A comprehensive statistical framework for designing and analyzing in vivo drug combination experiments.
You can install the development version of SynergyLMM from GitHub with:
# install.packages("pak")
pak::pak("RafRomB/SynergyLMM")This is a basic example which shows how to use SynergyLMM to analyze synergy in a 2-drug combination in vivo experiment.
library(SynergyLMM)We start by loading the data (in long format). We will use the example data provided in the package:
data("grwth_data")The first step is fitting the model from our data:
# Most simple model
lmm <- lmmModel(
data = grwth_data,
sample_id = "subject",
time = "Time",
treatment = "Treatment",
tumor_vol = "TumorVolume",
trt_control = "Control",
drug_a = "DrugA",
drug_b = "DrugB",
combination = "Combination"
)
We can
obtain the model estimates using:
lmmModel_estimates(lmm)
#> Control DrugA DrugB Combination sd_ranef sd_resid
#> estimate 0.07855242 0.07491984 0.06306986 0.03487933 0.03946667 0.2124122Bliss independence model
lmmSynergy(lmm, method = "Bliss")
#> $Contrasts
#> $Contrasts$Time3
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0649 0.0574 -1.13 0.258 2.0 -0.177 0.0476
#>
#>
#>
#> $Contrasts$Time6
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0326 0.0327 -0.996 0.319 1.6 -0.0968 0.0316
#>
#>
#>
#> $Contrasts$Time9
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.053 0.0207 -2.56 0.0103 6.6 -0.0935 -0.0125
#>
#>
#>
#> $Contrasts$Time12
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.039 0.0153 -2.55 0.0108 6.5 -0.069 -0.00901
#>
#>
#>
#> $Contrasts$Time15
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0401 0.0127 -3.15 0.00161 9.3 -0.065 -0.0152
#>
#>
#>
#> $Contrasts$Time18
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0366 0.0101 -3.62 <0.001 11.7 -0.0564 -0.0168
#>
#>
#>
#> $Contrasts$Time21
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0299 0.00846 -3.54 <0.001 11.3 -0.0465 -0.0134
#>
#>
#>
#> $Contrasts$Time24
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0278 0.00766 -3.63 <0.001 11.8 -0.0428 -0.0128
#>
#>
#>
#> $Contrasts$Time27
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0275 0.0069 -3.99 <0.001 13.9 -0.0411 -0.014
#>
#>
#>
#> $Contrasts$Time30
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0246 0.00645 -3.81 <0.001 12.8 -0.0372 -0.0119
#>
#>
#>
#>
#> $Synergy
#> Model Metric Estimate lwr upr pval Time
#> 1 Bliss CI 0.8229665 0.5872062 1.1533834 2.579032e-01 3
#> 2 Bliss CI 0.8221770 0.5593887 1.2084173 3.190110e-01 6
#> 3 Bliss CI 0.6208242 0.4312539 0.8937256 1.033643e-02 9
#> 4 Bliss CI 0.6263864 0.4371340 0.8975735 1.081171e-02 12
#> 5 Bliss CI 0.5478166 0.3769349 0.7961668 1.605259e-03 15
#> 6 Bliss CI 0.5176217 0.3623021 0.7395271 2.972850e-04 18
#> 7 Bliss CI 0.5332866 0.3764318 0.7555010 4.037916e-04 21
#> 8 Bliss CI 0.5132132 0.3580036 0.7357127 2.831685e-04 24
#> 9 Bliss CI 0.4754203 0.3300312 0.6848579 6.535614e-05 27
#> 10 Bliss CI 0.4786726 0.3275199 0.6995835 1.416473e-04 30
#> 11 Bliss SS 1.1313609 -0.8286031 3.0913249 2.579032e-01 3
#> 12 Bliss SS 0.9964923 -0.9634717 2.9564563 3.190110e-01 6
#> 13 Bliss SS 2.5643664 0.6044025 4.5243304 1.033643e-02 9
#> 14 Bliss SS 2.5487265 0.5887625 4.5086905 1.081171e-02 12
#> 15 Bliss SS 3.1549495 1.1949856 5.1149135 1.605259e-03 15
#> 16 Bliss SS 3.6176544 1.6576904 5.5776184 2.972850e-04 18
#> 17 Bliss SS 3.5375932 1.5776292 5.4975572 4.037916e-04 21
#> 18 Bliss SS 3.6302302 1.6702662 5.5901942 2.831685e-04 24
#> 19 Bliss SS 3.9925877 2.0326237 5.9525517 6.535614e-05 27
#> 20 Bliss SS 3.8052741 1.8453101 5.7652380 1.416473e-04 30
#>
#> attr(,"SynergyLMM")
#> [1] "lmmSynergy"
Highest Single Agent model
lmmSynergy(lmm, method = "HSA")
#> $Contrasts
#> $Contrasts$Time3
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0197 0.0406 -0.486 0.627 0.7 -0.0993 0.0598
#>
#>
#>
#> $Contrasts$Time6
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0347 0.0232 -1.5 0.134 2.9 -0.0801 0.0107
#>
#>
#>
#> $Contrasts$Time9
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0468 0.0146 -3.2 0.00135 9.5 -0.0754 -0.0182
#>
#>
#>
#> $Contrasts$Time12
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0389 0.0108 -3.6 <0.001 11.6 -0.0601 -0.0177
#>
#>
#>
#> $Contrasts$Time15
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0388 0.00899 -4.32 <0.001 16.0 -0.0565 -0.0212
#>
#>
#>
#> $Contrasts$Time18
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.034 0.00715 -4.75 <0.001 18.9 -0.048 -0.0199
#>
#>
#>
#> $Contrasts$Time21
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0309 0.00598 -5.17 <0.001 22.0 -0.0426 -0.0192
#>
#>
#>
#> $Contrasts$Time24
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0288 0.00541 -5.31 <0.001 23.1 -0.0394 -0.0181
#>
#>
#>
#> $Contrasts$Time27
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0285 0.00488 -5.84 <0.001 27.5 -0.038 -0.0189
#>
#>
#>
#> $Contrasts$Time30
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b3 -0.0282 0.00456 -6.18 <0.001 30.5 -0.0371 -0.0192
#>
#>
#>
#>
#> $Synergy
#> Model Metric Estimate lwr upr pval Time
#> 1 HSA CI 0.9425733 0.7424364 1.1966606 6.272090e-01 3
#> 2 HSA CI 0.8120893 0.6184990 1.0662733 1.341054e-01 6
#> 3 HSA CI 0.6562436 0.5071957 0.8490916 1.353136e-03 9
#> 4 HSA CI 0.6268633 0.4860749 0.8084303 3.199611e-04 12
#> 5 HSA CI 0.5584017 0.4286814 0.7273758 1.561099e-05 15
#> 6 HSA CI 0.5427317 0.4217207 0.6984663 2.053330e-06 18
#> 7 HSA CI 0.5224846 0.4084194 0.6684065 2.394746e-07 21
#> 8 HSA CI 0.5015173 0.3887649 0.6469709 1.088190e-07 24
#> 9 HSA CI 0.4637274 0.3582368 0.6002819 5.363760e-09 27
#> 10 HSA CI 0.4292500 0.3282301 0.5613609 6.512811e-10 30
#> 11 HSA SS 0.4856590 -1.4743050 2.4456229 6.272090e-01 3
#> 12 HSA SS 1.4981074 -0.4618566 3.4580714 1.341054e-01 6
#> 13 HSA SS 3.2044652 1.2445012 5.1644292 1.353136e-03 9
#> 14 HSA SS 3.5985787 1.6386147 5.5585426 3.199611e-04 12
#> 15 HSA SS 4.3198859 2.3599219 6.2798499 1.561099e-05 15
#> 16 HSA SS 4.7481035 2.7881395 6.7080675 2.053330e-06 18
#> 17 HSA SS 5.1657517 3.2057877 7.1257157 2.394746e-07 21
#> 18 HSA SS 5.3113453 3.3513813 7.2713092 1.088190e-07 24
#> 19 HSA SS 5.8354748 3.8755108 7.7954388 5.363760e-09 27
#> 20 HSA SS 6.1774914 4.2175274 8.1374554 6.512811e-10 30
#>
#> attr(,"SynergyLMM")
#> [1] "lmmSynergy"
Response Additivity
set.seed(123)
lmmSynergy(lmm, method = "RA", ra_nsim = 1000)
#> $Contrasts
#> NULL
#>
#> $Synergy
#> Model Metric Estimate lwr upr pval Time
#> 1 RA CI 0.9089179 0.7813434 1.0846505 0.218 3
#> 2 RA CI 0.9007998 0.7494092 1.1251799 0.306 6
#> 3 RA CI 0.7757545 0.6392168 0.9565893 0.020 9
#> 4 RA CI 0.7654962 0.6281900 0.9833419 0.036 12
#> 5 RA CI 0.7126844 0.5680455 0.9012317 0.006 15
#> 6 RA CI 0.6823963 0.5555088 0.8819816 0.004 18
#> 7 RA CI 0.6966459 0.5587736 0.9216748 0.010 21
#> 8 RA CI 0.6761002 0.5264396 0.8850202 0.004 24
#> 9 RA CI 0.6378541 0.4932419 0.8886775 0.008 27
#> 10 RA CI 0.6571783 0.4884503 0.9583366 0.040 30
#> 11 RA SS 1.1273375 -0.8996513 3.0688249 0.218 3
#> 12 RA SS 1.0017861 -1.0248908 2.8463802 0.306 6
#> 13 RA SS 2.2770890 0.3762641 4.3157772 0.020 9
#> 14 RA SS 2.2314878 0.1198712 4.1467019 0.036 12
#> 15 RA SS 2.5085219 0.7331476 4.5810408 0.006 15
#> 16 RA SS 2.8407722 0.8458634 4.7868026 0.004 18
#> 17 RA SS 2.5801212 0.4850124 4.4559420 0.010 21
#> 18 RA SS 2.5364751 0.7211025 4.5463547 0.004 24
#> 19 RA SS 2.6375599 0.5889487 4.6388547 0.008 27
#> 20 RA SS 2.1181025 0.1839581 4.0786818 0.040 30
#>
#> attr(,"SynergyLMM")
#> [1] "lmmSynergy"
Using Robust Estimates
lmmSynergy(lmm, method = "Bliss", robust = TRUE)
#> Registered S3 method overwritten by 'clubSandwich':
#> method from
#> bread.mlm sandwich
#> $Contrasts
#> $Contrasts$Time3
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0649 0.0574 -1.13 0.258 2.0 -0.177 0.0476
#>
#>
#>
#> $Contrasts$Time6
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0326 0.0327 -0.996 0.319 1.6 -0.0968 0.0316
#>
#>
#>
#> $Contrasts$Time9
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.053 0.0207 -2.56 0.0103 6.6 -0.0935 -0.0125
#>
#>
#>
#> $Contrasts$Time12
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.039 0.0153 -2.55 0.0108 6.5 -0.069 -0.00901
#>
#>
#>
#> $Contrasts$Time15
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0401 0.0127 -3.15 0.00161 9.3 -0.065 -0.0152
#>
#>
#>
#> $Contrasts$Time18
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0366 0.0101 -3.62 <0.001 11.7 -0.0564 -0.0168
#>
#>
#>
#> $Contrasts$Time21
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0299 0.00846 -3.54 <0.001 11.3 -0.0465 -0.0134
#>
#>
#>
#> $Contrasts$Time24
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0278 0.00766 -3.63 <0.001 11.8 -0.0428 -0.0128
#>
#>
#>
#> $Contrasts$Time27
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0275 0.0069 -3.99 <0.001 13.9 -0.0411 -0.014
#>
#>
#>
#> $Contrasts$Time30
#>
#> Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
#> b4=b2+b3-b1 -0.0246 0.00645 -3.81 <0.001 12.8 -0.0372 -0.0119
#>
#>
#>
#>
#> $Synergy
#> Model Metric Estimate lwr upr pval Time
#> 1 Bliss CI 0.8229665 0.5872062 1.1533834 2.579032e-01 3
#> 2 Bliss CI 0.8221770 0.5593887 1.2084173 3.190110e-01 6
#> 3 Bliss CI 0.6208242 0.4312539 0.8937256 1.033643e-02 9
#> 4 Bliss CI 0.6263864 0.4371340 0.8975735 1.081171e-02 12
#> 5 Bliss CI 0.5478166 0.3769351 0.7961665 1.605239e-03 15
#> 6 Bliss CI 0.5176217 0.3623022 0.7395270 2.972826e-04 18
#> 7 Bliss CI 0.5332866 0.3764318 0.7555010 4.037908e-04 21
#> 8 Bliss CI 0.5132132 0.3580036 0.7357127 2.831685e-04 24
#> 9 Bliss CI 0.4754203 0.3300312 0.6848579 6.535614e-05 27
#> 10 Bliss CI 0.4786726 0.3275199 0.6995835 1.416473e-04 30
#> 11 Bliss SS 1.1313609 -0.8286031 3.0913249 2.579032e-01 3
#> 12 Bliss SS 0.9964923 -0.9634717 2.9564563 3.190110e-01 6
#> 13 Bliss SS 2.5643665 0.6044025 4.5243305 1.033643e-02 9
#> 14 Bliss SS 2.5487265 0.5887625 4.5086905 1.081171e-02 12
#> 15 Bliss SS 3.1549531 1.1949891 5.1149171 1.605239e-03 15
#> 16 Bliss SS 3.6176565 1.6576925 5.5776205 2.972826e-04 18
#> 17 Bliss SS 3.5375938 1.5776298 5.4975577 4.037908e-04 21
#> 18 Bliss SS 3.6302303 1.6702663 5.5901942 2.831685e-04 24
#> 19 Bliss SS 3.9925877 2.0326237 5.9525517 6.535614e-05 27
#> 20 Bliss SS 3.8052741 1.8453101 5.7652380 1.416473e-04 30
#>
#> attr(,"SynergyLMM")
#> [1] "lmmSynergy"
We can perform the model diagnostics using the following functions:
Random Effects
ranefDiagnostics(lmm)
#>
#> Title:
#> Shapiro - Wilk Normality Test of random effects
#>
#> Test Results:
#> STATISTIC:
#> W: 0.9672
#> P VALUE:
#> 0.4269
#>
#>
#> Title:
#> D'Agostino Normality Test of random effects
#>
#> Test Results:
#> STATISTIC:
#> Chi2 | Omnibus: 2.2635
#> Z3 | Skewness: 0.6316
#> Z4 | Kurtosis: -1.3655
#> P VALUE:
#> Omnibus Test: 0.3225
#> Skewness Test: 0.5276
#> Kurtosis Test: 0.1721
#>
#>
#> Title:
#> Anderson - Darling Normality Test of random effects
#>
#> Test Results:
#> STATISTIC:
#> A: 0.3783
#> P VALUE:
#> 0.3867
#>
#>
#> Normalized Residuals Levene Homoscedasticity Test by Sample
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 31 0.874 0.6633
#> 288
#>
#> Normalized Residuals Fligner-Killeen Homoscedasticity Test by Sample
#>
#> Fligner-Killeen test of homogeneity of variances
#>
#> data: normalized_resid by SampleID
#> Fligner-Killeen:med chi-squared = 28.521, df = 31, p-value = 0.5942
Residuals Diagnostics
residDiagnostics(lmm)
#>
#> Title:
#> Shapiro - Wilk Normality Test
#>
#> Test Results:
#> STATISTIC:
#> W: 0.9895
#> P VALUE:
#> 0.02154
#>
#> Description:
#> Shapiro - Wilk Normality Test of normalized residuals
#>
#> Title:
#> D'Agostino Normality Test
#>
#> Test Results:
#> STATISTIC:
#> Chi2 | Omnibus: 9.4195
#> Z3 | Skewness: -2.704
#> Z4 | Kurtosis: 1.4519
#> P VALUE:
#> Omnibus Test: 0.009007
#> Skewness Test: 0.006851
#> Kurtosis Test: 0.1465
#>
#> Description:
#> D'Agostino Normality Test of normalized residuals
#>
#> Title:
#> Anderson - Darling Normality Test
#>
#> Test Results:
#> STATISTIC:
#> A: 0.6813
#> P VALUE:
#> 0.07456
#>
#> Description:
#> Anderson - Darling Normality Test of normalized residuals
#>
#> Normalized Residuals Levene Homoscedasticity Test by Time
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 9 0.4714 0.8934
#> 310
#>
#> Normalized Residuals Fligner-Killeen Homoscedasticity Test by Time
#>
#> Fligner-Killeen test of homogeneity of variances
#>
#> data: normalized_resid by as.factor(Time)
#> Fligner-Killeen:med chi-squared = 3.8143, df = 9, p-value = 0.9232
#>
#>
#> Normalized Residuals Levene Homoscedasticity Test by Treatment
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 3 0.5772 0.6304
#> 316
#>
#> Normalized Residuals Fligner-Killeen Homoscedasticity Test by Treatment
#>
#> Fligner-Killeen test of homogeneity of variances
#>
#> data: normalized_resid by Treatment
#> Fligner-Killeen:med chi-squared = 1.5405, df = 3, p-value = 0.673
#>
#>
#> Outlier observations
#> SampleID Time Treatment TV RTV logRTV TV0
#> 16 2 18 Control 512.1195 2.3886998 0.8707492 214.3926
#> 41 5 3 Control 197.1398 0.7938990 -0.2307990 248.3185
#> 51 6 3 Control 175.4958 0.6732778 -0.3955972 260.6588
#> 65 7 15 Control 357.3550 1.6397816 0.4945630 217.9284
#> 113 12 9 DrugA 514.0043 3.1708889 1.1540120 162.1010
#> 122 13 6 DrugA 179.3938 0.8896325 -0.1169469 201.6493
#> 135 14 15 DrugA 811.5854 5.8214346 1.7615467 139.4133
#> 149 15 27 DrugA 2182.0193 11.1771236 2.4138692 195.2219
#> 182 19 6 DrugB 425.3002 2.4226262 0.8848522 175.5534
#> 221 23 3 DrugB 187.7751 0.7226499 -0.3248305 259.8424
#> 243 25 9 Combination 185.9586 0.6374488 -0.4502813 291.7232
#> 272 28 6 Combination 317.8079 2.1773052 0.7780880 145.9639
#> 284 29 12 Combination 211.5939 0.8481839 -0.1646578 249.4670
#> 293 30 9 Combination 209.9097 0.8877339 -0.1190832 236.4557
#> 301 31 3 Combination 171.9011 0.7141648 -0.3366415 240.7023
#> 305 31 15 Combination 214.8480 0.8925879 -0.1136302 240.7023
#> 314 32 12 Combination 209.8804 0.8805177 -0.1272452 238.3602
#> normalized_resid
#> 16 -2.175456
#> 41 -2.107815
#> 51 -2.796859
#> 65 -2.948355
#> 113 2.013734
#> 122 -2.439570
#> 135 2.306236
#> 149 2.147614
#> 182 2.178362
#> 221 -2.256830
#> 243 -3.153712
#> 272 2.352650
#> 284 -2.467379
#> 293 -2.037821
#> 301 -2.012043
#> 305 -2.670916
#> 314 -2.113725
Observed versus Predicted Values
ObsvsPred(lmm)
#> # Indices of model performance
#>
#> AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | RMSE | Sigma
#> ------------------------------------------------------------------
#> 22.542 | 22.810 | 45.151 | 0.898 | 0.898 | 0.203 | 0.212
Influential Diagnostics
log likelihood displacements
logLikSubjectDisplacements(lmm)
#> [1] "Outliers with Log Likelihood displacement greater than: 0.534"
#> 6 8 25 28
#> 0.6308934 1.1633552 0.5465657 0.5354518
Cook’s distances
CookDistance(lmm)
#> [1] "Subjects with Cook's distance greater than: 0.091"
#> 6 8 23 28
#> 0.10566141 0.15445612 0.09189548 0.09125189
Post-Hoc Power Analysis
set.seed(123)
PostHocPwr(lmm, method = "Bliss", time = 30)
#> [1] 0.959A Priori Power Analysis
We will estimate the effect of sample size on statistical power based on the estimates from the model:
# Vector with different sample sizes per group
npg <- 3:15
# Obtain model estimates
(lmmestim <- lmmModel_estimates(lmm))
#> Control DrugA DrugB Combination sd_ranef sd_resid
#> estimate 0.07855242 0.07491984 0.06306986 0.03487933 0.03946667 0.2124122
# Obtain time points
(timepoints <- unique(lmm$dt1$Time))
#> [1] 0 3 6 9 12 15 18 21 24 27 30
# Calculate power depending on sample size per group
PwrSampleSize(
npg = npg,
time = timepoints,
grwrControl = round(lmmestim$Control,3),
grwrA = round(lmmestim$DrugA,3),
grwrB = round(lmmestim$DrugB,3),
grwrComb = round(lmmestim$Combination,3),
sd_ranef = round(lmmestim$sd_ranef,3),
sgma = round(lmmestim$sd_resid,3),
method = "Bliss"
)
#> N Power
#> 1 3 0.6276569
#> 2 4 0.7532860
#> 3 5 0.8415346
#> 4 6 0.9007933
#> 5 7 0.9392189
#> 6 8 0.9634444
#> 7 9 0.9783655
#> 8 10 0.9873764
#> 9 11 0.9927265
#> 10 12 0.9958562
#> 11 13 0.9976632
#> 12 14 0.9986944
#> 13 15 0.9992767