure","what":"Obtain final and intermediate graphs after rejections","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"final graph graph removing rejected hypotheses H1H_1, H2H_2, H4H_4. can obtained via test_results$outputs$graph. Rejected hypotheses get hypothesis weight NA transition weight NA. based printing method print.updated_graph. can also obtain non-NA graph calling hypothesis weights transition weights separately via test_results$outputs$graph$hypotheses test_results$outputs$graph$transitions. Note case, rejected hypotheses get 0 hypothesis weight 0 transition weight. mainly internal calculation updating graphs. also interested intermediate graphs - example, graph H2H_2 H1H_1 rejected - can specify verbose = TRUE graph_test_shortcut. Note intermediate graphs depend order rejections, .e., sequence hypotheses rejected. default order defined increasing adjusted p-values, followed earlier hypothesis numbering case ties. example, default order rejection H2→H1→H4H_2\\rightarrow H_1\\rightarrow H_4. obtain intermediate graphs based order rejection, one can specify test_results_verbose$details$results. example, graph H2H_2 H1H_1 rejected given test_results_verbose$details$results[[3]].","code":"test_results$outputs$graph # Final graph after H1, H2 and H4 rejected (as NA's) #> Updated graph #>  #> --- Hypothesis weights --- #> H1: NA #> H2: NA #> H3:  1 #> H4: NA #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1 NA NA NA NA #>  H2 NA NA NA NA #>  H3 NA NA  0 NA #>  H4 NA NA NA NA test_results$outputs$graph$hypotheses # Hypothesis weights of the final graph #> H1 H2 H3 H4  #>  0  0  1  0 test_results$outputs$graph$transitions # Transition weights of the final graph #>    H1 H2 H3 H4 #> H1  0  0  0  0 #> H2  0  0  0  0 #> H3  0  0  0  0 #> H4  0  0  0  0  test_results_verbose <- graph_test_shortcut(   g,   p = p_values,   alpha = 0.025,   verbose = TRUE )  # Intermediate graph after H1 and H2 rejected test_results_verbose$details$results[[3]] #> Updated graph #>  #> --- Hypothesis weights --- #> H1:  NA #> H2:  NA #> H3: 0.5 #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1 NA NA NA NA #>  H2 NA NA NA NA #>  H3 NA NA  0  1 #>  H4 NA NA  1  0"},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"obtain-possible-orders-of-rejections","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure","what":"Obtain possible orders of rejections","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"order rejections may unique orders valid. example, rejected hypotheses H1H_1, H2H_2 H4H_4. default order rejections H2→H1→H4H_2 \\rightarrow H_1 \\rightarrow H_4. Another valid order rejections H2→H4→H1H_2 \\rightarrow H_4 \\rightarrow H_1. However, first rejected hypothesis can H1H_1 H4H_4. obtain possible rejection orders, one can use function graph_rejection_orderings. intermediate final graphs can obtained using function graph_update particular order rejections.","code":"# Obtain all valid orders of rejections orders <- graph_rejection_orderings(test_results)$valid_orderings orders #> [[1]] #> H2 H1 H4  #>  2  1  4  #>  #> [[2]] #> H2 H4 H1  #>  2  4  1  # Intermediate graphs following the order of H2 and H4 graph_update(g, delete = orders[[2]])$intermediate_graphs[[3]] #> Updated graph #>  #> --- Hypothesis weights --- #> H1:  1 #> H2: NA #> H3:  0 #> H4: NA #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA  1 NA #>  H2 NA NA NA NA #>  H3  1 NA  0 NA #>  H4 NA NA NA NA"},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"obtain-adjusted-significance-levels","dir":"Articles","previous_headings":"Perform the graphical multiple comparison procedure","what":"Obtain adjusted significance levels","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"equivalent way obtain rejections adjusting significance levels. hypothesis rejected p-value less equal adjusted significance level. adjusted significance levels calculated order adjusted p-values: H2→H1→H4H_2 \\rightarrow H_1 \\rightarrow H_4, four steps checking rejections. First, H2H_2 rejected adjusted significance level 0.5 * alpha. Second, H1H_1 rejected adjusted significance level 0.75 * alpha, H2H_2 rejected. Third, H4H_4 rejected adjusted significance level 0.5 * alpha, H1H_1 H2H_2 rejected. Fourth finally, H3H_3 rejected adjusted significance level alpha, H1H_1, H2H_2 H4H_4 rejected. results can obtained specifying test_values = TRUE.","code":"test_results_test_values <- graph_test_shortcut(   g,   p = p_values,   alpha = 0.025,   test_values = TRUE )  test_results_test_values$test_values$results #>   Step Hypothesis     p Weight Alpha Inequality_holds #> 1    1         H2 0.010   0.50 0.025             TRUE #> 2    2         H1 0.018   0.75 0.025             TRUE #> 3    3         H4 0.006   0.50 0.025             TRUE #> 4    4         H3 0.105   1.00 0.025            FALSE"},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"power-simulation","dir":"Articles","previous_headings":"","what":"Power simulation","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Given graph, interested “power” trial. single null hypothesis, power probability true positive - , rejecting null hypothesis significance level alpha alternative hypothesis true. multiple null hypotheses, multiple versions “power”. example, power reject least one hypothesis vs power reject hypotheses, given alternative hypotheses true. graphical multiple comparison procedures, also important understand power reject hypothesis, given multiplicity adjustment. Sometimes, may want customize definitions power define success. Thus power calculation important aspect trial design.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"input-marginal-power-for-primary-hypotheses","dir":"Articles","previous_headings":"Power simulation","what":"Input: Marginal power for primary hypotheses","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Assume primary endpoint occurrence unfavorable clinical event. evaluate treatment effect, proportion patients event calculated, lower proportion preferred. Assume proportions 0.181 low high doses, 0.3 control. Using equal randomization among three treatment groups, clinical trial team chooses total sample size 600 200 per group. leads marginal power 80% H1H_1 H2H_2, respectively, using two-sample test difference proportions unpooled variance one-sided significance level 0.025. calculation, use marginal power combine information treatment effect, nuisance parameter, sample sizes hypothesis. Note significance level used marginal power calculation must alpha, used significance level FWER control. addition, marginal power one--one relationship noncentrality parameter, illustrated .","code":"alpha <- 0.025 prop <- c(0.3, 0.181, 0.181) sample_size <- rep(200, 3)  unpooled_variance <-   prop[-1] * (1 - prop[-1]) / sample_size[-1] +   prop[1] * (1 - prop[1]) / sample_size[1]  noncentrality_parameter_primary <-   -(prop[-1] - prop[1]) / sqrt(unpooled_variance)  power_marginal_primary <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_primary,   sd = 1,   lower.tail = FALSE )  names(power_marginal_primary) <- c(\"H1\", \"H2\") power_marginal_primary #>        H1        H2  #> 0.8028315 0.8028315"},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"input-marginal-power-for-secondary-hypotheses","dir":"Articles","previous_headings":"Power simulation","what":"Input: Marginal power for secondary hypotheses","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Assume secondary endpoint change total medication score baseline, continuous outcome. evaluate treatment effect, mean change calculated, greater reduction preferred. Assume mean change baseline reduction 7.5 8.25, respectively low high doses, 5 control. assume known common standard deviation 10. Given sample size 200 per treatment group, marginal power 71% 90% H3H_3 H4H_4, respectively, using two-sample zz-test difference means one-sided significance level 0.025.","code":"mean_change <- c(5, 7.5, 8.25) sd <- rep(10, 3) variance <- sd[-1]^2 / sample_size[-1] + sd[1]^2 / sample_size[1]  noncentrality_parameter_secondary <-   (mean_change[-1] - mean_change[1]) / sqrt(variance)  power_marginal_secondary <- pnorm(   qnorm(alpha, lower.tail = FALSE),   mean = noncentrality_parameter_secondary,   sd = 1,   lower.tail = FALSE )  names(power_marginal_secondary) <- c(\"H3\", \"H4\") power_marginal_secondary #>        H3        H4  #> 0.7054139 0.9014809"},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"input-correlation-structure-to-simulate-test-statistics","dir":"Articles","previous_headings":"Power simulation","what":"Input: Correlation structure to simulate test statistics","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"addition marginal power, also need make assumptions joint distribution test statistics. example, assume follow multivariate normal distribution means defined noncentrality parameters correlation matrix RR. obtain correlations, helpful understand two types correlations example. correlation two dose-control comparisons endpoint correlation endpoints. former correlation can calculated function sample size. example, correlation test statistics H1H_1 H2H_2 ρ12=(n1n1+n0)1/2(n2n3+n0)1/2\\rho_{12}=\\left(\\frac{n_1}{n_1+n_0}\\right)^{1/2}\\left(\\frac{n_2}{n_3+n_0}\\right)^{1/2}. equal randomization, correlation 0.5. correlation test statistics H3H_3 H4H_4 . hand, correlation endpoints dose-control comparison often estimated based prior knowledge previous trials. Without information, assume ρ13=ρ24=0.5\\rho_{13}=\\rho_{24}=0.5. practice, one set correlation parameter try multiple values assess sensitivity assumption. Regarding correlation test statistics H1H_1 H4H_4 H2H_2 H3H_3, even difficult estimate. use simple product rule, means correlation product correlations two previously assumed correlations. example, ρ14=ρ12*ρ24\\rho_{14}=\\rho_{12}*\\rho_{24} ρ23=ρ12*ρ13\\rho_{23}=\\rho_{12}*\\rho_{13}. practice, one may make assumptions instead using product rule.","code":"corr <- matrix(0, nrow = 4, ncol = 4)  corr[1, 2] <-   corr[3, 4] <-   sqrt(     sample_size[2] / sum(sample_size[1:2]) *       sample_size[3] / sum(sample_size[c(1, 3)])   )  rho <- 0.5 corr[1, 3] <- corr[2, 4] <- rho corr[1, 4] <- corr[2, 3] <- corr[1, 2] * rho corr <- corr + t(corr) diag(corr) <- 1 colnames(corr) <- hyp_names rownames(corr) <- hyp_names corr #>      H1   H2   H3   H4 #> H1 1.00 0.50 0.50 0.25 #> H2 0.50 1.00 0.25 0.50 #> H3 0.50 0.25 1.00 0.50 #> H4 0.25 0.50 0.50 1.00"},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"user-defined-success-criteria","dir":"Articles","previous_headings":"Power simulation","what":"User-defined success criteria","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"mentioned earlier, multiple versions “power” multiple hypotheses. Commonly used “power” definitions include: Local power: probability hypothesis rejected (multiplicity adjustment) Expected . rejections: expected number rejections Power reject 1 : probability reject least one hypothesis Power reject : probability reject hypotheses default outputs graph_calculate_power function. addition, user can customize success criteria define versions “power”.","code":"success_fns <- list(   # Probability to reject H1   H1 = function(x) x[1],    # Expected number of rejections   `Expected no. of rejections` = function(x) x[1] + x[2] + x[3] + x[4],    # Probability to reject at least one hypothesis   `AtLeast1` = function(x) x[1] | x[2] | x[3] | x[4],    # Probability to reject all hypotheses   `All` = function(x) x[1] & x[2] & x[3] & x[4],    # Probability to reject both H1 and H2   `H1andH2` = function(x) x[1] & x[2],    # Probability to reject both hypotheses for the low dose or the high dose   `(H1andH3)or(H2andH4)` = function(x) (x[1] & x[3]) | (x[2] & x[4]) )"},{"path":"https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html","id":"output-simulate-power","dir":"Articles","previous_headings":"Power simulation","what":"Output: Simulate power","title":"Sequentially rejective graphical multiple comparison procedures based on Bonferroni tests","text":"Given inputs, can estimate “power” via simulation graphical multiple comparison procedure one-sided significance level alpha = 0.025 using sim_n = 1e5 simulations random seed 1234. local power 0.758, 0.765, 0.689, 0.570, respectively H1,…,H4H_1, \\ldots, H_4. Note local power lower marginal power former adjusted multiplicity. power reject least one hypothesis 0.856 power reject hypotheses 0.512. expected number rejections 2.782. last two user-defined success criteria, probability reject H1H_1 H2H_2 0.667, probability reject least one pair (H1(H_1 H3)H_3) (H2(H_2 H4)H_4) 0.747. see detailed outputs simulated p-values rejection decisions hypotheses, specify verbose = TRUE. produce lot outputs. allow flexible printing functions, user can change following: indented space default setting indent = 2 precision numeric values (.e., number significant digits) default setting precision = 4","code":"set.seed(1234) power_output <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(power_marginal_primary, power_marginal_secondary),   sim_success = success_fns )  power_output$power #> $power_local #>      H1      H2      H3      H4  #> 0.76396 0.75887 0.56767 0.69133  #>  #> $rejection_expected #> [1] 2.78183 #>  #> $power_at_least_1 #> [1] 0.85557 #>  #> $power_all #> [1] 0.51205 #>  #> $power_success #>                         H1 Expected no. of rejections  #>                    0.76396                    2.78183  #>                   AtLeast1                        All  #>                    0.85557                    0.51205  #>                    H1andH2       (H1andH3)or(H2andH4)  #>                    0.66726                    0.74695 set.seed(1234) power_verbose_output <- graph_calculate_power(   g,   alpha = 0.025,   sim_corr = corr,   sim_n = 1e5,   power_marginal = c(power_marginal_primary, power_marginal_secondary),   sim_success = success_fns,   verbose = TRUE )  head(power_verbose_output$details$p_sim, 10) #>                 H1           H2           H3           H4 #>  [1,] 0.0308204265 0.0120653993 0.0041185823 9.324338e-02 #>  [2,] 0.0007933716 0.0006499046 0.0245177515 2.965604e-03 #>  [3,] 0.0302991819 0.0595395828 0.0543082956 2.625834e-02 #>  [4,] 0.0097433244 0.0033185711 0.0007417213 4.024688e-04 #>  [5,] 0.0197134942 0.0086161835 0.0164182765 2.418325e-07 #>  [6,] 0.0031206572 0.0067023099 0.0137441457 2.751703e-04 #>  [7,] 0.0302208038 0.1423757994 0.0060382838 2.117403e-02 #>  [8,] 0.0024975725 0.0294025573 0.0004142729 2.207786e-03 #>  [9,] 0.0618994292 0.0387257108 0.3166125781 5.699791e-02 #> [10,] 0.3677921053 0.1895975134 0.0702264885 1.189651e-02  print(power_verbose_output, indent = 4, precision = 6) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>     Initial graph #>  #>     --- Hypothesis weights --- #>     H1: 0.5 #>     H2: 0.5 #>     H3: 0.0 #>     H4: 0.0 #>  #>     --- Transition weights --- #>         H1  H2  H3  H4 #>     H1 0.0 0.5 0.5 0.0 #>     H2 0.5 0.0 0.0 0.5 #>     H3 0.0 1.0 0.0 0.0 #>     H4 1.0 0.0 0.0 0.0 #>  #>     Alpha = 0.025 #>  #>     Test types #>     bonferroni: (H1, H2, H3, H4) #>  #> Simulation parameters ($inputs) ------------------------------------------------ #>     Testing 100,000 simulations with multivariate normal params: #>  #>                           H1       H2       H3       H4 #>     Marginal power: 0.802831 0.802831 0.705414 0.901481 #>  #>     Correlation:      H1   H2   H3   H4 #>                  H1 1.00 0.50 0.50 0.25 #>                  H2 0.50 1.00 0.25 0.50 #>                  H3 0.50 0.25 1.00 0.50 #>                  H4 0.25 0.50 0.50 1.00 #>  #> Power calculation ($power) ----------------------------------------------------- #>                                      H1      H2      H3      H4 #>                    Local power: 0.76396 0.75887 0.56767 0.69133 #>  #>     Expected no. of rejections: 2.78183 #>      Power to reject 1 or more: 0.85557 #>            Power to reject all: 0.51205 #>  #>                Success measure   Power #>                             H1 0.76396 #>     Expected no. of rejections 2.78183 #>                       AtLeast1 0.85557 #>                            All 0.51205 #>                        H1andH2 0.66726 #>           (H1andH3)or(H2andH4) 0.74695 #>  #> Simulation details ($details) -------------------------------------------------- #>         p_sim_H1    p_sim_H2    p_sim_H3    p_sim_H4 rej_H1 rej_H2 rej_H3 rej_H4 #>      3.08204e-02 1.20654e-02 4.11858e-03 9.32434e-02  FALSE   TRUE  FALSE  FALSE #>      7.93372e-04 6.49905e-04 2.45178e-02 2.96560e-03   TRUE   TRUE   TRUE   TRUE #>      3.02992e-02 5.95396e-02 5.43083e-02 2.62583e-02  FALSE  FALSE  FALSE  FALSE #>      9.74332e-03 3.31857e-03 7.41721e-04 4.02469e-04   TRUE   TRUE   TRUE   TRUE #>      1.97135e-02 8.61618e-03 1.64183e-02 2.41833e-07   TRUE   TRUE   TRUE   TRUE #>      3.12066e-03 6.70231e-03 1.37441e-02 2.75170e-04   TRUE   TRUE   TRUE   TRUE #>      3.02208e-02 1.42376e-01 6.03828e-03 2.11740e-02  FALSE  FALSE  FALSE  FALSE #>      2.49757e-03 2.94026e-02 4.14273e-04 2.20779e-03   TRUE  FALSE   TRUE  FALSE #>      6.18994e-02 3.87257e-02 3.16613e-01 5.69979e-02  FALSE  FALSE  FALSE  FALSE #>      3.67792e-01 1.89598e-01 7.02265e-02 1.18965e-02  FALSE  FALSE  FALSE  FALSE #>     ... (Use `print(x, rows = <nn>)` for more)"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Dong Xi. Author, maintainer. Ethan Brockmann. Author. Gilead Sciences, Inc.. Copyright holder, funder.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Xi D, Brockmann E (2024). graphicalMCP: Graphical multiple comparison procedures, version 0.2.6 edition. https://CRAN.R-project.org/package=graphicalMCP.","code":"@Manual{,   title = {{graphicalMCP}: Graphical multiple comparison procedures},   author = {Dong Xi and Ethan Brockmann},   edition = {version 0.2.6},   year = {2024},   url = {https://CRAN.R-project.org/package=graphicalMCP}, }"},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/index.html","id":"introduction","dir":"","previous_headings":"","what":"Introduction","title":"Graphical Multiple Comparison Procedures","text":"Graphical approaches multiple comparison procedures (MCPs) general framework control family-wise error rate strongly pre-specified significance level 0<α<10<\\alpha<1. approach includes many commonly used MCPs special cases transparent visualizing MCPs better communications. graphicalMCP designed design analyze graphical MCPs flexible, informative efficient way.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/index.html","id":"release","dir":"","previous_headings":"","what":"Release","title":"Graphical Multiple Comparison Procedures","text":"can install current release version CRAN :","code":"install.packages(\"graphicalMCP\")"},{"path":"https://openpharma.github.io/graphicalMCP/index.html","id":"development","dir":"","previous_headings":"","what":"Development","title":"Graphical Multiple Comparison Procedures","text":"can install current development version GitHub :","code":"# install.packages(\"pak\") pak::pak(\"openpharma/graphicalMCP\")"},{"path":"https://openpharma.github.io/graphicalMCP/index.html","id":"documentation","dir":"","previous_headings":"","what":"Documentation","title":"Graphical Multiple Comparison Procedures","text":"basic usage instructions, see vignette(\"graphicalMCP\") become familiar graphical MCP terminologies, see vignette(\"glossary\") see vignette(\"shortcut-testing\") sequentially rejective graphical multiple comparison procedures based Bonferroni tests see vignette(\"closed-testing\") graphical multiple comparison procedures based closure principle see vignette(\"graph-examples\") common multiple comparison procedures illustrated using graphicalMCP see vignette(\"generate-closure\") rationales generate closure weighting strategy graph see vignette(\"comparisons\") comparisons R packages view vignettes R properly installing graphicalMCP, can build vignettes devtools::install(build_vignettes = TRUE), use browseVignettes(\"graphicalMCP\") view full list vignettes","code":""},{"path":"https://openpharma.github.io/graphicalMCP/index.html","id":"related-work","dir":"","previous_headings":"","what":"Related work","title":"Graphical Multiple Comparison Procedures","text":"Graphical MCPs - gMCP Lighter version gMCP removes rJava dependency - gMCPLite Graphical MCPs Simes tests - lrstat Built upon packages, hope implement graphical MCPs general framework, fewer dependencies simpler S3 classes, without losing computational efficiency.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/index.html","id":"acknowledgments","dir":"","previous_headings":"","what":"Acknowledgments","title":"Graphical Multiple Comparison Procedures","text":"Along authors contributors, thanks following people suggestions inspirations package: Frank Bretz, Willi Maurer, Ekkehard Glimm, Nan Chen, Jeremy Wildfire, Spencer Childress, Colleen McLaughlin, Matt Roumaya, Chelsea Dickens, Nan Xiao, Keaven Anderson, Ron Yu owe debt gratitude authors gMCP pioneering work, without package nearly extensive .","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_p.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate adjusted p-values — adjust_p_bonferroni","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"intersection hypothesis, adjusted p-value smallest significance level intersection hypothesis can rejected. intersection hypothesis can rejected adjusted p-value less equal \\(\\alpha\\). Currently, three test types supported: Bonferroni tests adjust_p_bonferroni(), Parametric tests adjust_p_parametric(), Note one-sided tests required parametric tests. Simes tests adjust_p_simes().","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_p.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"","code":"adjust_p_bonferroni(p, hypotheses)  adjust_p_parametric(   p,   hypotheses,   test_corr = NULL,   maxpts = 25000,   abseps = 1e-06,   releps = 0 )  adjust_p_simes(p, hypotheses)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_p.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match length hypotheses. hypotheses numeric vector hypothesis weights. Must vector values 0 & 1 (inclusive). length match length p. sum hypothesis weights exceed 1. test_corr (Optional) numeric matrix correlations test statistics, needed perform parametric tests using adjust_p_parametric(). number rows columns correlation matrix match length p. maxpts (Optional) integer scalar maximum number function values, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 25000. abseps (Optional) numeric scalar absolute error tolerance, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 1e-6. releps (Optional) numeric scalar relative error tolerance double, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 0.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_p.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"single adjusted p-value intersection hypothesis.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_p.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_p.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate adjusted p-values — adjust_p_bonferroni","text":"","code":"hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25) p <- c(0.019, 0.025, 0.05) adjust_p_bonferroni(p, hypotheses) #> [1] 0.038 set.seed(1234) hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25) p <- c(0.019, 0.025, 0.05) # Using the `mvtnorm::GenzBretz` algorithm corr <- matrix(0.5, nrow = 3, ncol = 3) diag(corr) <- 1 adjust_p_parametric(p, hypotheses, corr) #> [1] 0.03343516 hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25) p <- c(0.019, 0.025, 0.05) adjust_p_simes(p, hypotheses) #> [1] 0.03333333"},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate adjusted hypothesis weights — adjust_weights_parametric","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"intersection hypothesis can rejected p-values less equal adjusted significance levels, adjusted hypothesis weights times \\(\\alpha\\). Bonferroni tests, adjusted hypothesis weights hypothesis weights intersection hypothesis. Additional adjustment needed parametric Simes tests: Parametric tests adjust_weights_parametric(), Note one-sided tests required parametric tests. Simes tests adjust_weights_simes().","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"","code":"adjust_weights_parametric(   matrix_weights,   matrix_intersections,   test_corr,   alpha,   test_groups,   maxpts = 25000,   abseps = 1e-06,   releps = 0 )  adjust_weights_simes(matrix_weights, p, test_groups)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"matrix_weights (Optional) matrix hypothesis weights intersection hypotheses. can obtained second half columns output graph_generate_weights(). matrix_intersections (Optional) matrix hypothesis indicators intersection hypotheses. can obtained first half columns output graph_generate_weights(). test_corr (Optional) numeric matrix correlations test statistics, needed perform parametric tests using adjust_weights_parametric(). number rows columns correlation matrix match length p. alpha (Optional) numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. test_groups (Optional) list numeric vectors specifying hypotheses test together. Grouping needed correctly perform Simes parametric tests. maxpts (Optional) integer scalar maximum number function values, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 25000. abseps (Optional) numeric scalar absolute error tolerance, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 1e-6. releps (Optional) numeric scalar relative error tolerance double, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 0. p (Optional) numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number columns matrix_weights.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"adjust_weights_parametric() returns matrix dimensions matrix_weights, whose hypothesis weights adjusted according parametric tests. adjust_weights_simes() returns matrix dimensions matrix_weights, whose hypothesis weights adjusted according Simes tests.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate adjusted hypothesis weights — adjust_weights_parametric","text":"","code":"alpha <- 0.025 p <- c(0.018, 0.01, 0.105, 0.006) num_hyps <- length(p) g <- bonferroni_holm(rep(1 / 4, 4)) weighting_strategy <- graph_generate_weights(g) matrix_intersections <- weighting_strategy[, seq_len(num_hyps)] matrix_weights <- weighting_strategy[, -seq_len(num_hyps)]  set.seed(1234) adjust_weights_parametric(   matrix_weights = matrix_weights,   matrix_intersections = matrix_intersections,   test_corr = diag(4),   alpha = alpha,   test_groups = list(1:4) ) #>           H1        H2        H3        H4 #> 1  0.2523785 0.2523785 0.2523785 0.2523785 #> 2  0.3361503 0.3361503 0.3361503 0.0000000 #> 3  0.3361503 0.3361503 0.0000000 0.3361503 #> 4  0.5031647 0.5031647 0.0000000 0.0000000 #> 5  0.3361503 0.0000000 0.3361503 0.3361503 #> 6  0.5031647 0.0000000 0.5031647 0.0000000 #> 7  0.5031647 0.0000000 0.0000000 0.5031647 #> 8  1.0000000 0.0000000 0.0000000 0.0000000 #> 9  0.0000000 0.3361503 0.3361503 0.3361503 #> 10 0.0000000 0.5031647 0.5031647 0.0000000 #> 11 0.0000000 0.5031647 0.0000000 0.5031647 #> 12 0.0000000 1.0000000 0.0000000 0.0000000 #> 13 0.0000000 0.0000000 0.5031647 0.5031647 #> 14 0.0000000 0.0000000 1.0000000 0.0000000 #> 15 0.0000000 0.0000000 0.0000000 1.0000000 alpha <- 0.025 p <- c(0.018, 0.01, 0.105, 0.006) num_hyps <- length(p) g <- bonferroni_holm(rep(1 / 4, 4)) weighting_strategy <- graph_generate_weights(g) matrix_intersections <- weighting_strategy[, seq_len(num_hyps)] matrix_weights <- weighting_strategy[, -seq_len(num_hyps)]  adjust_weights_simes(   matrix_weights = matrix_weights,   p = p,   test_groups = list(1:4) ) #>           H4        H2        H1 H3 #> 1  0.2500000 0.5000000 0.7500000  1 #> 2  0.0000000 0.3333333 0.6666667  1 #> 3  0.3333333 0.6666667 1.0000000  1 #> 4  0.0000000 0.5000000 1.0000000  1 #> 5  0.3333333 0.3333333 0.6666667  1 #> 6  0.0000000 0.0000000 0.5000000  1 #> 7  0.5000000 0.5000000 1.0000000  1 #> 8  0.0000000 0.0000000 1.0000000  1 #> 9  0.3333333 0.6666667 0.6666667  1 #> 10 0.0000000 0.5000000 0.5000000  1 #> 11 0.5000000 1.0000000 1.0000000  1 #> 12 0.0000000 1.0000000 1.0000000  1 #> 13 0.5000000 0.5000000 0.5000000  1 #> 14 0.0000000 0.0000000 0.0000000  1 #> 15 1.0000000 1.0000000 1.0000000  1"},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"intersection hypothesis can rejected p-values less equal adjusted significance levels, adjusted hypothesis weights times \\(\\alpha\\). Bonferroni tests, adjusted hypothesis weights hypothesis weights intersection hypothesis. Additional adjustment needed parametric tests: Parametric tests adjust_weights_parametric(), Note one-sided tests required parametric tests.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"","code":"c_value_function(   x,   hypotheses,   test_corr,   alpha,   maxpts = 25000,   abseps = 1e-06,   releps = 0 )  solve_c_parametric(   hypotheses,   test_corr,   alpha,   maxpts = 25000,   abseps = 1e-06,   releps = 0 )"},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"x root solve stats::uniroot(). hypotheses numeric vector hypothesis weights. Must vector values 0 & 1 (inclusive). sum hypothesis weights exceed 1. test_corr (Optional) numeric matrix correlations test statistics, needed perform parametric tests using adjust_weights_parametric(). number rows columns correlation matrix match length p. alpha (Optional) numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. maxpts (Optional) integer scalar maximum number function values, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 25000. abseps (Optional) numeric scalar absolute error tolerance, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 1e-6. releps (Optional) numeric scalar relative error tolerance double, needed perform parametric tests using mvtnorm::GenzBretz algorithm. default 0.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"c_value_function() returns difference \\(\\alpha\\) Type error parametric test \\(c\\) value x, adjusted correlation test statistics using parametric tests based equation (6) Xi et al. (2017). solve_c_parametric() returns c value adjusted correlation test statistics using parametric tests based equation (6) Xi et al. (2017).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate adjusted hypothesis weights for parametric tests — c_value_function","text":"Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/as_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"Graph objects different structures attributes graphicalMCP, gMCP, igraph R packages. functions convert different classes increase compatibility. Note igraph gMCP additional attributes vertices, edges, graph . conversion functions handle attributes related hypothesis names, hypothesis weights transition weights. attributes dropped converting.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/as_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"","code":"as_initial_graph(graph)  # S3 method for class 'graphMCP' as_initial_graph(graph)  # S3 method for class 'igraph' as_initial_graph(graph)  as_graphMCP(graph)  # S3 method for class 'initial_graph' as_graphMCP(graph)  as_igraph(graph)  # S3 method for class 'initial_graph' as_igraph(graph)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/as_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"graph initial_graph object graphicalMCP package, graphMCP object gMCP package, igraph object igraph package, depending conversion type.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/as_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"as_graphMCP() returns graphMCP object gMCP package. as_igraph() returns igraph object igraph package. as_initial_graph() returns initial_graph object graphicalMCP package.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/as_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"Csardi, G., Nepusz, T., Traag, V., Horvat, S., Zanini, F., Noom, D., Mueller, K. (2024). igraph: Network analysis visualization R. R package version 2.0.3. https://CRAN.R-project.org/package=igraph. Rohmeyer, K., Klinglmueller, K. (2024). gMCP: Graph based multiple test procedures. R package version 0.8-17. https://cran.r-project.org/package=gMCP.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/as_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert between graphicalMCP, gMCP, and igraph graph classes — as_initial_graph","text":"","code":"g_graphicalMCP <- random_graph(5)  if (requireNamespace(\"gMCP\", quietly = TRUE)) {   g_gMCP <- as_graphMCP(g_graphicalMCP)    all.equal(g_graphicalMCP, as_initial_graph(g_gMCP)) } #> [1] TRUE  if (requireNamespace(\"igraph\", quietly = TRUE)) {   g_igraph <- as_igraph(g_graphicalMCP)    all.equal(g_graphicalMCP, as_initial_graph(g_igraph)) } #> [1] TRUE"},{"path":"https://openpharma.github.io/graphicalMCP/reference/edge_pairs.html","id":null,"dir":"Reference","previous_headings":"","what":"Find pairs of vertices that are connected in both directions — edge_pairs","title":"Find pairs of vertices that are connected in both directions — edge_pairs","text":"initial graph, find pairs hypotheses connected directions. used plot graphs using plot.initial_graph().","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/edge_pairs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find pairs of vertices that are connected in both directions — edge_pairs","text":"","code":"edge_pairs(graph)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/edge_pairs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find pairs of vertices that are connected in both directions — edge_pairs","text":"graph initial graph returned graph_create().","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/edge_pairs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find pairs of vertices that are connected in both directions — edge_pairs","text":"list vertex pairs connected directions. NULL pairs found.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/example_graphs.html","id":null,"dir":"Reference","previous_headings":"","what":"Example graphs of commonly used multiple comparison procedures — bonferroni","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"Built-functions quickly generate select graphical multiple comparison procedures.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/example_graphs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"","code":"bonferroni(hypotheses, hyp_names = NULL)  bonferroni_holm(hypotheses, hyp_names = NULL)  huque_etal(hyp_names = NULL)  fallback(hypotheses, hyp_names = NULL)  fallback_improved_1(hypotheses, hyp_names = NULL)  fallback_improved_2(hypotheses, epsilon = 1e-04, hyp_names = NULL)  fixed_sequence(num_hyps, hyp_names = NULL)  simple_successive_1(hyp_names = NULL)  simple_successive_2(hyp_names = NULL)  random_graph(num_hyps, hyp_names = NULL)  two_doses_two_primary_two_secondary(hyp_names = NULL)  three_doses_two_primary_two_secondary(hyp_names = NULL)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/example_graphs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"hypotheses (Optional) numeric vector hypothesis weights graphical multiple comparison procedure. Must vector values 0 & 1 (inclusive). length match num_hyps length hyp_names. sum hypothesis weights exceed 1. hyp_names (Optional) character vector hypothesis names. length match num_hyps length hypotheses. hyp_names specified, hypotheses named sequentially H1, H2, ....... epsilon (Optional) numeric scalar indicating value \\(\\epsilon\\) edge. much smaller value hypothesis transition weights. default 1e-4. num_hyps (Optional) Number hypotheses graphical multiple comparison procedure.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/example_graphs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"S3 object returned graph_create().","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/example_graphs.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Huque, M. F., Alosh, M., Bhore, R. (2011). Addressing multiplicity issues composite endpoint components clinical trials. Journal Biopharmaceutical Statistics, 21(4), 610-634. Maurer, W., Hothorn, L., Lehmacher, W. (1995). Multiple comparisons drug clinical trials preclinical assays: -priori ordered hypotheses. Biometrie der chemisch-pharmazeutischen Industrie, 6, 3-18. Westfall, P. H., Krishen, . (2001). Optimally weighted, fixed sequence gatekeeper multiple testing procedures. Journal Statistical Planning Inference, 99(1), 25-40. Wiens, B. L. (2003). fixed sequence Bonferroni procedure testing multiple endpoints. Pharmaceutical Statistics, 2(3), 211-215. Wiens, B. L., Dmitrienko, . (2005). fallback procedure evaluating single family hypotheses. Journal Biopharmaceutical Statistics, 15(6), 929-942. Xi, D., Bretz, F. (2019). Symmetric graphs equally weighted tests, application Hochberg procedure. Statistics Medicine, 38(27), 5268-5282.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/example_graphs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Example graphs of commonly used multiple comparison procedures — bonferroni","text":"","code":"# Bretz et al. (2009) bonferroni(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>     H1 H2 H3 #>  H1  0  0  0 #>  H2  0  0  0 #>  H3  0  0  0 # Bretz et al. (2009) bonferroni_holm(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>      H1  H2  H3 #>  H1 0.0 0.5 0.5 #>  H2 0.5 0.0 0.5 #>  H3 0.5 0.5 0.0 # Huque et al. (2011) huque_etal() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 1 #> H2: 0 #> H3: 0 #> H4: 0 #>  #> --- Transition weights --- #>      H1  H2  H3  H4 #>  H1 0.0 0.5 0.5 0.0 #>  H2 0.0 0.0 0.0 1.0 #>  H3 0.0 0.5 0.0 0.5 #>  H4 0.0 1.0 0.0 0.0 # Wiens (2003) fallback(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>     H1 H2 H3 #>  H1  0  1  0 #>  H2  0  0  1 #>  H3  0  0  0 # Wiens and Dmitrienko (2005) fallback_improved_1(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>      H1  H2  H3 #>  H1 0.0 1.0 0.0 #>  H2 0.0 0.0 1.0 #>  H3 0.5 0.5 0.0 # Bretz et al. (2009) fallback_improved_2(hypotheses = rep(1 / 3, 3)) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>         H1     H2     H3 #>  H1 0.0000 1.0000 0.0000 #>  H2 0.9999 0.0000 0.0001 #>  H3 1.0000 0.0000 0.0000 # Maurer et al. (1995); Westfall and Krishen (2001) fixed_sequence(num_hyps = 3) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 1 #> H2: 0 #> H3: 0 #>  #> --- Transition weights --- #>     H1 H2 H3 #>  H1  0  1  0 #>  H2  0  0  1 #>  H3  0  0  0 # Figure 1 in Bretz et al. (2011) simple_successive_1() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 # Figure 4 in Bretz et al. (2011) simple_successive_2() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>      H1  H2  H3  H4 #>  H1 0.0 0.5 0.5 0.0 #>  H2 0.5 0.0 0.0 0.5 #>  H3 0.0 1.0 0.0 0.0 #>  H4 1.0 0.0 0.0 0.0 # Create a random graph with three hypotheses random_graph(num_hyps = 3) #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.3333 #> H3: 0.3333 #>  #> --- Transition weights --- #>         H1     H2     H3 #>  H1 0.0000 0.6000 0.4000 #>  H2 0.6667 0.0000 0.3333 #>  H3 0.7500 0.2500 0.0000 # Figure 6 in Xi and Bretz et al. (2019) two_doses_two_primary_two_secondary() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.0 #> H3: 0.0 #> H4: 0.5 #> H5: 0.0 #> H6: 0.0 #>  #> --- Transition weights --- #>         H1     H2     H3     H4     H5     H6 #>  H1 0.0000 0.5000 0.5000 0.0000 0.0000 0.0000 #>  H2 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 #>  H3 0.0000 0.9999 0.0000 0.0001 0.0000 0.0000 #>  H4 0.0000 0.0000 0.0000 0.0000 0.5000 0.5000 #>  H5 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 #>  H6 0.0001 0.0000 0.0000 0.0000 0.9999 0.0000 # Add another dose to Figure 6 in Xi and Bretz et al. (2019) three_doses_two_primary_two_secondary() #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.3333 #> H2: 0.0000 #> H3: 0.0000 #> H4: 0.3333 #> H5: 0.0000 #> H6: 0.0000 #> H7: 0.3333 #> H8: 0.0000 #> H9: 0.0000 #>  #> --- Transition weights --- #>          H1      H2      H3      H4      H5      H6      H7      H8      H9 #>  H1 0.00000 0.50000 0.50000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 #>  H2 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 #>  H3 0.00000 0.99990 0.00000 0.00005 0.00000 0.00000 0.00005 0.00000 0.00000 #>  H4 0.00000 0.00000 0.00000 0.00000 0.50000 0.50000 0.00000 0.00000 0.00000 #>  H5 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 #>  H6 0.00005 0.00000 0.00000 0.00000 0.99990 0.00000 0.00005 0.00000 0.00000 #>  H7 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.50000 0.50000 #>  H8 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 #>  H9 0.00005 0.00000 0.00000 0.00005 0.00000 0.00000 0.00000 0.99990 0.00000"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_calculate_power.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"alternative hypotheses, distribution test statistics assumed multivariate normal distribution. Given distribution, function calculates power values graphical multiple comparison procedure. default, calculate local power, probability reject individual hypothesis, probability reject least one hypothesis, probability reject hypotheses, expected number rejections, probability user-defined success criteria. See vignette(\"shortcut-testing\") vignette(\"closed-testing\") illustration power calculation.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"","code":"graph_calculate_power(   graph,   alpha = 0.025,   power_marginal = rep(alpha, length(graph$hypotheses)),   test_groups = list(seq_along(graph$hypotheses)),   test_types = c(\"bonferroni\"),   test_corr = rep(list(NA), length(test_types)),   sim_n = 1e+05,   sim_corr = diag(length(graph$hypotheses)),   sim_success = NULL,   verbose = FALSE )"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"graph initial graph returned graph_create(). alpha numeric value one-sided overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing. Note one-sided tests supported. power_marginal numeric vector marginal power values use simulating p-values. See Details simulation process. test_groups list numeric vectors specifying hypotheses test together. Grouping needed correctly perform Simes parametric tests. test_types character vector test types apply test group. needed correctly perform Simes parametric tests. length match number elements test_groups. test_corr (Optional) list numeric correlation matrices. entry list correspond test group. test group using Bonferroni Simes tests, corresponding entry test_corr NA. test group using parametric tests, corresponding entry test_corr numeric correlation matrix specifying correlation test statistics hypotheses test group. length match number elements test_groups. sim_n integer scalar specifying number simulations. default 1e5. sim_corr numeric matrix correlations test statistics hypotheses. dimensions match number hypotheses graph. sim_success list user-defined functions specify success criteria. Functions must take one simulation's logical vector results input, return length-one logical vector. instance, \"success\" means rejecting hypotheses 1 2, use sim_success = list(\"1 2\" = function(x) x[1] && x[2]). list named, function body used name. Lambda functions also work starting R 4.1, e.g. sim_success = list(\\(x) x[3] || x[4]). verbose logical scalar specifying whether details power simulations included results. default verbose = FALSE.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"power_report object list 3 elements: inputs - Input parameters, list : graph - Initial graph, alpha - Overall significance level, test_groups - Groups hypotheses different types tests, test_types - Different types tests, test_corr - Correlation matrices parametric tests, sim_n - Number simulations, power_marginal - Marginal power hypotheses sim_corr - Correlation matrices simulations, sim_success - User-defined success criteria. power - list power values power_local - Local power hypotheses, proportion simulations hypothesis rejected, rejection_expected - Expected (average) number rejected hypotheses, power_at_least_1 - Power reject least one hypothesis, power_all - Power reject hypotheses, power_success - Power user-defined success, proportion simulations user-defined success criterion sim_success met. details - optional list datasets showing simulated p-values results simulation.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"simulation-details","dir":"Reference","previous_headings":"","what":"Simulation details","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"power calculation based simulations. distribution simulate determined multivariate normal distribution power_marginal sim_corr. particular, power_marginal vector marginal power values hypotheses. marginal power power reject null hypothesis significance level alpha without multiplicity adjustment. value readily available standard software R packages. can determine mean multivariate normal distribution $$\\Phi^{-1}\\left(1-\\alpha\\right)-\\Phi^{-1}\\left(1-d_i\\right)$$, often called non-centrality parameter drift parameter. \\(d_i\\) marginal power power_marginal hypothesis \\(\\). Given correlation matrix sim_corr, can simulate multivariate normal distribution using mvtnorm R package (Genz Bretz, 2009). set simulated values can used calculate corresponding one-sided p-values. set p-values plugged graphical multiple comparison procedure determine hypotheses rejected. process repeated n_sim times produce power values proportion simulations particular success criterion met.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011a). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Bretz, F., Maurer, W., Hommel, G. (2011b). Test power considerations multiple endpoint analyses using sequentially rejective graphical procedures. Statistics Medicine, 30(13), 1489-1501. Genz, ., Bretz, F. (2009). Computation Multivariate Normal t Probabilities, series Lecture Notes Statistics. Springer-Verlag, Heidelberg. Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_calculate_power.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate power values for a graphical multiple comparison procedure — graph_calculate_power","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011a). alpha <- 0.025 hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  marginal_power <- c(0.8, 0.8, 0.7, 0.9) corr1 <- matrix(0.5, nrow = 2, ncol = 2) diag(corr1) <- 1 corr <- rbind(   cbind(corr1, 0.5 * corr1),   cbind(0.5 * corr1, corr1) ) success_fns <- list(   # Probability to reject both H1 and H2   `H1andH2` = function(x) x[1] & x[2],   # Probability to reject both (H1 and H3) or (H2 and H4)   `(H1andH3)or(H2andH4)` = function(x) (x[1] & x[3]) | (x[2] & x[4]) ) set.seed(1234) # Bonferroni tests # Reduce the number of simulations to save time for package compilation power_output <- graph_calculate_power(   g,   alpha,   sim_corr = corr,   sim_n = 1e2,   power_marginal = marginal_power,   sim_success = success_fns )  # Parametric tests for H1 and H2; Simes tests for H3 and H4 # User-defined success: to reject H1 or H2; to reject H1 and H2 # Reduce the number of simulations to save time for package compilation graph_calculate_power(   g,   alpha,   test_groups = list(1:2, 3:4),   test_types = c(\"parametric\", \"simes\"),   test_corr = list(corr1, NA),   sim_n = 1e2,   sim_success = list(     function(.) .[1] || .[2],     function(.) .[1] && .[2]   ) ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>   Parametric testing correlation:     H1  H2 #>                                   H1 1.0 0.5 #>                                   H2 0.5 1.0 #>  #>   Test types #>   parametric: (H1, H2) #>        simes: (H3, H4) #>  #> Simulation parameters ($inputs) ------------------------------------------------ #>   Testing 100 simulations with multivariate normal params: #>  #>                      H1    H2    H3    H4 #>   Marginal power: 0.025 0.025 0.025 0.025 #>  #>   Correlation:    H1 H2 H3 H4 #>                H1  1  0  0  0 #>                H2  0  1  0  0 #>                H3  0  0  1  0 #>                H4  0  0  0  1 #>  #> Power calculation ($power) ----------------------------------------------------- #>                                 H1   H2   H3   H4 #>                  Local power: 0.02 0.01 0.00 0.00 #>  #>   Expected no. of rejections: 0.03 #>    Power to reject 1 or more: 0.03 #>          Power to reject all: 0 #>  #>   Success measure Power #>      .[1] || .[2]  0.03 #>      .[1] && .[2]  0.00 #>"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_create.html","id":null,"dir":"Reference","previous_headings":"","what":"Create the initial graph for a multiple comparison procedure — graph_create","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"graphical multiple comparison procedure represented 1) vector initial hypothesis weights hypotheses, 2) matrix initial transition weights transitions. function creates initial graph object using hypothesis weights transition weights.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_create.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"","code":"graph_create(hypotheses, transitions, hyp_names = NULL)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_create.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"hypotheses numeric vector hypothesis weights graphical multiple comparison procedure. Must vector values 0 & 1 (inclusive). length match row column lengths transitions. sum hypothesis weights exceed 1. transitions numeric matrix transition weights hypotheses graphical multiple comparison procedure. Must square matrix values 0 & 1 (inclusive). row column lengths match length hypotheses. row (Transition weights leaving hypothesis) can sum 1. diagonal entries (Transition weights hypothesis ) must 0s. hyp_names (Optional) character vector hypothesis names. provided, names hypotheses transitions used. names specified, hypotheses named sequentially H1, H2, .......","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_create.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"S3 object class initial_graph list 2 elements: Hypothesis weights hypotheses. Transition weights transitions.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_create.html","id":"validation-of-inputs","dir":"Reference","previous_headings":"","what":"Validation of inputs","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"Inputs also validated make sure validity graph: Hypothesis weights hypotheses numeric. Transition weights transitions numeric. Length hypotheses dimensions transitions match. Hypothesis weights hypotheses must non-negative sum 1. Transition weights transitions: Values must non-negative. Rows must sum 1. Diagonal entries must 0. Hypothesis names hyp_names override names hypotheses transitions.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_create.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_create.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create the initial graph for a multiple comparison procedure — graph_create","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) hyp_names <- c(\"H11\", \"H12\", \"H21\", \"H22\") g <- graph_create(hypotheses, transitions, hyp_names) g #> Initial graph #>  #> --- Hypothesis weights --- #> H11: 0.5 #> H12: 0.5 #> H21: 0.0 #> H22: 0.0 #>  #> --- Transition weights --- #>      H11 H12 H21 H22 #>  H11   0   0   1   0 #>  H12   0   0   0   1 #>  H21   0   1   0   0 #>  H22   1   0   0   0  # Explicit names override names in `hypotheses` (with a warning) hypotheses <- c(h1 = 0.5, h2 = 0.5, h3 = 0, h4 = 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions, hyp_names) #> Warning: Hypothesis names specified - overriding names in #>                     `hypotheses` and `transitions` g #> Initial graph #>  #> --- Hypothesis weights --- #> H11: 0.5 #> H12: 0.5 #> H21: 0.0 #> H22: 0.0 #>  #> --- Transition weights --- #>      H11 H12 H21 H22 #>  H11   0   0   1   0 #>  H12   0   0   0   1 #>  H21   0   1   0   0 #>  H22   1   0   0   0  # Use names in `transitions` hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   H1 = c(0, 0, 1, 0),   H2 = c(0, 0, 0, 1),   H3 = c(0, 1, 0, 0),   H4 = c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions) g #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0  # Unmatched names in `hypotheses` and `transitions` (with an error) hypotheses <- c(h1 = 0.5, h2 = 0.5, h3 = 0, h4 = 0) transitions <- rbind(   H1 = c(0, 0, 1, 0),   H2 = c(0, 0, 0, 1),   H3 = c(0, 1, 0, 0),   H4 = c(1, 0, 0, 0) ) try( g <- graph_create(hypotheses, transitions) ) #> Error in graph_create(hypotheses, transitions) :  #>   Names provided in `hypotheses` and `transitions` should match  # When names are not specified, hypotheses are numbered sequentially as # H1, H2, ... hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions) g #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_generate_weights.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"graphical multiple comparison procedure defines closed test procedure, tests intersection hypothesis reject individual hypothesis intersection hypotheses involving rejected. intersection hypothesis represents parameter space individual null hypotheses involved true simultaneously. closure based graph consists updated graphs (corresponding intersection hypotheses) combinations hypotheses deleted. graphical multiple comparison procedure \\(m\\) hypotheses, \\(2^{m}-1\\) updated graphs (intersection hypotheses), including initial graph (overall intersection hypothesis). weighting strategy graph consists hypothesis weights \\(2^{m}-1\\) updated graphs (intersection hypotheses). algorithm derive weighting strategy based Algorithm 1 Bretz et al. (2011).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"","code":"graph_generate_weights(graph)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"graph initial graph returned graph_create().","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"numeric matrix intersection hypotheses hypothesis weights. graphical multiple comparison procedure \\(m\\) hypotheses, number rows \\(2^{m}-1\\), corresponds intersection hypothesis. number columns \\(2\\cdot m\\). first \\(m\\) columns indicate individual hypotheses included given intersection hypothesis second half columns provide hypothesis weights individual hypothesis given intersection hypothesis.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"performance","dir":"Reference","previous_headings":"","what":"Performance","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"Generation intersection hypotheses closely related power set given set indices. number hypotheses increases, memory time usage can grow quickly (e.g., rate \\(O(2^n)\\)). also multiple ways implement Algorithm 1 Bretz et al. (2011). See vignette(\"generate-closure\") information generating intersection hypotheses comparisons different approaches calculate weighting strategies.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_generate_weights.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate the weighting strategy based on a graphical multiple comparison procedure — graph_generate_weights","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  graph_generate_weights(g) #>    H1 H2 H3 H4  H1  H2  H3  H4 #> 1   1  1  1  1 0.5 0.5 0.0 0.0 #> 2   1  1  1  0 0.5 0.5 0.0 0.0 #> 3   1  1  0  1 0.5 0.5 0.0 0.0 #> 4   1  1  0  0 0.5 0.5 0.0 0.0 #> 5   1  0  1  1 0.5 0.0 0.0 0.5 #> 6   1  0  1  0 1.0 0.0 0.0 0.0 #> 7   1  0  0  1 0.5 0.0 0.0 0.5 #> 8   1  0  0  0 1.0 0.0 0.0 0.0 #> 9   0  1  1  1 0.0 0.5 0.5 0.0 #> 10  0  1  1  0 0.0 0.5 0.5 0.0 #> 11  0  1  0  1 0.0 1.0 0.0 0.0 #> 12  0  1  0  0 0.0 1.0 0.0 0.0 #> 13  0  0  1  1 0.0 0.0 0.5 0.5 #> 14  0  0  1  0 0.0 0.0 1.0 0.0 #> 15  0  0  0  1 0.0 0.0 0.0 1.0"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":null,"dir":"Reference","previous_headings":"","what":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"multiple hypotheses rejected using graph_test_shortcut(), may multiple orderings sequences hypotheses rejected one one. default order graph_test_shortcut() based adjusted p-values, smallest largest. function graph_rejection_orderings() provides possible valid orders (sequences) rejections. Although order rejection affect final rejection decisions Bretz et al. (2009), different sequences offer different ways explain step--step process shortcut graphical multiple comparison procedures.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"","code":"graph_rejection_orderings(shortcut_test_result)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"shortcut_test_result graph_report object returned graph_test_shortcut().","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"modified graph_report object containing valid orderings rejections hypotheses","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_rejection_orderings.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Find alternate rejection orderings (sequences) for shortcut tests — graph_rejection_orderings","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  p <- c(0.018, 0.01, 0.105, 0.006) alpha <- 0.025  shortcut_testing <- graph_test_shortcut(g, p, alpha, verbose = TRUE)  # Reject H1, H2, and H4 shortcut_testing$outputs$rejected #>    H1    H2    H3    H4  #>  TRUE  TRUE FALSE  TRUE   # Default order of rejections: H2, H1, H4 shortcut_testing$details$del_seq #> [1] \"H2\" \"H1\" \"H4\"  # There is another valid sequence of rejection: H2, H4, H1 graph_rejection_orderings(shortcut_testing)$valid_orderings #> [[1]] #> H2 H1 H4  #>  2  1  4  #>  #> [[2]] #> H2 H4 H1  #>  2  4  1  #>   # Finally, intermediate updated graphs can be obtained by providing the order # of rejections into `[graph_update()]` graph_update(g, delete = c(2, 4, 1)) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>      H1  H2  H3  H4 #>  H1 0.0 0.5 0.5 0.0 #>  H2 0.5 0.0 0.0 0.5 #>  H3 0.0 1.0 0.0 0.0 #>  H4 1.0 0.0 0.0 0.0 #>  #> Updated graph after deleting hypotheses 2, 4, 1 #>  #> --- Hypothesis weights --- #> H1: NA #> H2: NA #> H3:  1 #> H4: NA #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1 NA NA NA NA #>  H2 NA NA NA NA #>  H3 NA NA  0 NA #>  H4 NA NA NA NA #>  #> Deletion sequence ($intermediate_graphs) --------------------------------------- #>  #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>     Step 1: Updated graph after removing hypothesis 2 #>  #>     --- Hypothesis weights --- #>     H1: 0.75 #>     H2:   NA #>     H3: 0.00 #>     H4: 0.25 #>  #>     --- Transition weights --- #>              H1       H2       H3       H4 #>     H1 0.000000       NA 0.666667 0.333333 #>     H2       NA       NA       NA       NA #>     H3 0.500000       NA 0.000000 0.500000 #>     H4 1.000000       NA 0.000000 0.000000 #>  #>       Step 2: Updated graph after removing hypotheses 2, 4 #>  #>       --- Hypothesis weights --- #>       H1:  1 #>       H2: NA #>       H3:  0 #>       H4: NA #>  #>       --- Transition weights --- #>          H1 H2 H3 H4 #>       H1  0 NA  1 NA #>       H2 NA NA NA NA #>       H3  1 NA  0 NA #>       H4 NA NA NA NA #>  #>         Step 3: Updated graph after removing hypotheses 2, 4, 1 #>  #>         --- Hypothesis weights --- #>         H1: NA #>         H2: NA #>         H3:  1 #>         H4: NA #>  #>         --- Transition weights --- #>            H1 H2 H3 H4 #>         H1 NA NA NA NA #>         H2 NA NA NA NA #>         H3 NA NA  0 NA #>         H4 NA NA NA NA #>  #>   Final updated graph after removing deleted hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_closure.html","id":null,"dir":"Reference","previous_headings":"","what":"Perform closed graphical multiple comparison procedures — graph_test_closure","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"Closed graphical multiple comparison procedures, graphical multiple comparison procedures based closure, generate closure based graph consisting intersection hypotheses. tests intersection hypothesis rejects individual hypothesis intersection hypotheses involving rejected. intersection hypothesis represents parameter space individual null hypotheses involved true simultaneously. graphical multiple comparison procedure $m$ hypotheses, \\(2^m-1\\) intersection hypotheses. intersection hypothesis, test type chosen determine reject intersection hypothesis. Current choices test types include Bonferroni, Simes parametric. implementation offers general framework covering Bretz et al. (2011), Lu (2016), Xi et al. (2017). See vignette(\"closed-testing\") illustration closed test procedures interpretation outputs.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_closure.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"","code":"graph_test_closure(   graph,   p,   alpha = 0.025,   test_groups = list(seq_along(graph$hypotheses)),   test_types = c(\"bonferroni\"),   test_corr = rep(list(NA), length(test_types)),   verbose = FALSE,   test_values = FALSE )"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_closure.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"graph initial graph returned graph_create(). p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. alpha numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. test_groups list numeric vectors specifying hypotheses test together. Grouping needed correctly perform Simes parametric tests. test_types character vector test types apply test group. needed correctly perform Simes parametric tests. length match number elements test_groups. test_corr (Optional) list numeric correlation matrices. entry list correspond test group. test group using Bonferroni Simes tests, corresponding entry test_corr NA. test group using parametric tests, corresponding entry test_corr numeric correlation matrix specifying correlation test statistics hypotheses test group. length match number elements test_groups. verbose logical scalar specifying whether details adjusted p-value calculations included results. verbose = TRUE, adjusted p-values provided intersection hypothesis. default verbose = FALSE. test_values logical scalar specifying whether adjusted significance levels provided hypothesis. test_values = TRUE, provides equivalent way performing graphical multiple comparison procedures comparing p-value significance level. p-value hypothesis less equal significance level, hypothesis rejected. default test_values = FALSE.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_closure.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"graph_report object list 4 elements: inputs - Input parameters, list : graph - Initial graph, p - (Unadjusted raw) p-values, alpha - Overall significance level, test_groups - Groups hypotheses different types tests, test_types - Different types tests, test_corr - Correlation matrices parametric tests. outputs - Output parameters, list : adjusted_p - Adjusted p-values, rejected - Rejected hypotheses, graph - Updated graph deleting rejected hypotheses. details - Verbose outputs adjusted p-values intersection hypotheses, verbose = TRUE. test_values - Adjusted significance levels, test_values = TRUE.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_closure.html","id":"details-for-test-specification","dir":"Reference","previous_headings":"","what":"Details for test specification","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"Test specification includes three components: test_groups, test_types, test_corr. Alignment among entries components important correct implementation. two ways provide test specification. first approach \"unnamed\" approach, assumes 3 components ordered way, .e., $n$-th element test_types test_corr apply $n$-th group test_groups. second \"named\" approach uses name element component connect element test_types test_corr correct element test_groups. Consistency ensured correct implementation.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_closure.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_closure.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Perform closed graphical multiple comparison procedures — graph_test_closure","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses # (H1 and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  p <- c(0.018, 0.01, 0.105, 0.006) alpha <- 0.025  # Closed graphical multiple comparison procedure using Bonferroni tests # Same results as `graph_test_shortcut(g, p, alpha)` graph_test_closure(g, p, alpha) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Test types #>   bonferroni: (H1, H2, H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1        0.024   TRUE #>           H2        0.020   TRUE #>           H3        0.105  FALSE #>           H4        0.024   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>   # Closed graphical multiple comparison procedure using parametric tests for # H1 and H2, and Bonferroni tests for H3 and H4 set.seed(1234) corr_list <- list(matrix(c(1, 0.5, 0.5, 1), nrow = 2), NA) graph_test_closure(   graph = g,   p = p,   alpha = alpha,   test_groups = list(1:2, 3:4),   test_types = c(\"parametric\", \"bonferroni\"),   test_corr = corr_list ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Correlation matrix:     H1  H2 #>                       H1 1.0 0.5 #>                       H2 0.5 1.0 #>  #>   Test types #>   parametric: (H1, H2) #>   bonferroni: (H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1      0.02400   TRUE #>           H2      0.01871   TRUE #>           H3      0.10500  FALSE #>           H4      0.02400   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>  # The \"named\" approach to obtain the same results # Note that \"group2\" appears before \"group1\" in `test_groups` set.seed(1234) corr_list <- list(group1 = matrix(c(1, 0.5, 0.5, 1), nrow = 2), group2 = NA) graph_test_closure(   graph = g,   p = p,   alpha = alpha,   test_groups = list(group1 = 1:2, group2 = 3:4),   test_types = c(group2 = \"bonferroni\", group1 = \"parametric\"),   test_corr = corr_list ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Correlation matrix:     H1  H2 #>                       H1 1.0 0.5 #>                       H2 0.5 1.0 #>  #>   Test types #>   parametric: (H1, H2) #>   bonferroni: (H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1      0.02400   TRUE #>           H2      0.01871   TRUE #>           H3      0.10500  FALSE #>           H4      0.02400   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>   # Closed graphical multiple comparison procedure using parametric tests for # H1 and H2, and Simes tests for H3 and H4 set.seed(1234) graph_test_closure(   graph = g,   p = p,   alpha = alpha,   test_groups = list(group1 = 1:2, group2 = 3:4),   test_types = c(group1 = \"parametric\", group2 = \"simes\"),   test_corr = corr_list ) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>       H1  H2  H3  H4 #>   H1 0.0 0.5 0.5 0.0 #>   H2 0.5 0.0 0.0 0.5 #>   H3 0.0 1.0 0.0 0.0 #>   H4 1.0 0.0 0.0 0.0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Correlation matrix:     H1  H2 #>                       H1 1.0 0.5 #>                       H2 0.5 1.0 #>  #>   Test types #>   parametric: (H1, H2) #>        simes: (H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1      0.02400   TRUE #>           H2      0.01871   TRUE #>           H3      0.10500  FALSE #>           H4      0.02400   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_fast.html","id":null,"dir":"Reference","previous_headings":"","what":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","title":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","text":"functions performs similarly graph_test_closure() graph_test_shortcut() optimized efficiently calculating power. example, generating weights calculating adjusted weights can done . Vectorization applied possible.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_fast.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","text":"","code":"graph_test_closure_fast(p, alpha, adjusted_weights, matrix_intersections)  graph_test_shortcut_fast(p, alpha, adjusted_weights)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_fast.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","text":"p numeric vector one-sided p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. alpha numeric value one-sided overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing. Note one-sided tests supported. adjusted_weights adjusted hypothesis weights, second half columns graph_generate_weights() output, adjusted appropriate test types (Bonferroni, Simes, parametric). matrix_intersections matrix hypothesis indicators weighting strategy, first half graph_generate_weights() output.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_fast.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Perform graphical multiple comparison procedures efficiently for power calculation — graph_test_closure_fast","text":"logical integer vector indicating whether hypothesis can rejected .","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":null,"dir":"Reference","previous_headings":"","what":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"Shortcut graphical multiple comparison procedures sequentially rejective procedure based Bretz et al. (2009). $m$ hypotheses, $m$ steps obtain rejection decisions. procedure equivalent closed graphical multiple comparison procedures using Bonferroni tests intersection hypotheses, shortcut procedures faster perform. See vignette(\"shortcut-testing\") illustration shortcut procedures interpretation outputs.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"","code":"graph_test_shortcut(   graph,   p,   alpha = 0.025,   verbose = FALSE,   test_values = FALSE )"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"graph initial graph returned graph_create(). p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. alpha numeric scalar overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. verbose logical scalar specifying whether details intermediate update graphs included results. verbose = TRUE, intermediate update graphs provided deleting hypothesis, rejected. default verbose = FALSE. test_values logical scalar specifying whether adjusted significance levels provided hypothesis. test_values = TRUE, provides equivalent way performing graphical multiple comparison procedures comparing p-value significance level. p-value hypothesis less equal significance level, hypothesis rejected. order rejection based order adjusted p-values smallest largest. default test_values = FALSE.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"S3 object class graph_report list 4 elements: inputs - Input parameters, list : graph - Initial graph, *p - (Unadjusted raw) p-values, alpha - Overall significance level, test_groups - Groups hypotheses different types tests, list hypotheses graph_test_shortcut(), test_types - Different types tests, \"bonferroni\" graph_test_shortcut(). Output parameters outputs, list : adjusted_p - Adjusted p-values, rejected - Rejected hypotheses, graph - Updated graph deleting rejected hypotheses. details - Verbose outputs intermediate updated graphs, verbose = TRUE. test_values - Adjusted significance levels, test_values = TRUE.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_test_shortcut.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Perform shortcut (sequentially rejective) graphical multiple comparison procedures — graph_test_shortcut","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  p <- c(0.018, 0.01, 0.105, 0.006) alpha <- 0.025 graph_test_shortcut(g, p, alpha) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0  0  1  0 #>   H2  0  0  0  1 #>   H3  0  1  0  0 #>   H4  1  0  0  0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Test types #>   bonferroni: (H1, H2, H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1        0.020   TRUE #>           H2        0.020   TRUE #>           H3        0.105  FALSE #>           H4        0.020   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_update.html","id":null,"dir":"Reference","previous_headings":"","what":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"hypothesis deleted, initial graph updated. deleted hypothesis hypothesis weight 0 transition weight 0. Remaining hypotheses updated hypothesis weights transition weights according Algorithm 1 Bretz et al. (2009).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_update.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"","code":"graph_update(graph, delete)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_update.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"graph initial graph returned graph_create(). delete logical integer vector, denoting hypotheses delete. logical vector results \"unordered mode\", means hypotheses corresponding TRUE delete deleted. sequence deletion follow sequence TRUE's delete. case, length logical vector must match number hypotheses graph. integer vector results \"ordered mode\", means delete specifies sequence hypotheses deleted indicating location deleted hypotheses, e.g., 1st, 2nd, etc. case, integer vector can length, must contain valid hypothesis numbers (greater 0, less equal number hypotheses graph).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_update.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"S3 object class updated_graph list 4 elements: initial_graph: initial graph object. updated_graph: updated graph object specified hypotheses deleted. deleted: numeric vector indicating hypotheses deleted. intermediate_graphs: using ordered mode, list intermediate updated graphs hypothesis deleted according sequence specified delete.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_update.html","id":"sequence-of-deletion","dir":"Reference","previous_headings":"","what":"Sequence of deletion","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"multiple hypotheses deleted graph, many sequences deletion initial graph updated updated graph. interest updated graph hypotheses specified delete deleted, updated graph matter sequence deletion used. property proved Bretz et al. (2009). interest intermediate updated graph hypothesis deleted according sequence specified delete, integer vector delete specified detailed outputs provided.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_update.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/graph_update.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Obtain an updated graph by updating an initial graphical after deleting hypotheses — graph_update","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  # Delete the second and third hypotheses in the \"unordered mode\" graph_update(g, delete = c(FALSE, TRUE, TRUE, FALSE)) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 2, 3 #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2:  NA #> H3:  NA #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA NA  1 #>  H2 NA NA NA NA #>  H3 NA NA NA NA #>  H4  1 NA NA  0  # Equivalent way in the \"ordered mode\" to obtain the updated graph after # deleting the second and third hypotheses # Additional intermediate updated graphs are also provided graph_update(g, delete = 2:3) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 2, 3 #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2:  NA #> H3:  NA #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA NA  1 #>  H2 NA NA NA NA #>  H3 NA NA NA NA #>  H4  1 NA NA  0 #>  #> Deletion sequence ($intermediate_graphs) --------------------------------------- #>  #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0  0  1  0 #>   H2  0  0  0  1 #>   H3  0  1  0  0 #>   H4  1  0  0  0 #>  #>     Step 1: Updated graph after removing hypothesis 2 #>  #>     --- Hypothesis weights --- #>     H1: 0.5 #>     H2:  NA #>     H3: 0.0 #>     H4: 0.5 #>  #>     --- Transition weights --- #>        H1 H2 H3 H4 #>     H1  0 NA  1  0 #>     H2 NA NA NA NA #>     H3  0 NA  0  1 #>     H4  1 NA  0  0 #>  #>       Step 2: Updated graph after removing hypotheses 2, 3 #>  #>       --- Hypothesis weights --- #>       H1: 0.5 #>       H2:  NA #>       H3:  NA #>       H4: 0.5 #>  #>       --- Transition weights --- #>          H1 H2 H3 H4 #>       H1  0 NA NA  1 #>       H2 NA NA NA NA #>       H3 NA NA NA NA #>       H4  1 NA NA  0 #>  #>   Final updated graph after removing deleted hypotheses #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2:  NA #>   H3:  NA #>   H4: 0.5 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0 NA NA  1 #>   H2 NA NA NA NA #>   H3 NA NA NA NA #>   H4  1 NA NA  0 #>"},{"path":"https://openpharma.github.io/graphicalMCP/reference/graphicalMCP-package.html","id":null,"dir":"Reference","previous_headings":"","what":"graphicalMCP: Graphical Multiple Comparison Procedures — graphicalMCP-package","title":"graphicalMCP: Graphical Multiple Comparison Procedures — graphicalMCP-package","text":"Multiple comparison procedures (MCPs) control familywise error rate clinical trials. Graphical MCPs include many commonly used procedures special cases; see Bretz et al. (2011) doi:10.1002/bimj.201000239 , Lu (2016) doi:10.1002/sim.6985 , Xi et al. (2017) doi:10.1002/bimj.201600233 . package low-dependency implementation graphical MCPs allow mixed types tests. also includes power simulations visualization graphical MCPs.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/graphicalMCP-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"graphicalMCP: Graphical Multiple Comparison Procedures — graphicalMCP-package","text":"Maintainer: Dong Xi dong.xi1@gilead.com Authors: Ethan Brockmann ethan.brockmann@atorusresearch.com contributors: Gilead Sciences, Inc. [copyright holder, funder]","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/input_val.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate inputs for testing and power simulations — test_input_val","title":"Validate inputs for testing and power simulations — test_input_val","text":"Validate inputs testing power simulations","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/input_val.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate inputs for testing and power simulations — test_input_val","text":"","code":"test_input_val(   graph,   p,   alpha,   test_groups = list(seq_along(graph$hypotheses)),   test_types = c(\"bonferroni\"),   test_corr,   verbose,   test_values )  power_input_val(graph, sim_n, power_marginal, test_corr, success)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/input_val.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate inputs for testing and power simulations — test_input_val","text":"graph initial graph returned graph_create(). p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. alpha numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. test_groups list numeric vectors specifying hypotheses test together. Grouping needed correctly perform Simes parametric tests. test_types character vector test types apply test group. needed correctly perform Simes parametric tests. length match number elements test_groups. test_corr (Optional) list numeric correlation matrices. entry list correspond test group. test group using Bonferroni Simes tests, corresponding entry test_corr NA. test group using parametric tests, corresponding entry test_corr numeric correlation matrix specifying correlation test statistics hypotheses test group. length match number elements test_groups. verbose logical scalar specifying whether details adjusted p-value calculations included results. verbose = TRUE, adjusted p-values provided intersection hypothesis. default verbose = FALSE. test_values logical scalar specifying whether adjusted significance levels provided hypothesis. test_values = TRUE, provides equivalent way performing graphical multiple comparison procedures comparing p-value significance level. p-value hypothesis less equal significance level, hypothesis rejected. default test_values = FALSE. sim_n integer scalar specifying number simulations. default 1e5. power_marginal numeric vector marginal power values use simulating p-values. See Details simulation process. success list user-defined functions specify success criteria. Functions must take one simulation's logical vector results input, return length-one logical vector. instance, \"success\" means rejecting hypotheses 1 2, use sim_success = list(\"1 2\" = function(x) x[1] && x[2]). list named, function body used name. Lambda functions also work starting R 4.1, e.g. sim_success = list(\\(x) x[3] || x[4]).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/input_val.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate inputs for testing and power simulations — test_input_val","text":"Returns graph invisibly","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.initial_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 plot method for class initial_graph — plot.initial_graph","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"plot initial_graph translates hypotheses vertices transitions edges create network plot. Vertices labeled hypothesis names hypothesis weights, edges labeled transition weights. See vignette(\"graph-examples\") illustration commonly used multiple comparison procedure using graphs.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"","code":"# S3 method for class 'initial_graph' plot(   x,   ...,   v_palette = c(\"#6baed6\", \"#cccccc\"),   layout = \"grid\",   nrow = NULL,   ncol = NULL,   edge_curves = NULL,   precision = 4,   eps = NULL,   background_color = \"white\",   margins = c(0, 0, 0, 0) )"},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"x object class initial_graph plot. ... arguments passed igraph::plot.igraph(). v_palette character vector length two specifying colors retained deleted hypotheses. extensive color customization must done vertex.color. layout igraph layout specification (See ?igraph.plotting), \"grid\", lays hypotheses left--right top--bottom. nrow ncol control grid shape. nrow integer scalar specifying number rows vertex grid. row column counts specified, vertices laid close square possible. ncol integer scalar specifying number columns vertex grid. row column counts specified, vertices laid close square possible. edge_curves named numeric vector specifying curvature specific edges. Edge pairs (two vertices share edge possible direction) detected automatically get 0.25 curvature. Adjust edges adding entry name \"vertex1|vertex2, adjust default edge pairs curvature adding entry name \"pairs\" - edge_curves = c(\"pairs\" = 0.5, \"H1|H3\" = 0.25, \"H3|H4\" = 0.75). precision integer scalar indicating number decimal places display. eps numeric scalar. transition weight eps displayed \\(\\epsilon\\), indicates edges infinitesimally small weights. See Bretz et al. (2009) details. background_color character scalar specifying background color whole plotting area. Passed directly graphics::par() (bg). margins length 4 numeric vector specifying margins plot. Defaults 0, since igraph plots tend large margins. passed directly graphics::par() (mar).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"object x class initial_graph, plotting initial graph.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"customization-of-graphs","dir":"Reference","previous_headings":"","what":"Customization of graphs","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"values igraph::plot.igraph() get defaults changed graphicalMCP. values can still changed passing arguments plot.initial_graph(). new defaults: vertex.color = \"#6baed6\", vertex.label.color = \"black\", vertex.size = 20, edge.arrow.size = 1, edge.arrow.width = 1, edge.label.color = \"black\" asp = 0. Neither graphicalMCP igraph anything overlapping edge labels. run problem, vertices practically moved enough avoid collisions edge labels, using edge curves can help. igraph puts edge labels closer tail edge edge straight, closer head edge curved. setting edge's curve small value, effectively straight edge can shifted new position.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Xi, D., Bretz, F. (2019). Symmetric graphs equally weighted tests, application Hochberg procedure. Statistics Medicine, 38(27), 5268-5282.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.initial_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 plot method for class initial_graph — plot.initial_graph","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions) plot(g)   # A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and four secondary hypotheses (H31, H32, H41, and H42) # See Figure 6 in Xi and Bretz (2019). hypotheses <- c(0.5, 0.5, 0, 0, 0, 0) epsilon <- 1e-5 transitions <- rbind(   c(0, 0.5, 0.25, 0, 0.25, 0),   c(0.5, 0, 0, 0.25, 0, 0.25),   c(0, 0, 0, 0, 1, 0),   c(epsilon, 0, 0, 0, 0, 1 - epsilon),   c(0, epsilon, 1 - epsilon, 0, 0, 0),   c(0, 0, 0, 1, 0, 0) ) hyp_names <- c(\"H1\", \"H2\", \"H31\", \"H32\", \"H41\", \"H42\") g <- graph_create(hypotheses, transitions, hyp_names)  plot_layout <- rbind(   c(0.15, 0.5),   c(0.65, 0.5),   c(0, 0),   c(0.5, 0),   c(0.3, 0),   c(0.8, 0) )  plot(g, layout = plot_layout, eps = epsilon, edge_curves = c(pairs = .5))"},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.updated_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 plot method for the class updated_graph — plot.updated_graph","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"Plotting updated graph light wrapper around plot.initial_graph(), changing default vertex color use gray deleted hypotheses.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"","code":"# S3 method for class 'updated_graph' plot(x, ...)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"x object class updated_graph plot. ... Arguments passed plot.initial_graph v_palette character vector length two specifying colors retained deleted hypotheses. extensive color customization must done vertex.color. layout igraph layout specification (See ?igraph.plotting), \"grid\", lays hypotheses left--right top--bottom. nrow ncol control grid shape. nrow integer scalar specifying number rows vertex grid. row column counts specified, vertices laid close square possible. ncol integer scalar specifying number columns vertex grid. row column counts specified, vertices laid close square possible. edge_curves named numeric vector specifying curvature specific edges. Edge pairs (two vertices share edge possible direction) detected automatically get 0.25 curvature. Adjust edges adding entry name \"vertex1|vertex2, adjust default edge pairs curvature adding entry name \"pairs\" - edge_curves = c(\"pairs\" = 0.5, \"H1|H3\" = 0.25, \"H3|H4\" = 0.75). precision integer scalar indicating number decimal places display. eps numeric scalar. transition weight eps displayed \\(\\epsilon\\), indicates edges infinitesimally small weights. See Bretz et al. (2009) details. background_color character scalar specifying background color whole plotting area. Passed directly graphics::par() (bg). margins length 4 numeric vector specifying margins plot. Defaults 0, since igraph plots tend large margins. passed directly graphics::par() (mar).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"object x class updated_graph, plotting updated graph.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/plot.updated_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 plot method for the class updated_graph — plot.updated_graph","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  # Delete the second and third hypotheses in the \"unordered mode\" plot(   graph_update(     g,     c(FALSE, TRUE, TRUE, FALSE)   ),   layout = \"grid\" )"},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.graph_report.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 print method for the class graph_report — print.graph_report","title":"S3 print method for the class graph_report — print.graph_report","text":"printed graph_report displays initial graph, p-values significance levels, rejection decisions, optional detailed test results.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.graph_report.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 print method for the class graph_report — print.graph_report","text":"","code":"# S3 method for class 'graph_report' print(x, ..., precision = 4, indent = 2, rows = 10)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.graph_report.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 print method for the class graph_report — print.graph_report","text":"x object class graph_report print. ... values passed methods (currently unused) precision integer scalar indicating number decimal places display. indent integer scalar indicating many spaces indent results. rows integer scalar indicating many rows detailed test results print.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.graph_report.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 print method for the class graph_report — print.graph_report","text":"object x class graph_report, printing report conducting graphical multiple comparison procedure.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.graph_report.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 print method for the class graph_report — print.graph_report","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.graph_report.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 print method for the class graph_report — print.graph_report","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  p <- c(0.018, 0.01, 0.105, 0.006) alpha <- 0.025 graph_test_shortcut(g, p, alpha) #>  #> Test parameters ($inputs) ------------------------------------------------------ #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0  0  1  0 #>   H2  0  0  0  1 #>   H3  0  1  0  0 #>   H4  1  0  0  0 #>  #>   Alpha = 0.025 #>  #>                           H1    H2    H3    H4 #>   Unadjusted p-values: 0.018 0.010 0.105 0.006 #>  #>   Test types #>   bonferroni: (H1, H2, H3, H4) #>  #> Test summary ($outputs) -------------------------------------------------------- #>   Hypothesis Adj. P-value Reject #>           H1        0.020   TRUE #>           H2        0.020   TRUE #>           H3        0.105  FALSE #>           H4        0.020   TRUE #>  #>   Final updated graph after removing rejected hypotheses #>  #>   --- Hypothesis weights --- #>   H1: NA #>   H2: NA #>   H3:  1 #>   H4: NA #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1 NA NA NA NA #>   H2 NA NA NA NA #>   H3 NA NA  0 NA #>   H4 NA NA NA NA #>"},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.initial_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 print method for the class initial_graph — print.initial_graph","title":"S3 print method for the class initial_graph — print.initial_graph","text":"printed initial_graph displays header stating \"Initial graph\", hypothesis weights, transition weights.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.initial_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 print method for the class initial_graph — print.initial_graph","text":"","code":"# S3 method for class 'initial_graph' print(x, ..., precision = 4, indent = 0)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.initial_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 print method for the class initial_graph — print.initial_graph","text":"x object class initial_graph print. ... values passed methods (currently unused). precision integer scalar indicating number decimal places display. indent integer scalar indicating many spaces indent results.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.initial_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 print method for the class initial_graph — print.initial_graph","text":"object x class initial_graph, printing initial graph.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.initial_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 print method for the class initial_graph — print.initial_graph","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.initial_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 print method for the class initial_graph — print.initial_graph","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) hyp_names <- c(\"H11\", \"H12\", \"H21\", \"H22\") g <- graph_create(hypotheses, transitions, hyp_names) g #> Initial graph #>  #> --- Hypothesis weights --- #> H11: 0.5 #> H12: 0.5 #> H21: 0.0 #> H22: 0.0 #>  #> --- Transition weights --- #>      H11 H12 H21 H22 #>  H11   0   0   1   0 #>  H12   0   0   0   1 #>  H21   0   1   0   0 #>  H22   1   0   0   0"},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.power_report.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 print method for the class power_report — print.power_report","title":"S3 print method for the class power_report — print.power_report","text":"printed power_report displays initial graph, testing simulation options, power outputs, optional detailed simulations test results.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.power_report.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 print method for the class power_report — print.power_report","text":"","code":"# S3 method for class 'power_report' print(x, ..., precision = 4, indent = 2, rows = 10)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.power_report.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 print method for the class power_report — print.power_report","text":"x object class power_report print ... values passed methods (currently unused) precision integer scalar indicating number decimal places display. indent integer scalar indicating many spaces indent results. rows integer scalar indicating many rows detailed test results print.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.power_report.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 print method for the class power_report — print.power_report","text":"object x class power_report, printing report conducting power simulations based graphical multiple comparison procedure.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.power_report.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 print method for the class power_report — print.power_report","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011a). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913. Bretz, F., Maurer, W., Hommel, G. (2011b). Test power considerations multiple endpoint analyses using sequentially rejective graphical procedures. Statistics Medicine, 30(13), 1489-1501.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.power_report.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 print method for the class power_report — print.power_report","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 4 in Bretz et al. (2011). alpha <- 0.025 hypotheses <- c(0.5, 0.5, 0, 0) delta <- 0.5 transitions <- rbind(   c(0, delta, 1 - delta, 0),   c(delta, 0, 0, 1 - delta),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  marginal_power <- c(0.8, 0.8, 0.7, 0.9) corr1 <- matrix(0.5, nrow = 2, ncol = 2) diag(corr1) <- 1 corr <- rbind(   cbind(corr1, 0.5 * corr1),   cbind(0.5 * corr1, corr1) ) success_fns <- list(   # Probability to reject both H1 and H2   `H1andH2` = function(x) x[1] & x[2],   # Probability to reject both (H1 and H3) or (H2 and H4)   `(H1andH3)or(H2andH4)` = function(x) (x[1] & x[3]) | (x[2] & x[4]) ) set.seed(1234) # Bonferroni tests power_output <- graph_calculate_power(   g,   alpha,   sim_corr = corr,   sim_n = 1e5,   power_marginal = marginal_power,   sim_success = success_fns )"},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.updated_graph.html","id":null,"dir":"Reference","previous_headings":"","what":"S3 print method for the class updated_graph — print.updated_graph","title":"S3 print method for the class updated_graph — print.updated_graph","text":"printed updated_graph displays initial graph, (final) updated graph, sequence intermediate updated graphs hypotheses deleted (available).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.updated_graph.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"S3 print method for the class updated_graph — print.updated_graph","text":"","code":"# S3 method for class 'updated_graph' print(x, ..., precision = 6, indent = 2)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.updated_graph.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"S3 print method for the class updated_graph — print.updated_graph","text":"x object class updated_graph print. ... values passed methods (currently unused). precision integer scalar indicating number decimal places display. indent integer scalar indicating many spaces indent results.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.updated_graph.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"S3 print method for the class updated_graph — print.updated_graph","text":"object x class updated_graph, printing updated graph.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.updated_graph.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"S3 print method for the class updated_graph — print.updated_graph","text":"Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., Rohmeyer, K. (2011a). Graphical approaches multiple comparison procedures using weighted Bonferroni, Simes, parametric tests. Biometrical Journal, 53(6), 894-913.","code":""},{"path":[]},{"path":"https://openpharma.github.io/graphicalMCP/reference/print.updated_graph.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"S3 print method for the class updated_graph — print.updated_graph","text":"","code":"# A graphical multiple comparison procedure with two primary hypotheses (H1 # and H2) and two secondary hypotheses (H3 and H4) # See Figure 1 in Bretz et al. (2011). hypotheses <- c(0.5, 0.5, 0, 0) transitions <- rbind(   c(0, 0, 1, 0),   c(0, 0, 0, 1),   c(0, 1, 0, 0),   c(1, 0, 0, 0) ) g <- graph_create(hypotheses, transitions)  # Delete the second and third hypotheses in the \"unordered mode\" graph_update(g, delete = c(FALSE, TRUE, TRUE, FALSE)) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 2, 3 #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2:  NA #> H3:  NA #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA NA  1 #>  H2 NA NA NA NA #>  H3 NA NA NA NA #>  H4  1 NA NA  0  # Equivalent way in the \"ordered mode\" to obtain the updated graph after # deleting the second and third hypotheses # Additional intermediate updated graphs are also provided graph_update(g, delete = 2:3) #> Initial and final graphs ------------------------------------------------------- #>  #> Initial graph #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2: 0.5 #> H3: 0.0 #> H4: 0.0 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0  0  1  0 #>  H2  0  0  0  1 #>  H3  0  1  0  0 #>  H4  1  0  0  0 #>  #> Updated graph after deleting hypotheses 2, 3 #>  #> --- Hypothesis weights --- #> H1: 0.5 #> H2:  NA #> H3:  NA #> H4: 0.5 #>  #> --- Transition weights --- #>     H1 H2 H3 H4 #>  H1  0 NA NA  1 #>  H2 NA NA NA NA #>  H3 NA NA NA NA #>  H4  1 NA NA  0 #>  #> Deletion sequence ($intermediate_graphs) --------------------------------------- #>  #>   Initial graph #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2: 0.5 #>   H3: 0.0 #>   H4: 0.0 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0  0  1  0 #>   H2  0  0  0  1 #>   H3  0  1  0  0 #>   H4  1  0  0  0 #>  #>     Step 1: Updated graph after removing hypothesis 2 #>  #>     --- Hypothesis weights --- #>     H1: 0.5 #>     H2:  NA #>     H3: 0.0 #>     H4: 0.5 #>  #>     --- Transition weights --- #>        H1 H2 H3 H4 #>     H1  0 NA  1  0 #>     H2 NA NA NA NA #>     H3  0 NA  0  1 #>     H4  1 NA  0  0 #>  #>       Step 2: Updated graph after removing hypotheses 2, 3 #>  #>       --- Hypothesis weights --- #>       H1: 0.5 #>       H2:  NA #>       H3:  NA #>       H4: 0.5 #>  #>       --- Transition weights --- #>          H1 H2 H3 H4 #>       H1  0 NA NA  1 #>       H2 NA NA NA NA #>       H3 NA NA NA NA #>       H4  1 NA NA  0 #>  #>   Final updated graph after removing deleted hypotheses #>  #>   --- Hypothesis weights --- #>   H1: 0.5 #>   H2:  NA #>   H3:  NA #>   H4: 0.5 #>  #>   --- Transition weights --- #>      H1 H2 H3 H4 #>   H1  0 NA NA  1 #>   H2 NA NA NA NA #>   H3 NA NA NA NA #>   H4  1 NA NA  0 #>"},{"path":"https://openpharma.github.io/graphicalMCP/reference/test_values.html","id":null,"dir":"Reference","previous_headings":"","what":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"intersection hypothesis can tested mixture test types including Bonferroni, parametric Simes tests. function organize outputs testing prepare graph_report.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/test_values.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"","code":"test_values_bonferroni(p, hypotheses, alpha, intersection = NA)  test_values_parametric(p, hypotheses, alpha, intersection = NA, test_corr)  test_values_simes(p, hypotheses, alpha, intersection = NA)"},{"path":"https://openpharma.github.io/graphicalMCP/reference/test_values.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"p numeric vector p-values (unadjusted, raw), whose values 0 & 1. length match number hypotheses graph. hypotheses numeric vector hypothesis weights graphical multiple comparison procedure. Must vector values 0 & 1 (inclusive). length match row column lengths transitions. sum hypothesis weights exceed 1. alpha numeric value overall significance level, 0 & 1. default 0.025 one-sided hypothesis testing problems; another common choice 0.05 two-sided hypothesis testing problems. Note parametric tests used, one-sided tests supported. intersection (optional) numeric scalar used name intersection hypothesis weighting strategy. test_corr (Optional) list numeric correlation matrices. entry list correspond test group. test group using Bonferroni Simes tests, corresponding entry test_corr NA. test group using parametric tests, corresponding entry test_corr numeric correlation matrix specifying correlation test statistics hypotheses test group. length match number elements test_groups.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/test_values.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"data frame rows corresponding individual hypotheses involved intersection hypothesis hypothesis weights hypotheses. following columns: Intersection - Name intersection hypothesis, Hypothesis - Name individual hypothesis, Test - Test type individual hypothesis, p - (Unadjusted raw) p-values individual hypothesis, c_value- C value parametric tests, Weight - Hypothesis weight individual hypothesis, Alpha - Overall significance level \\(\\alpha\\), Inequality_holds - Indicator show p-value less equal significance level. Bonferroni Simes tests, significance level hypothesis weight times \\(\\alpha\\). parametric tests, significance level c value times hypothesis weight times \\(\\alpha\\).","code":""},{"path":"https://openpharma.github.io/graphicalMCP/reference/test_values.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Organize outputs for testing an intersection hypothesis — test_values_bonferroni","text":"Bretz, F., Maurer, W., Brannath, W., Posch, M. (2009). graphical approach sequentially rejective multiple test procedures. Statistics Medicine, 28(4), 586-604. Lu, K. (2016). Graphical approaches using Bonferroni mixture weighted Simes tests. Statistics Medicine, 35(22), 4041-4055. Xi, D., Glimm, E., Maurer, W., Bretz, F. (2017). unified framework weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-010","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.1.0","title":"graphicalMCP 0.1.0","text":"First release","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-011","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.1.1","title":"graphicalMCP 0.1.1","text":"Added compilation vignettes (#73) Removed duplicated columns “*” test values (#75)","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-012","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.1.2","title":"graphicalMCP 0.1.2","text":"Updated function documentation Updated references","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-020","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.0","title":"graphicalMCP 0.2.0","text":"Corrected typos Updated function documentation CRAN release","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-021","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.1","title":"graphicalMCP 0.2.1","text":"Corrected typos First CRAN release","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-022","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.2","title":"graphicalMCP 0.2.2","text":"Updated citations Resubmission first CRAN release","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-023","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.3","title":"graphicalMCP 0.2.3","text":"Included cran-comments.ms .Rbuildignore Resubmission first CRAN release","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-024","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.4","title":"graphicalMCP 0.2.4","text":"Updated documentation according issue #84 Resubmission first CRAN release","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-025","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.5","title":"graphicalMCP 0.2.5","text":"CRAN release: 2024-07-13 Updated adjust_weights_parametric_util.Rd Resubmission first CRAN release","code":""},{"path":"https://openpharma.github.io/graphicalMCP/news/index.html","id":"graphicalmcp-026","dir":"Changelog","previous_headings":"","what":"graphicalMCP 0.2.6","title":"graphicalMCP 0.2.6","text":"Github repo transferred openpharma Submission CRAN release","code":""}]
diff --git a/sitemap.xml b/sitemap.xml
index 6e88e27..f483c9a 100644
--- a/sitemap.xml
+++ b/sitemap.xml
@@ -1,40 +1,40 @@
 <urlset xmlns = 'http://www.sitemaps.org/schemas/sitemap/0.9'>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/404.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/LICENSE.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/articles/closed-testing.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/articles/comparisons.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/articles/generate-closure.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/articles/glossary.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/articles/graph-examples.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/articles/graphicalMCP.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/articles/index.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/articles/shortcut-testing.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/authors.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/index.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/news/index.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/adjust_p.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/as_graph.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/edge_pairs.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/example_graphs.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graph_calculate_power.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graph_create.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graph_generate_weights.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graph_rejection_orderings.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_closure.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_fast.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graph_test_shortcut.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graph_update.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/graphicalMCP-package.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/index.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/input_val.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/plot.initial_graph.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/plot.updated_graph.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/print.graph_report.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/print.initial_graph.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/print.power_report.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/print.updated_graph.html</loc></url>
-<url><loc>https://gilead-biostats.github.io/graphicalMCP/reference/test_values.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/404.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/LICENSE.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/articles/closed-testing.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/articles/comparisons.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/articles/generate-closure.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/articles/glossary.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/articles/graph-examples.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/articles/graphicalMCP.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/articles/index.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/articles/shortcut-testing.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/authors.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/index.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/news/index.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/adjust_p.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/adjust_weights.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/adjust_weights_parametric_util.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/as_graph.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/edge_pairs.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/example_graphs.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graph_calculate_power.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graph_create.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graph_generate_weights.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graph_rejection_orderings.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graph_test_closure.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graph_test_fast.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graph_test_shortcut.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graph_update.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/graphicalMCP-package.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/index.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/input_val.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/plot.initial_graph.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/plot.updated_graph.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/print.graph_report.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/print.initial_graph.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/print.power_report.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/print.updated_graph.html</loc></url>
+<url><loc>https://openpharma.github.io/graphicalMCP/reference/test_values.html</loc></url>
 </urlset>