Resolved merge conflict in wpgsd_corr_example.Rmd

vignettes/wpgsd_corr_example.Rmd

@@ -3,10 +3,10 @@ title: "Correlation Matrix Calculation"
 author: "Chenguang Zhang"
 date: "2024-05-14"
 output: html_document
-bibliography: citations.bib
+bibliography: wpgsd.bib
 ---
 
-The weighted parametric group sequential design (WPGSD) (@anderson_unified_2022) approach allows one to take advantage of the known correlation structure in constructing efficacy bounds to control family-wise error rate (FWER) for a group sequential design. Here correlation may be due to common observations in nested populations, due to common observations in overlapping populations, or due to common observations in the control arm. 
+The weighted parametric group sequential design (WPGSD) (@anderson2022unified) approach allows one to take advantage of the known correlation structure in constructing efficacy bounds to control family-wise error rate (FWER) for a group sequential design. Here correlation may be due to common observations in nested populations, due to common observations in overlapping populations, or due to common observations in the control arm. 
 
 ## Notation
 
@@ -19,7 +19,7 @@ $$Corr(Z_{ik},Z_{i'k'})=\frac{n_{i \wedge i',k \wedge k'}}{\sqrt{n_{ik}*n_{i'k'}
 
 ## Examples
 
-In a 2-arm controlled clinical trial example with one primary endpoint (@anderson_unified_2022), there are 3 patient populations defined by the status of two biomarkers A and B :
+In a 2-arm controlled clinical trial example with one primary endpoint (@anderson2022unified), there are 3 patient populations defined by the status of two biomarkers A and B :
 
 * Biomarker A positive, the population 1,
 * Biomarker B positive, the population 2,
@@ -145,15 +145,14 @@ event %>%
   gt() %>%
   tab_header(title = "Number of events at each population & analyses")
 ```
-* "H1" refers to one hypothesis, selected depending on the interest, while "H2" refers to the other hypothesis, both of which are listed for multiplicity testing. For example, "H1" means the experimental treatment is superior to the control in the population 1/experimental arm 1; "H2" means the experimental treatment is superior to the control in the population 2/experimental arm 2; 
 
+* "H1" refers to one hypothesis, selected depending on the interest, while "H2" refers to the other hypothesis, both of which are listed for multiplicity testing. For example, "H1" means the experimental treatment is superior to the control in the population 1/experimental arm 1; "H2" means the experimental treatment is superior to the control in the population 2/experimental arm 2; 
 * "Analysis" means different analysis stages, for example, 1 means the interim analysis, and 2 means the final analysis;
 
 * "Event" is the common events overlap by H1 and H2.
 
+For example: H1=1, H2=1, Analysis=1, Event=100 indicates that in the first population, there are 100 cases where the experimental treatment is superior to the control in the interim analysis.
 
-For example: H1=1, H2=1, Analysis=1, Event=100 means in the first population, there are 100 cases of experimental treatment is superior to the control in the interim analysis.
-
-Another example: H1=1, H2=2, Analysis=2, Event=160 means the overlap number of experimental treatment superior to the control in population 1 and 2 in the final analysis is 160.
+Another example: H1=1, H2=2, Analysis=2, Event=160 indicates that the number of overlapping cases where the experimental treatment is superior to the control in population 1 and 2 in the final analysis is 160.
 
-*To be noticed, the column names in this function are fixed to be 'H1, H2, Analysis, Event'.
+*To be noticed, the column names in this function are fixed to be 'H1, H2, Analysis, Event'.