ASSISTant
is an R package for Adaptive Subgroup Selection In Sequential Trials. This vignette reproduces all the simulations in the original paper of Lai, Lavori and Liao [-@Lai2014191].
library(ASSISTant)
data(LLL.SETTINGS)
str(LLL.SETTINGS)
## List of 3
## $ trialParameters:List of 4
## ..$ N : num [1:3] 300 400 500
## ..$ type1Error: num 0.05
## ..$ eps : num 0.5
## ..$ type2Error: num 0.2
## $ scenarios :List of 11
## ..$ S0 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0 0 0 0 0 0 0 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ S1 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0.3 0 0.3 0 0.3 0 0.3 0 0.3 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ S2 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0.3 0 0.3 0 0.3 0 0.3 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ S3 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0.3 0 0.3 0 0 0 0 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ S4 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0 0 0 0 0.3 0 0.3 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ S5 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0.6 0 0 0 0 0 0 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ S6 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0.5 0 0 0 0 0 0 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ S7 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0.5 0 0.4 0 0.3 0 0 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ S8 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0.5 0 0.4 0 0.3 0 0 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 2 1 1.5 1 1 1 0.5 1 0.5 ...
## ..$ S9 :List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0.5 0 0.4 0 0.3 0 0 0 0 ...
## .. ..$ sd : num [1:2, 1:6] 1 0.5 1 1 1 1.5 1 2 1 2 ...
## ..$ S10:List of 2
## .. ..$ mean: num [1:2, 1:6] 0 0 0 0 0 0 0 0.3 0 0.4 ...
## .. ..$ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ prevalences :List of 2
## ..$ table1: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## ..$ table2: num [1:6] 0.2 0.1 0.3 0.1 0.1 0.2
The LLL.SETTINGS
list contains all the scenarios used for the null and alternative cases in Lai, Lavori and Liao [-@Lai2014191].
The results shown here should closely approximate those in Table 1 of Lai, Lavori and Liao [-@Lai2014191].
This is the null setting.
scenario <- LLL.SETTINGS$scenarios$S0
designParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
designA <- ASSISTDesign$new(trialParameters = LLL.SETTINGS$trialParameters,
designParameters = designParameters)
print(designA)
## Design Parameters:
## Number of Groups: 6
## Prevalence:
##
## Group1 Group2 Group3 Group4 Group5 Group6
## ---------- ---------- ---------- ---------- ---------- ----------
## 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##
## Using Discrete Rankin scores? FALSE
##
## Normal Rankin Distribution means (null row, alt. row):
##
##
## Group1 Group2 Group3 Group4 Group5 Group6
## ----- ------- ------- ------- ------- ------- -------
## Null 0 0 0 0 0 0
## Alt 0 0 0 0 0 0
##
## Normal Rankin Distribution SDs (null row, alt. row):
##
##
## Group1 Group2 Group3 Group4 Group5 Group6
## ----- ------- ------- ------- ------- ------- -------
## Null 1 1 1 1 1 1
## Alt 1 1 1 1 1 1
##
## Trial Parameters:
## List of 5
## $ N : num [1:3] 300 400 500
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0642
##
## Boundaries:
##
##
## btilde b c
## ---------- --------- ---------
## -1.460993 2.390404 2.491775
result <- designA$explore(numberOfSimulations = 25000, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.015720; P(Reject H0_subgp) = 0.021520; P(Reject H0) = 0.037240
## P(Early stop for efficacy [futility]) = 0.021680 [0.551640]
## Mean [SD] Randomized N = 422.940000 [75.588259]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.19728
## 2 0.37604
## 3 0.42668
##
## Mean [SD] Lost N = 183.079080 [92.140910]
## Mean [SD] Analyzed N = 239.860920 [97.090027]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.06551 6.505267
## 1 2 200.00203 8.154904
## 1 3 150.16620 8.346300
## 1 4 100.00972 8.101806
## 1 5 49.86783 6.502325
## 2 1 333.39802 7.343570
## 2 2 266.72910 9.561764
## 2 3 199.64773 9.832610
## 2 4 133.08841 9.191855
## 2 5 66.74314 7.428316
## 3 1 415.78818 8.423654
## 3 2 333.04252 10.739814
## 3 3 250.23131 11.191329
## 3 4 166.77711 10.644704
## 3 5 83.37944 8.433986
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 217 0.00868
## 2 134 0.00536
## 3 88 0.00352
## 4 63 0.00252
## 5 36 0.00144
## 6 393 0.01572
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ----- -----
## 1 6259 3450 2491 2161 2527
## 2 809 598 528 509 802
## 3 694 635 709 830 1605
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.96276 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9720433 7762 217
## 0.9713859 4683 134
## 0.9763948 3728 88
## 0.9820000 3500 63
## 0.9927037 4934 36
## 0.0000000 393 393
## NULL
scenario <- LLL.SETTINGS$scenarios$S1
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.819480; P(Reject H0_subgp) = 0.041320; P(Reject H0) = 0.860800
## P(Early stop for efficacy [futility]) = 0.738760 [0.004400]
## Mean [SD] Randomized N = 369.756000 [85.128082]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.55928
## 2 0.18388
## 3 0.25684
##
## Mean [SD] Lost N = 30.983720 [80.251024]
## Mean [SD] Analyzed N = 338.772280 [77.840612]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.74803 6.845191
## 1 2 199.69000 8.585512
## 1 3 151.00000 9.284578
## 1 4 101.27536 7.204745
## 1 5 50.47368 6.879765
## 2 1 333.81250 7.642992
## 2 2 266.90323 8.821772
## 2 3 197.07143 10.811272
## 2 4 131.88235 10.641207
## 2 5 68.48485 8.419179
## 3 1 417.05574 8.219051
## 3 2 333.57279 10.804541
## 3 3 249.69643 11.374125
## 3 4 166.51711 10.276570
## 3 5 83.35188 8.242731
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 198 0.00792
## 2 202 0.00808
## 3 185 0.00740
## 4 216 0.00864
## 5 232 0.00928
## 6 20487 0.81948
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- -----
## 1 127 100 60 69 114
## 2 32 31 28 17 33
## 3 305 419 448 789 1941
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.1392 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.5732759 464 198
## 0.6327273 550 202
## 0.6548507 536 185
## 0.7531429 875 216
## 0.8888889 2088 232
## 0.0000000 20487 20487
## NULL
scenario <- LLL.SETTINGS$scenarios$S2
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.444520; P(Reject H0_subgp) = 0.302720; P(Reject H0) = 0.747240
## P(Early stop for efficacy [futility]) = 0.422360 [0.010240]
## Mean [SD] Randomized N = 432.208000 [84.202900]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.24532
## 2 0.18728
## 3 0.56740
##
## Mean [SD] Lost N = 105.824320 [114.155552]
## Mean [SD] Analyzed N = 326.383680 [92.122986]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.06935 6.288181
## 1 2 199.14115 8.462123
## 1 3 150.57754 8.686286
## 1 4 101.57600 8.149609
## 1 5 50.34978 6.742603
## 2 1 332.94286 7.950070
## 2 2 267.72455 8.767866
## 2 3 199.81893 10.605244
## 2 4 133.65535 9.752769
## 2 5 66.58929 6.701558
## 3 1 415.89153 8.565840
## 3 2 333.14062 10.516930
## 3 3 250.22757 11.341056
## 3 4 167.04975 10.530577
## 3 5 84.11860 8.296960
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 965 0.03860
## 2 1099 0.04396
## 3 1586 0.06344
## 4 3400 0.13600
## 5 518 0.02072
## 6 11113 0.44452
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- ----- ----- -----
## 1 620 503 561 875 223
## 2 175 167 243 383 112
## 3 590 1024 1705 5045 1661
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.25276 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.3032491 1385 965
## 0.3512397 1694 1099
## 0.3678756 2509 1586
## 0.4605743 6303 3400
## 0.7404810 1996 518
## 0.0000000 11113 11113
## NULL
scenario <- LLL.SETTINGS$scenarios$S3
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.119920; P(Reject H0_subgp) = 0.483400; P(Reject H0) = 0.603320
## P(Early stop for efficacy [futility]) = 0.310760 [0.036120]
## Mean [SD] Randomized N = 455.568000 [66.467843]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.09744
## 2 0.24944
## 3 0.65312
##
## Mean [SD] Lost N = 214.930040 [116.264237]
## Mean [SD] Analyzed N = 240.637960 [101.810594]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 249.99010 6.363654
## 1 2 200.69111 8.110211
## 1 3 150.69974 8.354582
## 1 4 100.35740 8.006240
## 1 5 50.32763 6.353959
## 2 1 333.25714 7.515349
## 2 2 266.78197 9.517153
## 2 3 200.83493 10.004269
## 2 4 134.26860 9.824084
## 2 5 67.76437 7.492323
## 3 1 416.56916 8.565990
## 3 2 332.64176 10.645336
## 3 3 249.99475 10.837450
## 3 4 166.25416 10.285499
## 3 5 83.35851 8.447371
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 3353 0.13412
## 2 6881 0.27524
## 3 1257 0.05028
## 4 428 0.01712
## 5 166 0.00664
## 6 2998 0.11992
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ----- -----
## 1 2625 3969 1139 554 409
## 2 665 1431 418 242 174
## 3 1446 4871 1713 1141 1205
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.39668 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.2920186 4736 3353
## 0.3300555 10271 6881
## 0.6155963 3270 1257
## 0.7790398 1937 428
## 0.9071588 1788 166
## 0.0000000 2998 2998
## NULL
scenario <- LLL.SETTINGS$scenarios$S4
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.117720; P(Reject H0_subgp) = 0.092480; P(Reject H0) = 0.210200
## P(Early stop for efficacy [futility]) = 0.109280 [0.221080]
## Mean [SD] Randomized N = 451.676000 [74.531961]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.15288
## 2 0.17748
## 3 0.66964
##
## Mean [SD] Lost N = 125.679680 [82.598267]
## Mean [SD] Analyzed N = 325.996320 [89.660781]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.10337 6.499087
## 1 2 199.26116 8.388557
## 1 3 150.03446 8.389836
## 1 4 100.10910 8.013028
## 1 5 50.31102 6.601388
## 2 1 333.86538 7.490690
## 2 2 266.46970 9.298833
## 2 3 199.29499 10.203912
## 2 4 133.53675 9.479584
## 2 5 66.78419 7.552403
## 3 1 415.84257 8.287152
## 3 2 332.02041 11.028529
## 3 3 249.39495 12.095256
## 3 4 166.46920 10.588489
## 3 5 83.27237 8.374691
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 94 0.00376
## 2 23 0.00092
## 3 283 0.01132
## 4 1525 0.06100
## 5 387 0.01548
## 6 2943 0.11772
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ----- ----- -----
## 1 1693 448 1248 3538 1897
## 2 312 66 339 1347 797
## 3 343 98 752 5324 3855
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.7898 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9599659 2348 94
## 0.9624183 612 23
## 0.8790081 2339 283
## 0.8506220 10209 1525
## 0.9409070 6549 387
## 0.0000000 2943 2943
## NULL
scenario <- LLL.SETTINGS$scenarios$S5
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.112200; P(Reject H0_subgp) = 0.712720; P(Reject H0) = 0.824920
## P(Early stop for efficacy [futility]) = 0.458320 [0.009160]
## Mean [SD] Randomized N = 439.888000 [71.209201]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.13364
## 2 0.33384
## 3 0.53252
##
## Mean [SD] Lost N = 272.505440 [130.984436]
## Mean [SD] Analyzed N = 167.382560 [109.854833]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.61911 6.350835
## 1 2 201.28187 8.096758
## 1 3 151.29754 8.615794
## 1 4 101.04831 7.970674
## 1 5 49.88679 6.507608
## 2 1 333.59851 7.425682
## 2 2 267.68451 10.119995
## 2 3 200.02098 10.522590
## 2 4 134.60294 11.486708
## 2 5 66.31111 6.947276
## 3 1 415.93086 8.274362
## 3 2 333.39952 10.055650
## 3 3 251.62166 11.412356
## 3 4 167.36384 10.148569
## 3 5 83.91832 8.045223
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 14881 0.59524
## 2 2049 0.08196
## 3 575 0.02300
## 4 223 0.00892
## 5 90 0.00360
## 6 2805 0.11220
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ---- ---- ----
## 1 7157 1114 447 207 106
## 2 2289 355 143 68 45
## 3 7478 1259 637 437 453
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.17508 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1207161 16924 14881
## 0.2489003 2728 2049
## 0.5313773 1227 575
## 0.6867978 712 223
## 0.8509934 604 90
## 0.0000000 2805 2805
## NULL
scenario <- LLL.SETTINGS$scenarios$S6
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.088200; P(Reject H0_subgp) = 0.647760; P(Reject H0) = 0.735960
## P(Early stop for efficacy [futility]) = 0.438480 [0.023120]
## Mean [SD] Randomized N = 443.132000 [67.783585]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.10708
## 2 0.35452
## 3 0.53840
##
## Mean [SD] Lost N = 262.750280 [123.651895]
## Mean [SD] Analyzed N = 180.381720 [108.608932]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.51889 6.450511
## 1 2 200.90226 8.124082
## 1 3 150.83535 8.403142
## 1 4 100.71105 7.656794
## 1 5 50.50570 6.403047
## 2 1 333.58966 7.190907
## 2 2 267.28571 9.585064
## 2 3 201.29353 9.338544
## 2 4 135.09322 8.838520
## 2 5 67.34343 6.805103
## 3 1 416.17383 8.299780
## 3 2 333.59795 10.716808
## 3 3 250.24868 10.787442
## 3 4 166.92284 10.596297
## 3 5 83.36292 8.215925
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 13363 0.53452
## 2 1912 0.07648
## 3 581 0.02324
## 4 242 0.00968
## 5 96 0.00384
## 6 2205 0.08820
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ---- ---- ----
## 1 7516 1463 662 353 263
## 2 2264 448 201 118 99
## 3 6006 1363 760 648 631
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.26404 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1534904 15786 13363
## 0.4160049 3274 1912
## 0.6420209 1623 581
## 0.7837355 1119 242
## 0.9033233 993 96
## 0.0000000 2205 2205
## NULL
scenario <- LLL.SETTINGS$scenarios$S7
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.433400; P(Reject H0_subgp) = 0.454320; P(Reject H0) = 0.887720
## P(Early stop for efficacy [futility]) = 0.469720 [0.002000]
## Mean [SD] Randomized N = 427.720000 [83.818152]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.25108
## 2 0.22064
## 3 0.52828
##
## Mean [SD] Lost N = 144.721680 [140.721373]
## Mean [SD] Analyzed N = 282.998320 [106.573779]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.65160 6.357390
## 1 2 201.11829 7.879522
## 1 3 151.74350 8.617223
## 1 4 101.46341 7.951070
## 1 5 49.38889 5.644890
## 2 1 333.56855 7.207968
## 2 2 267.12276 9.561154
## 2 3 202.55902 9.926593
## 2 4 134.51899 10.117085
## 2 5 68.83333 7.124158
## 3 1 416.90893 8.489855
## 3 2 333.34991 10.374732
## 3 3 250.60999 11.257656
## 3 4 167.80642 11.008029
## 3 5 84.16252 8.974761
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1830 0.07320
## 2 3492 0.13968
## 3 5059 0.20236
## 4 789 0.03156
## 5 188 0.00752
## 6 10835 0.43340
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ----- ----
## 1 752 913 885 164 54
## 2 248 391 449 79 24
## 3 1153 2715 4787 1028 523
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.11228 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1500232 2153 1830
## 0.1311271 4019 3492
## 0.1735011 6121 5059
## 0.3792290 1271 789
## 0.6871880 601 188
## 0.0000000 10835 10835
## NULL
scenario <- LLL.SETTINGS$scenarios$S8
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.267640; P(Reject H0_subgp) = 0.415960; P(Reject H0) = 0.683600
## P(Early stop for efficacy [futility]) = 0.334600 [0.017600]
## Mean [SD] Randomized N = 449.700000 [74.270658]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1508
## 2 0.2014
## 3 0.6478
##
## Mean [SD] Lost N = 167.374000 [123.307633]
## Mean [SD] Analyzed N = 282.326000 [98.454282]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.12849 6.448017
## 1 2 200.50748 8.145799
## 1 3 150.83234 8.941759
## 1 4 101.12919 8.191214
## 1 5 50.96708 6.061577
## 2 1 333.25620 6.800872
## 2 2 266.26551 9.695436
## 2 3 200.65301 10.049219
## 2 4 134.25532 10.510943
## 2 5 67.35000 7.933177
## 3 1 415.90075 8.739815
## 3 2 333.21799 10.440185
## 3 3 250.18955 10.990600
## 3 4 166.68026 10.518131
## 3 5 83.35916 8.453743
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1887 0.07548
## 2 2315 0.09260
## 3 5207 0.20828
## 4 787 0.03148
## 5 203 0.00812
## 6 6691 0.26764
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ----- -----
## 1 1253 1137 1843 418 243
## 2 363 403 830 188 120
## 3 937 1890 6067 1520 1097
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.3164 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.2608696 2553 1887
## 0.3250729 3430 2315
## 0.4042334 8740 5207
## 0.6298213 2126 787
## 0.8609589 1460 203
## 0.0000000 6691 6691
## NULL
scenario <- LLL.SETTINGS$scenarios$S9
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.478400; P(Reject H0_subgp) = 0.465840; P(Reject H0) = 0.944240
## P(Early stop for efficacy [futility]) = 0.510800 [0.000560]
## Mean [SD] Randomized N = 419.260000 [86.464741]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.29604
## 2 0.21532
## 3 0.48864
##
## Mean [SD] Lost N = 147.749440 [154.151954]
## Mean [SD] Analyzed N = 271.510560 [118.438153]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.57766 6.389644
## 1 2 201.62012 8.075404
## 1 3 151.94715 8.924055
## 1 4 101.82979 6.614806
## 1 5 51.33333 5.844129
## 2 1 333.76087 7.203882
## 2 2 268.37566 8.897092
## 2 3 202.06173 9.562771
## 2 4 136.93617 8.501673
## 2 5 66.00000 6.845228
## 3 1 416.32754 8.271757
## 3 2 333.63458 10.359139
## 3 3 250.71265 10.884472
## 3 4 167.93820 10.939887
## 3 5 83.21127 8.272165
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 3075 0.12300
## 2 4418 0.17672
## 3 3408 0.13632
## 4 612 0.02448
## 5 133 0.00532
## 6 11960 0.47840
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ---- ----
## 1 985 845 492 94 27
## 2 322 378 243 47 8
## 3 2015 3522 3066 712 284
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.05576 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.0743528 3322 3075
## 0.0689146 4745 4418
## 0.1033938 3801 3408
## 0.2825322 853 612
## 0.5830721 319 133
## 0.0000000 11960 11960
## NULL
scenario <- LLL.SETTINGS$scenarios$S10
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.432040; P(Reject H0_subgp) = 0.002920; P(Reject H0) = 0.434960
## P(Early stop for efficacy [futility]) = 0.350120 [0.129760]
## Mean [SD] Randomized N = 422.784000 [87.207761]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.29228
## 2 0.18760
## 3 0.52012
##
## Mean [SD] Lost N = 76.621080 [104.348815]
## Mean [SD] Analyzed N = 346.162920 [104.312231]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 249.68459 6.224808
## 1 2 200.08596 7.690011
## 1 3 149.12162 9.407011
## 1 4 98.04444 7.517110
## 1 5 48.97054 6.529214
## 2 1 333.07500 7.336613
## 2 2 264.21875 9.159640
## 2 3 195.56000 7.665290
## 2 4 133.75000 8.837739
## 2 5 65.46154 7.110348
## 3 1 417.21726 8.612445
## 3 2 334.16169 10.703262
## 3 3 247.20000 8.558473
## 3 4 165.81653 10.650585
## 3 5 82.94360 8.387382
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 38 0.00152
## 2 7 0.00028
## 4 1 0.00004
## 5 27 0.00108
## 6 10801 0.43204
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- --- ---- -----
## 1 967 349 74 225 1290
## 2 280 96 25 72 663
## 3 1008 402 60 496 8192
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.56504 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9831486 2255 38
## 0.9917355 847 7
## 1.0000000 159 0
## 0.9987390 793 1
## 0.9973386 10145 27
## 0.0000000 10801 10801
## NULL
scenario <- LLL.SETTINGS$scenarios$S0
designParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
designA <- ASSISTDesign$new(trialParameters = LLL.SETTINGS$trialParameters,
designParameters = designParameters)
print(designA)
## Design Parameters:
## Number of Groups: 6
## Prevalence:
##
## Group1 Group2 Group3 Group4 Group5 Group6
## ------- ------- ------- ------- ------- -------
## 0.2 0.1 0.3 0.1 0.1 0.2
##
## Using Discrete Rankin scores? FALSE
##
## Normal Rankin Distribution means (null row, alt. row):
##
##
## Group1 Group2 Group3 Group4 Group5 Group6
## ----- ------- ------- ------- ------- ------- -------
## Null 0 0 0 0 0 0
## Alt 0 0 0 0 0 0
##
## Normal Rankin Distribution SDs (null row, alt. row):
##
##
## Group1 Group2 Group3 Group4 Group5 Group6
## ----- ------- ------- ------- ------- ------- -------
## Null 1 1 1 1 1 1
## Alt 1 1 1 1 1 1
##
## Trial Parameters:
## List of 5
## $ N : num [1:3] 300 400 500
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0642
##
## Boundaries:
##
##
## btilde b c
## ---------- --------- ---------
## -1.460993 2.371573 2.467677
result <- designA$explore(numberOfSimulations = 25000, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.015480; P(Reject H0_subgp) = 0.021920; P(Reject H0) = 0.037400
## P(Early stop for efficacy [futility]) = 0.022520 [0.562960]
## Mean [SD] Randomized N = 419.416000 [77.279090]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.22036
## 2 0.36512
## 3 0.41452
##
## Mean [SD] Lost N = 177.251640 [87.868516]
## Mean [SD] Analyzed N = 242.164360 [95.059262]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 239.93296 7.009866
## 1 2 210.06027 7.711790
## 1 3 120.40245 8.572703
## 1 4 89.98533 7.962544
## 1 5 60.20870 7.075884
## 2 1 320.01062 7.861324
## 2 2 279.97753 9.439236
## 2 3 159.90580 9.654945
## 2 4 120.59717 8.877900
## 2 5 80.12467 8.296030
## 3 1 400.11838 8.659173
## 3 2 348.57247 10.783606
## 3 3 200.05105 10.664735
## 3 4 150.01267 10.295253
## 3 5 99.78576 8.844766
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 196 0.00784
## 2 175 0.00700
## 3 90 0.00360
## 4 48 0.00192
## 5 39 0.00156
## 6 387 0.01548
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ----- -----
## 1 5817 4015 2614 1977 2597
## 2 753 623 552 494 762
## 3 642 683 764 789 1531
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9626 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9728231 7212 196
## 0.9671114 5321 175
## 0.9770992 3930 90
## 0.9852761 3260 48
## 0.9920245 4890 39
## 0.0000000 387 387
## NULL
scenario <- LLL.SETTINGS$scenarios$S1
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.822120; P(Reject H0_subgp) = 0.043000; P(Reject H0) = 0.865120
## P(Early stop for efficacy [futility]) = 0.739360 [0.005000]
## Mean [SD] Randomized N = 369.356000 [85.078992]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.56208
## 2 0.18228
## 3 0.25564
##
## Mean [SD] Lost N = 31.487880 [79.797985]
## Mean [SD] Analyzed N = 337.868120 [76.300228]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 240.48361 6.127075
## 1 2 210.93750 8.054158
## 1 3 120.49412 8.687188
## 1 4 91.45588 9.049505
## 1 5 60.42202 7.395311
## 2 1 320.26923 8.720356
## 2 2 279.89286 9.619961
## 2 3 164.14634 10.563051
## 2 4 122.39130 6.780581
## 2 5 80.21622 7.409210
## 3 1 399.80473 9.178596
## 3 2 350.01205 10.401475
## 3 3 199.81931 10.995747
## 3 4 150.47657 10.841927
## 3 5 99.75089 9.117869
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 219 0.00876
## 2 206 0.00824
## 3 237 0.00948
## 4 181 0.00724
## 5 232 0.00928
## 6 20553 0.82212
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- -----
## 1 122 80 85 68 109
## 2 26 28 41 23 37
## 3 338 415 642 747 1686
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.13488 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.5493827 486 219
## 0.6061185 523 206
## 0.6914062 768 237
## 0.7840095 838 181
## 0.8733624 1832 232
## 0.0000000 20553 20553
## NULL
scenario <- LLL.SETTINGS$scenarios$S2
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.490520; P(Reject H0_subgp) = 0.277040; P(Reject H0) = 0.767560
## P(Early stop for efficacy [futility]) = 0.457520 [0.008720]
## Mean [SD] Randomized N = 425.164000 [86.751796]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.28212
## 2 0.18412
## 3 0.53376
##
## Mean [SD] Lost N = 90.377160 [106.438122]
## Mean [SD] Analyzed N = 334.786840 [86.687693]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 239.98475 7.150731
## 1 2 211.02058 8.194516
## 1 3 120.37222 8.659738
## 1 4 91.19156 7.720672
## 1 5 60.93333 7.375446
## 2 1 321.01324 7.373816
## 2 2 279.92517 8.537659
## 2 3 161.24201 10.183224
## 2 4 121.04934 8.933982
## 2 5 80.50000 8.145293
## 3 1 399.09626 9.044019
## 3 2 349.41278 10.387528
## 3 3 200.11816 11.298750
## 3 4 150.46675 10.347723
## 3 5 100.57906 9.135956
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 796 0.03184
## 2 966 0.03864
## 3 1722 0.06888
## 4 2655 0.10620
## 5 787 0.03148
## 6 12263 0.49052
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ----- ----- -----
## 1 459 486 540 616 240
## 2 151 147 219 304 108
## 3 561 814 2175 4045 1872
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.23244 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.3202391 1171 796
## 0.3324119 1447 966
## 0.4130879 2934 1722
## 0.4652568 4965 2655
## 0.6454955 2220 787
## 0.0000000 12263 12263
## NULL
scenario <- LLL.SETTINGS$scenarios$S3
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.104040; P(Reject H0_subgp) = 0.489480; P(Reject H0) = 0.593520
## P(Early stop for efficacy [futility]) = 0.321320 [0.045920]
## Mean [SD] Randomized N = 453.780000 [66.219989]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.09496
## 2 0.27228
## 3 0.63276
##
## Mean [SD] Lost N = 220.699160 [115.906973]
## Mean [SD] Analyzed N = 233.080840 [103.625942]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 240.35287 6.785554
## 1 2 210.72978 7.798721
## 1 3 120.96732 8.488045
## 1 4 90.57411 7.890977
## 1 5 60.96203 6.886472
## 2 1 319.82549 8.203131
## 2 2 280.60638 9.369014
## 2 3 160.55215 9.237484
## 2 4 120.77720 9.325542
## 2 5 80.30769 8.552307
## 3 1 399.74068 9.112486
## 3 2 349.46174 10.434419
## 3 3 200.41482 11.320456
## 3 4 150.65514 11.042862
## 3 5 100.31903 9.166864
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 4140 0.16560
## 2 7051 0.28204
## 3 604 0.02416
## 4 272 0.01088
## 5 170 0.00680
## 6 2601 0.10404
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ---- -----
## 1 3174 4500 918 533 474
## 2 871 1504 326 193 195
## 3 1797 4561 1309 925 1119
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.40648 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.2913386 5842 4140
## 0.3326077 10565 7051
## 0.7634156 2553 604
## 0.8352514 1651 272
## 0.9049217 1788 170
## 0.0000000 2601 2601
## NULL
scenario <- LLL.SETTINGS$scenarios$S4
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.171160; P(Reject H0_subgp) = 0.113800; P(Reject H0) = 0.284960
## P(Early stop for efficacy [futility]) = 0.150960 [0.168120]
## Mean [SD] Randomized N = 451.836000 [75.815955]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.16256
## 2 0.15652
## 3 0.68092
##
## Mean [SD] Lost N = 111.862200 [74.557333]
## Mean [SD] Analyzed N = 339.973800 [79.632068]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 240.09662 7.024022
## 1 2 208.77568 8.647004
## 1 3 120.13578 8.604491
## 1 4 90.28927 7.935467
## 1 5 60.37818 6.883419
## 2 1 318.76437 8.503430
## 2 2 280.01613 8.259107
## 2 3 159.17625 10.185024
## 2 4 120.51129 9.285243
## 2 5 80.20257 8.401125
## 3 1 400.10163 8.756679
## 3 2 351.23958 10.523902
## 3 3 199.70407 10.801328
## 3 4 149.85161 10.359235
## 3 5 100.04298 9.125262
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 52 0.00208
## 2 25 0.00100
## 3 611 0.02444
## 4 1570 0.06280
## 5 587 0.02348
## 6 4279 0.17116
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ----- ----- -----
## 1 1035 370 1473 2693 1650
## 2 174 62 522 1107 701
## 3 246 96 1622 5061 3909
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.71504 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9642612 1455 52
## 0.9526515 528 25
## 0.8310755 3617 611
## 0.8228191 8861 1570
## 0.9062300 6260 587
## 0.0000000 4279 4279
## NULL
scenario <- LLL.SETTINGS$scenarios$S5
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.159920; P(Reject H0_subgp) = 0.711600; P(Reject H0) = 0.871520
## P(Early stop for efficacy [futility]) = 0.457600 [0.006000]
## Mean [SD] Randomized N = 438.208000 [73.807633]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.15432
## 2 0.30928
## 3 0.53640
##
## Mean [SD] Lost N = 259.455560 [138.729982]
## Mean [SD] Analyzed N = 178.752440 [111.464756]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 241.04717 6.792332
## 1 2 211.31729 7.733041
## 1 3 121.17814 8.772222
## 1 4 92.71304 7.192546
## 1 5 61.20408 7.477746
## 2 1 320.45116 7.890766
## 2 2 280.55275 9.052819
## 2 3 162.91111 10.006340
## 2 4 121.36364 8.447074
## 2 5 81.36364 8.957602
## 3 1 399.48654 8.808806
## 3 2 350.13428 10.134943
## 3 3 199.62069 11.530224
## 3 4 149.51361 10.121016
## 3 5 100.92568 9.153005
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 14074 0.56296
## 2 3069 0.12276
## 3 406 0.01624
## 4 157 0.00628
## 5 84 0.00336
## 6 3998 0.15992
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ---- ---- ----
## 1 5682 1330 247 115 98
## 2 2068 436 90 44 33
## 3 7915 1832 522 294 296
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.12848 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1015640 15665 14074
## 0.1470261 3598 3069
## 0.5273574 859 406
## 0.6534216 453 157
## 0.8032787 427 84
## 0.0000000 3998 3998
## NULL
scenario <- LLL.SETTINGS$scenarios$S6
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.119600; P(Reject H0_subgp) = 0.666840; P(Reject H0) = 0.786440
## P(Early stop for efficacy [futility]) = 0.441520 [0.014600]
## Mean [SD] Randomized N = 442.452000 [69.501230]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.11936
## 2 0.33676
## 3 0.54388
##
## Mean [SD] Lost N = 254.886520 [128.090445]
## Mean [SD] Analyzed N = 187.565480 [107.934224]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 240.63833 6.904159
## 1 2 210.91460 7.813404
## 1 3 120.92793 8.394841
## 1 4 90.95902 7.934296
## 1 5 60.85027 7.061103
## 2 1 320.14427 7.821407
## 2 2 280.24689 9.118114
## 2 3 160.94118 10.042826
## 2 4 120.08235 8.696211
## 2 5 79.36486 8.141849
## 3 1 399.35508 8.987618
## 3 2 350.29394 10.106608
## 3 3 200.16940 10.718318
## 3 4 149.91060 9.983231
## 3 5 100.15222 8.916708
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 12594 0.50376
## 2 3293 0.13172
## 3 472 0.01888
## 4 194 0.00776
## 5 118 0.00472
## 6 2990 0.11960
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ---- ---- ----
## 1 6340 1733 444 244 187
## 2 1927 563 153 85 74
## 3 6531 1997 732 481 519
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.21356 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1489390 14798 12594
## 0.2329373 4293 3293
## 0.6448457 1329 472
## 0.7604938 810 194
## 0.8487179 780 118
## 0.0000000 2990 2990
## NULL
scenario <- LLL.SETTINGS$scenarios$S7
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.570240; P(Reject H0_subgp) = 0.341000; P(Reject H0) = 0.911240
## P(Early stop for efficacy [futility]) = 0.545080 [0.001640]
## Mean [SD] Randomized N = 411.972000 [87.894142]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.33356
## 2 0.21316
## 3 0.45328
##
## Mean [SD] Lost N = 101.566960 [131.828404]
## Mean [SD] Analyzed N = 310.405040 [101.613328]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 240.65370 6.281002
## 1 2 210.74820 7.746752
## 1 3 121.99058 8.818821
## 1 4 91.55714 7.828441
## 1 5 62.46296 6.784313
## 2 1 319.28125 7.252995
## 2 2 280.52093 9.574513
## 2 3 161.60000 9.361770
## 2 4 119.47059 9.020760
## 2 5 78.44444 7.064595
## 3 1 399.42247 8.481709
## 3 2 350.72670 10.199406
## 3 3 200.76054 10.775413
## 3 4 151.30739 10.122888
## 3 5 100.90267 8.689463
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1487 0.05948
## 2 2296 0.09184
## 3 3652 0.14608
## 4 816 0.03264
## 5 274 0.01096
## 6 14256 0.57024
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ----- ----
## 1 514 556 531 140 54
## 2 160 215 235 51 18
## 3 1077 1921 3746 1002 524
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.08876 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1507710 1751 1487
## 0.1471025 2692 2296
## 0.1906028 4512 3652
## 0.3160101 1193 816
## 0.5402685 596 274
## 0.0000000 14256 14256
## NULL
scenario <- LLL.SETTINGS$scenarios$S8
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.390640; P(Reject H0_subgp) = 0.333680; P(Reject H0) = 0.724320
## P(Early stop for efficacy [futility]) = 0.391320 [0.014280]
## Mean [SD] Randomized N = 437.304000 [82.257414]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.22136
## 2 0.18424
## 3 0.59440
##
## Mean [SD] Lost N = 122.008800 [116.341514]
## Mean [SD] Analyzed N = 315.295200 [91.545802]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 240.15817 6.656479
## 1 2 210.54138 7.901309
## 1 3 121.13788 8.266286
## 1 4 91.44940 7.990879
## 1 5 61.10924 7.266814
## 2 1 319.26389 7.791456
## 2 2 280.31780 9.205263
## 2 3 161.29106 9.749710
## 2 4 120.92701 8.862209
## 2 5 81.24762 8.161567
## 3 1 400.02474 9.037408
## 3 2 349.23420 10.544889
## 3 3 200.29170 10.889219
## 3 4 150.25675 9.904950
## 3 5 100.12308 9.052280
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1244 0.04976
## 2 1545 0.06180
## 3 4385 0.17540
## 4 839 0.03356
## 5 329 0.01316
## 6 9766 0.39064
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- ----- ----- -----
## 1 765 737 1262 336 238
## 2 216 236 615 137 105
## 3 768 1187 5869 1593 1170
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.27568 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.2887364 1749 1244
## 0.2847222 2160 1545
## 0.4339014 7746 4385
## 0.5939013 2066 839
## 0.7825512 1513 329
## 0.0000000 9766 9766
## NULL
scenario <- LLL.SETTINGS$scenarios$S9
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.590720; P(Reject H0_subgp) = 0.369480; P(Reject H0) = 0.960200
## P(Early stop for efficacy [futility]) = 0.569680 [0.000280]
## Mean [SD] Randomized N = 406.648000 [88.837603]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.36356
## 2 0.20640
## 3 0.43004
##
## Mean [SD] Lost N = 114.614480 [150.787216]
## Mean [SD] Analyzed N = 292.033520 [117.101314]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 241.35735 6.804991
## 1 2 212.41235 7.745659
## 1 3 123.02963 8.327355
## 1 4 92.73438 7.346832
## 1 5 63.33333 5.131601
## 2 1 320.76062 8.401079
## 2 2 281.62308 8.766614
## 2 3 162.69672 9.285988
## 2 4 118.21053 8.593143
## 2 5 76.50000 5.567764
## 3 1 400.14625 8.626274
## 3 2 350.53538 10.280757
## 3 3 201.41770 10.529119
## 3 4 151.14667 10.151037
## 3 5 100.86626 9.140855
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 2772 0.11088
## 2 3429 0.13716
## 3 2271 0.09084
## 4 543 0.02172
## 5 222 0.00888
## 6 14768 0.59072
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ----- ---- ----
## 1 694 599 270 64 21
## 2 259 260 122 19 4
## 3 2024 2798 2169 600 329
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.0398 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.0688613 2977 2772
## 0.0623462 3657 3429
## 0.1132370 2561 2271
## 0.2049780 683 543
## 0.3728814 354 222
## 0.0000000 14768 14768
## NULL
scenario <- LLL.SETTINGS$scenarios$S10
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 25000, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.326920; P(Reject H0_subgp) = 0.003120; P(Reject H0) = 0.330040
## P(Early stop for efficacy [futility]) = 0.262840 [0.181480]
## Mean [SD] Randomized N = 430.104000 [84.836531]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.25464
## 2 0.18968
## 3 0.55568
##
## Mean [SD] Lost N = 115.456520 [121.973133]
## Mean [SD] Analyzed N = 314.647480 [114.139067]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 239.68386 6.985419
## 1 2 209.93041 8.039438
## 1 3 118.55769 8.117079
## 1 4 88.30640 7.419641
## 1 5 58.94565 6.911589
## 2 1 320.09717 8.333726
## 2 2 280.28839 9.672610
## 2 3 160.20000 8.963563
## 2 4 120.60674 10.572926
## 2 5 78.82129 7.938058
## 3 1 400.03851 8.964494
## 3 2 349.99443 10.406245
## 3 3 198.23881 10.888649
## 3 4 149.15813 9.535865
## 3 5 99.84582 8.748413
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 51 0.00204
## 2 19 0.00076
## 3 2 0.00008
## 4 1 0.00004
## 5 5 0.00020
## 6 8173 0.32692
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ---- ---- -----
## 1 1512 776 156 297 1380
## 2 494 267 45 89 761
## 3 1662 1077 201 664 7446
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.66996 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9860960 3668 51
## 0.9910377 2120 19
## 0.9950249 402 2
## 0.9990476 1050 1
## 0.9994785 9587 5
## 0.0000000 8173 8173
## NULL