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 (2014).
NOTE The number of simulations has been drastically reduced in this vignette in order to avoid taxing CRAN servers. The full_doc sources contain the complete sources and output; see files in the directory
system.file("full_doc", package="ASSISTant")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 0.2The LLL.SETTINGS list contains all the scenarios described in the paper.
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 2.491775result <- designA$explore(numberOfSimulations = 50, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.020000; P(Reject H0_subgp) = 0.000000; P(Reject H0) = 0.020000
## P(Early stop for efficacy [futility]) = 0.020000 [0.640000]
## Mean [SD] Randomized N = 414.000000 [72.871147]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.20
## 2 0.46
## 3 0.34
##
## Mean [SD] Lost N = 183.880000 [85.293644]
## Mean [SD] Analyzed N = 230.120000 [92.989716]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 250.94118 4.955686
## 1 2 201.42857 6.241184
## 1 3 152.33333 3.511885
## 1 4 107.66667 6.027714
## 1 5 52.80000 4.266146
## 2 1 328.00000 12.727922
## 2 2 267.33333 25.026653
## 2 5 71.66667 15.143756
## 3 3 232.00000 NA
## 3 4 161.50000 9.192388
## 3 5 82.00000 12.529964
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 6 1 0.02
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 17 7 3 3 5
## 2 2 3 0 0 3
## 3 0 0 1 2 3
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.98 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## --------- -------------- --------------
## 1 19 0
## 1 10 0
## 1 4 0
## 1 5 0
## 1 11 0
## 0 1 1
## NULLscenario <- LLL.SETTINGS$scenarios$S1
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.780000; P(Reject H0_subgp) = 0.040000; P(Reject H0) = 0.820000
## P(Early stop for efficacy [futility]) = 0.700000 [0.000000]
## Mean [SD] Randomized N = 372.000000 [90.441096]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.58
## 2 0.12
## 3 0.30
##
## Mean [SD] Lost N = 45.500000 [112.449762]
## Mean [SD] Analyzed N = 326.500000 [94.545368]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ---------
## 1 5 48.0000 NA
## 2 1 330.0000 NA
## 3 1 415.6667 8.504900
## 3 3 246.0000 NA
## 3 5 80.8000 8.228001
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1 0.02
## 3 1 0.02
## 6 39 0.78
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 0 0 0 0 1
## 2 1 0 0 0 0
## 3 3 0 1 0 5
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.18 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## --------- -------------- --------------
## 0.75 4 1
## 0.00 1 1
## 1.00 6 0
## 0.00 39 39
## NULLscenario <- LLL.SETTINGS$scenarios$S2
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.400000; P(Reject H0_subgp) = 0.320000; P(Reject H0) = 0.720000
## P(Early stop for efficacy [futility]) = 0.420000 [0.000000]
## Mean [SD] Randomized N = 436.000000 [82.709228]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.22
## 2 0.20
## 3 0.58
##
## Mean [SD] Lost N = 122.160000 [123.479381]
## Mean [SD] Analyzed N = 313.840000 [100.538014]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 254.0000 2.828427
## 1 2 199.0000 8.485281
## 1 3 141.5000 21.920310
## 1 4 96.0000 11.313709
## 1 5 50.0000 NA
## 2 4 133.0000 5.656854
## 3 1 423.5000 7.778175
## 3 2 334.3333 7.505554
## 3 3 241.2500 6.701990
## 3 4 167.6667 5.267827
## 3 5 87.0000 NA
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 2 0.04
## 2 4 0.08
## 3 4 0.08
## 4 6 0.12
## 6 20 0.40
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 2 2 2 2 1
## 2 0 0 0 2 0
## 3 2 3 4 9 1
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.28 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.5000000 4 2
## 0.2000000 5 4
## 0.3333333 6 4
## 0.5384615 13 6
## 1.0000000 2 0
## 0.0000000 20 20
## NULLscenario <- LLL.SETTINGS$scenarios$S3
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.120000; P(Reject H0_subgp) = 0.420000; P(Reject H0) = 0.540000
## P(Early stop for efficacy [futility]) = 0.260000 [0.020000]
## Mean [SD] Randomized N = 460.000000 [69.985421]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.12
## 2 0.16
## 3 0.72
##
## Mean [SD] Lost N = 223.540000 [126.875837]
## Mean [SD] Analyzed N = 236.460000 [122.725546]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- -----------
## 1 1 251.6667 4.3204938
## 1 2 199.7500 7.8898669
## 1 3 142.0000 8.4852814
## 1 4 108.0000 NA
## 1 5 49.0000 NA
## 2 1 335.7500 6.7515430
## 2 2 267.0000 NA
## 2 3 209.0000 NA
## 2 5 65.0000 NA
## 3 1 416.8000 5.8480766
## 3 2 334.3750 9.8841504
## 3 3 261.6667 11.5902258
## 3 4 166.8000 9.8843310
## 3 5 82.5000 0.7071068
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 12 0.24
## 2 6 0.12
## 3 2 0.04
## 5 1 0.02
## 6 6 0.12
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 6 4 2 1 1
## 2 4 1 1 0 1
## 3 5 8 3 5 2
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.46 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.2000000 15 12
## 0.5384615 13 6
## 0.6666667 6 2
## 1.0000000 6 0
## 0.7500000 4 1
## 0.0000000 6 6
## NULLscenario <- LLL.SETTINGS$scenarios$S4
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.060000; P(Reject H0_subgp) = 0.100000; P(Reject H0) = 0.160000
## P(Early stop for efficacy [futility]) = 0.040000 [0.180000]
## Mean [SD] Randomized N = 466.000000 [68.838765]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.12
## 2 0.10
## 3 0.78
##
## Mean [SD] Lost N = 146.480000 [84.999457]
## Mean [SD] Analyzed N = 319.520000 [101.819015]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 251.80000 1.483240
## 1 4 100.25000 8.811518
## 1 5 52.66667 1.527525
## 2 4 130.00000 8.366600
## 2 5 66.50000 24.748737
## 3 1 416.00000 NA
## 3 3 251.66667 8.524475
## 3 4 170.91667 11.712141
## 3 5 79.16667 5.980524
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1 0.02
## 3 1 0.02
## 4 1 0.02
## 5 2 0.04
## 6 3 0.06
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 5 0 0 8 3
## 2 0 0 0 4 2
## 3 1 0 6 12 6
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.84 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.8333333 6 1
## 0.8333333 6 1
## 0.9583333 24 1
## 0.8181818 11 2
## 0.0000000 3 3
## NULLscenario <- LLL.SETTINGS$scenarios$S5
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.140000; P(Reject H0_subgp) = 0.660000; P(Reject H0) = 0.800000
## P(Early stop for efficacy [futility]) = 0.460000 [0.000000]
## Mean [SD] Randomized N = 444.000000 [67.491496]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.10
## 2 0.36
## 3 0.54
##
## Mean [SD] Lost N = 270.120000 [141.724314]
## Mean [SD] Analyzed N = 173.880000 [126.469427]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 248.6923 5.807820
## 1 2 206.5000 2.121320
## 1 3 157.0000 4.242641
## 1 4 104.5000 4.949747
## 2 1 333.3333 4.457204
## 3 1 417.3125 5.313113
## 3 2 330.0000 12.727922
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 30 0.60
## 2 1 0.02
## 3 1 0.02
## 4 1 0.02
## 6 7 0.14
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 13 2 2 2 0
## 2 6 0 0 0 0
## 3 16 2 0 0 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.2 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1428571 35 30
## 0.7500000 4 1
## 0.5000000 2 1
## 0.5000000 2 1
## 0.0000000 7 7
## NULLscenario <- LLL.SETTINGS$scenarios$S6
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.060000; P(Reject H0_subgp) = 0.720000; P(Reject H0) = 0.780000
## P(Early stop for efficacy [futility]) = 0.480000 [0.040000]
## Mean [SD] Randomized N = 436.000000 [69.282032]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.12
## 2 0.40
## 3 0.48
##
## Mean [SD] Lost N = 254.060000 [123.124196]
## Mean [SD] Analyzed N = 181.940000 [115.743808]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 249.85714 7.336496
## 1 2 189.66667 5.507570
## 1 4 102.66667 11.718931
## 1 5 49.00000 8.485281
## 2 1 330.42857 6.106203
## 2 2 267.00000 14.142136
## 3 1 416.55556 3.574602
## 3 2 336.75000 12.685293
## 3 5 95.66667 7.023769
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 26 0.52
## 2 6 0.12
## 4 1 0.02
## 5 3 0.06
## 6 3 0.06
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 14 3 0 3 2
## 2 7 2 0 0 0
## 3 9 4 0 0 3
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.22 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1333333 30 26
## 0.3333333 9 6
## 0.6666667 3 1
## 0.4000000 5 3
## 0.0000000 3 3
## NULLscenario <- LLL.SETTINGS$scenarios$S7
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.420000; P(Reject H0_subgp) = 0.480000; P(Reject H0) = 0.900000
## P(Early stop for efficacy [futility]) = 0.460000 [0.000000]
## Mean [SD] Randomized N = 428.000000 [85.809471]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.26
## 2 0.20
## 3 0.54
##
## Mean [SD] Lost N = 137.180000 [132.051735]
## Mean [SD] Analyzed N = 290.820000 [102.494338]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- -----------
## 1 1 243.5000 12.0208153
## 1 2 198.7500 5.5000000
## 1 3 153.5000 0.7071068
## 1 4 95.0000 NA
## 2 3 206.0000 8.4852814
## 3 1 422.0000 NA
## 3 2 341.0000 6.1644140
## 3 3 257.0000 5.0709255
## 3 4 165.6667 1.5275252
## 3 5 83.0000 NA
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 3 0.06
## 2 9 0.18
## 3 9 0.18
## 4 3 0.06
## 6 21 0.42
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 2 4 2 1 0
## 2 0 0 2 0 0
## 3 1 5 8 3 1
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.1 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## --------- -------------- --------------
## 0.00 3 3
## 0.00 9 9
## 0.25 12 9
## 0.25 4 3
## 1.00 1 0
## 0.00 21 21
## NULLscenario <- LLL.SETTINGS$scenarios$S8
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.180000; P(Reject H0_subgp) = 0.500000; P(Reject H0) = 0.680000
## P(Early stop for efficacy [futility]) = 0.260000 [0.000000]
## Mean [SD] Randomized N = 460.000000 [72.843136]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.14
## 2 0.12
## 3 0.74
##
## Mean [SD] Lost N = 170.720000 [104.977556]
## Mean [SD] Analyzed N = 289.280000 [85.082682]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 250.0000 5.291503
## 1 3 147.6000 2.509980
## 1 4 106.0000 6.055301
## 2 1 322.0000 NA
## 2 3 207.0000 NA
## 3 2 331.3333 11.590226
## 3 3 250.7647 10.195155
## 3 4 160.0000 1.732051
## 3 5 89.5000 3.109126
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 4 0.08
## 2 3 0.06
## 3 14 0.28
## 4 3 0.06
## 5 1 0.02
## 6 9 0.18
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 3 0 5 4 0
## 2 1 0 1 0 0
## 3 0 3 17 3 4
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.32 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.0000000 4 4
## 0.0000000 3 3
## 0.3913043 23 14
## 0.5714286 7 3
## 0.7500000 4 1
## 0.0000000 9 9
## NULLscenario <- LLL.SETTINGS$scenarios$S9
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.560000; P(Reject H0_subgp) = 0.360000; P(Reject H0) = 0.920000
## P(Early stop for efficacy [futility]) = 0.480000 [0.000000]
## Mean [SD] Randomized N = 426.000000 [85.260705]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.26
## 2 0.22
## 3 0.52
##
## Mean [SD] Lost N = 125.840000 [153.421968]
## Mean [SD] Analyzed N = 300.160000 [127.468341]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 235.0000 NA
## 1 2 194.0000 NA
## 2 1 329.6667 2.081666
## 3 1 418.5000 4.949747
## 3 2 330.6250 13.394429
## 3 3 243.2500 7.365460
## 3 4 168.0000 1.414214
## 3 5 83.0000 NA
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 5 0.10
## 2 8 0.16
## 3 3 0.06
## 4 1 0.02
## 5 1 0.02
## 6 28 0.56
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 1 1 0 0 0
## 2 3 0 0 0 0
## 3 2 8 4 2 1
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.08 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1666667 6 5
## 0.1111111 9 8
## 0.2500000 4 3
## 0.5000000 2 1
## 0.0000000 1 1
## 0.0000000 28 28
## NULLscenario <- LLL.SETTINGS$scenarios$S10
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.420000; P(Reject H0_subgp) = 0.000000; P(Reject H0) = 0.420000
## P(Early stop for efficacy [futility]) = 0.300000 [0.160000]
## Mean [SD] Randomized N = 422.000000 [91.003476]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.32
## 2 0.14
## 3 0.54
##
## Mean [SD] Lost N = 78.100000 [118.835206]
## Mean [SD] Analyzed N = 343.900000 [117.819345]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ---------
## 1 1 252.00000 NA
## 1 5 50.42857 4.035556
## 3 1 418.25000 9.979145
## 3 2 331.00000 NA
## 3 5 81.00000 8.074652
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 6 21 0.42
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 1 0 0 0 7
## 2 0 0 0 0 0
## 3 4 1 0 0 16
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.58 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## --------- -------------- --------------
## 1 5 0
## 1 1 0
## 1 23 0
## 0 21 21
## NULLscenario <- LLL.SETTINGS$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 2.467677result <- designA$explore(numberOfSimulations = 50, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.020000; P(Reject H0_subgp) = 0.020000; P(Reject H0) = 0.040000
## P(Early stop for efficacy [futility]) = 0.040000 [0.620000]
## Mean [SD] Randomized N = 406.000000 [79.308234]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.28
## 2 0.38
## 3 0.34
##
## Mean [SD] Lost N = 175.400000 [80.752835]
## Mean [SD] Analyzed N = 230.600000 [105.285811]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 240.0000 9.518403
## 1 2 211.3333 7.364946
## 1 3 116.0000 16.970563
## 1 4 86.0000 7.071068
## 1 5 59.0000 3.162278
## 2 1 325.0000 NA
## 2 2 283.0000 4.242641
## 2 3 158.5000 14.849242
## 2 4 111.0000 NA
## 2 5 94.0000 NA
## 3 1 369.0000 NA
## 3 3 192.0000 7.071068
## 3 4 156.0000 NA
## 3 5 105.0000 7.937254
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 2 1 0.02
## 6 1 0.02
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 11 12 2 5 5
## 2 1 2 2 1 1
## 3 1 0 2 1 3
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.96 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 13 0
## 0.9285714 14 1
## 1.0000000 6 0
## 1.0000000 7 0
## 1.0000000 9 0
## 0.0000000 1 1
## NULLscenario <- LLL.SETTINGS$scenarios$S1
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.780000; P(Reject H0_subgp) = 0.060000; P(Reject H0) = 0.840000
## P(Early stop for efficacy [futility]) = 0.760000 [0.000000]
## Mean [SD] Randomized N = 366.000000 [84.780629]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.58
## 2 0.18
## 3 0.24
##
## Mean [SD] Lost N = 44.200000 [97.398403]
## Mean [SD] Analyzed N = 321.800000 [67.726340]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ---------
## 2 2 282.0000 NA
## 3 2 347.6667 4.725816
## 3 3 205.0000 NA
## 3 4 133.5000 3.535534
## 3 5 103.2500 1.707825
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 2 1 0.02
## 3 1 0.02
## 5 1 0.02
## 6 39 0.78
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 0 0 0 0 0
## 2 0 1 0 0 0
## 3 0 3 1 2 4
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.16 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## --------- -------------- --------------
## 0.75 4 1
## 0.00 1 1
## 1.00 2 0
## 0.75 4 1
## 0.00 39 39
## NULLscenario <- LLL.SETTINGS$scenarios$S2
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.520000; P(Reject H0_subgp) = 0.220000; P(Reject H0) = 0.740000
## P(Early stop for efficacy [futility]) = 0.520000 [0.020000]
## Mean [SD] Randomized N = 424.000000 [79.693290]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.22
## 2 0.32
## 3 0.46
##
## Mean [SD] Lost N = 79.800000 [98.886866]
## Mean [SD] Analyzed N = 344.200000 [80.416264]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 237.00000 NA
## 1 2 222.00000 NA
## 1 3 122.00000 NA
## 1 4 87.00000 5.567764
## 2 2 281.00000 NA
## 2 4 137.00000 NA
## 3 2 353.00000 4.242641
## 3 3 198.00000 26.870058
## 3 4 149.00000 11.302655
## 3 5 95.66667 5.686241
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1 0.02
## 2 1 0.02
## 4 8 0.16
## 5 1 0.02
## 6 26 0.52
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 1 1 1 3 0
## 2 0 1 0 1 0
## 3 0 2 2 9 3
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.26 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.0000000 1 1
## 0.7500000 4 1
## 1.0000000 3 0
## 0.3846154 13 8
## 0.6666667 3 1
## 0.0000000 26 26
## NULLscenario <- LLL.SETTINGS$scenarios$S3
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.060000; P(Reject H0_subgp) = 0.560000; P(Reject H0) = 0.620000
## P(Early stop for efficacy [futility]) = 0.300000 [0.040000]
## Mean [SD] Randomized N = 458.000000 [64.174507]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.08
## 2 0.26
## 3 0.66
##
## Mean [SD] Lost N = 244.860000 [104.019035]
## Mean [SD] Analyzed N = 213.140000 [90.550022]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- -----------
## 1 1 240.1250 7.7170960
## 1 2 209.8000 7.5099933
## 1 4 100.0000 NA
## 2 1 323.0000 4.2426407
## 2 2 277.5000 6.3639610
## 2 4 116.0000 NA
## 2 5 75.0000 NA
## 3 1 401.5000 2.1213203
## 3 2 345.6667 12.6923299
## 3 3 187.5000 0.7071068
## 3 4 151.0000 NA
## 3 5 109.0000 1.4142136
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 9 0.18
## 2 18 0.36
## 4 1 0.02
## 6 3 0.06
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 8 10 0 1 0
## 2 2 2 0 1 1
## 3 2 15 2 1 2
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.38 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.2500000 12 9
## 0.3333333 27 18
## 1.0000000 2 0
## 0.6666667 3 1
## 1.0000000 3 0
## 0.0000000 3 3
## NULLscenario <- LLL.SETTINGS$scenarios$S4
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.160000; P(Reject H0_subgp) = 0.120000; P(Reject H0) = 0.280000
## P(Early stop for efficacy [futility]) = 0.140000 [0.160000]
## Mean [SD] Randomized N = 452.000000 [78.869564]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.18
## 2 0.12
## 3 0.70
##
## Mean [SD] Lost N = 103.560000 [60.185143]
## Mean [SD] Analyzed N = 348.440000 [65.372140]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 238.00000 NA
## 1 3 127.00000 8.485281
## 1 4 96.33333 8.594572
## 1 5 61.50000 9.071935
## 3 3 196.00000 22.538855
## 3 4 151.64286 7.601692
## 3 5 102.80000 10.347302
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 4 5 0.10
## 5 1 0.02
## 6 8 0.16
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 1 0 2 6 6
## 2 0 0 0 0 0
## 3 0 0 3 14 10
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.72 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## --------- -------------- --------------
## 1.0000 1 0
## 1.0000 5 0
## 0.7500 20 5
## 0.9375 16 1
## 0.0000 8 8
## NULLscenario <- LLL.SETTINGS$scenarios$S5
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.100000; P(Reject H0_subgp) = 0.740000; P(Reject H0) = 0.840000
## P(Early stop for efficacy [futility]) = 0.400000 [0.000000]
## Mean [SD] Randomized N = 446.000000 [73.429127]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.14
## 2 0.26
## 3 0.60
##
## Mean [SD] Lost N = 282.580000 [122.120230]
## Mean [SD] Analyzed N = 163.420000 [104.629783]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 238.8182 7.769404
## 1 2 200.3333 10.503967
## 2 1 330.0000 9.183318
## 2 2 278.0000 NA
## 2 4 113.0000 NA
## 3 1 399.2667 10.746871
## 3 2 357.6000 6.655824
## 3 3 211.5000 3.535534
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 28 0.56
## 2 8 0.16
## 3 1 0.02
## 6 5 0.10
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 11 3 0 0 0
## 2 7 1 0 1 0
## 3 15 5 2 0 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.16 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.1515152 33 28
## 0.1111111 9 8
## 0.5000000 2 1
## 1.0000000 1 0
## 0.0000000 5 5
## NULLscenario <- LLL.SETTINGS$scenarios$S6
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.080000; P(Reject H0_subgp) = 0.680000; P(Reject H0) = 0.760000
## P(Early stop for efficacy [futility]) = 0.320000 [0.000000]
## Mean [SD] Randomized N = 456.000000 [70.450446]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.12
## 2 0.20
## 3 0.68
##
## Mean [SD] Lost N = 275.360000 [129.742722]
## Mean [SD] Analyzed N = 180.640000 [114.948215]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 236.8750 7.453427
## 1 2 199.5000 13.435029
## 1 3 126.0000 NA
## 1 4 106.0000 NA
## 1 5 61.0000 NA
## 2 1 326.8000 6.648308
## 2 4 134.0000 NA
## 3 1 395.0526 9.507153
## 3 2 359.0000 14.000000
## 3 3 204.3333 8.504900
## 3 4 132.0000 NA
## 3 5 85.0000 NA
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 26 0.52
## 2 5 0.10
## 3 3 0.06
## 6 4 0.08
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 8 2 1 1 1
## 2 5 0 0 1 0
## 3 19 3 3 1 1
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.24 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## --------- -------------- --------------
## 0.1875 32 26
## 0.0000 5 5
## 0.2500 4 3
## 1.0000 3 0
## 1.0000 2 0
## 0.0000 4 4
## NULLscenario <- LLL.SETTINGS$scenarios$S7
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.580000; P(Reject H0_subgp) = 0.380000; P(Reject H0) = 0.960000
## P(Early stop for efficacy [futility]) = 0.540000 [0.000000]
## Mean [SD] Randomized N = 416.000000 [86.567185]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.30
## 2 0.24
## 3 0.46
##
## Mean [SD] Lost N = 104.820000 [132.987446]
## Mean [SD] Analyzed N = 311.180000 [105.744144]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ---------
## 1 2 212.5000 5.00000
## 1 3 123.0000 NA
## 2 2 290.0000 NA
## 3 1 393.0000 NA
## 3 2 345.2000 10.94075
## 3 3 206.5556 12.74864
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1 0.02
## 2 10 0.20
## 3 8 0.16
## 6 29 0.58
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 0 4 1 0 0
## 2 0 1 0 0 0
## 3 1 5 9 0 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.04 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## --------- -------------- --------------
## 0.0 1 1
## 0.0 10 10
## 0.2 10 8
## 0.0 29 29
## NULLscenario <- LLL.SETTINGS$scenarios$S8
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.360000; P(Reject H0_subgp) = 0.480000; P(Reject H0) = 0.840000
## P(Early stop for efficacy [futility]) = 0.400000 [0.000000]
## Mean [SD] Randomized N = 438.000000 [83.029378]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.22
## 2 0.18
## 3 0.60
##
## Mean [SD] Lost N = 121.880000 [114.118563]
## Mean [SD] Analyzed N = 316.120000 [89.724440]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ------ ----------
## 1 2 209.0 12.727922
## 1 3 120.0 5.385165
## 1 4 87.0 NA
## 3 1 393.0 NA
## 3 2 350.5 11.030261
## 3 3 198.0 11.162437
## 3 4 153.5 4.203173
## 3 5 100.5 9.110434
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 1 0.02
## 2 5 0.10
## 3 11 0.22
## 4 3 0.06
## 5 4 0.08
## 6 18 0.36
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 0 2 5 1 0
## 2 0 0 0 0 0
## 3 1 4 11 4 4
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.16 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.0000000 1 1
## 0.1666667 6 5
## 0.3125000 16 11
## 0.4000000 5 3
## 0.0000000 4 4
## 0.0000000 18 18
## NULLscenario <- LLL.SETTINGS$scenarios$S9
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.540000; P(Reject H0_subgp) = 0.420000; P(Reject H0) = 0.960000
## P(Early stop for efficacy [futility]) = 0.480000 [0.000000]
## Mean [SD] Randomized N = 426.000000 [85.260705]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.26
## 2 0.22
## 3 0.52
##
## Mean [SD] Lost N = 124.200000 [148.980207]
## Mean [SD] Analyzed N = 301.800000 [115.994370]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 234.0000 NA
## 1 2 219.5000 2.121320
## 1 5 65.0000 NA
## 2 2 288.0000 NA
## 3 1 384.0000 2.828427
## 3 2 346.6667 15.491933
## 3 3 195.4000 7.300685
## 3 4 159.5000 10.606602
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 3 0.06
## 2 11 0.22
## 3 5 0.10
## 4 2 0.04
## 6 27 0.54
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 1 2 0 0 1
## 2 0 1 0 0 0
## 3 2 9 5 2 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.04 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.0000000 3 3
## 0.0833333 12 11
## 0.0000000 5 5
## 0.0000000 2 2
## 1.0000000 1 0
## 0.0000000 27 27
## NULLscenario <- LLL.SETTINGS$scenarios$S10
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
mean = scenario$mean,
sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))## P(Reject H0_ITT) = 0.280000; P(Reject H0_subgp) = 0.020000; P(Reject H0) = 0.300000
## P(Early stop for efficacy [futility]) = 0.260000 [0.280000]
## Mean [SD] Randomized N = 420.000000 [83.299313]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.26
## 2 0.28
## 3 0.46
##
## Mean [SD] Lost N = 105.280000 [101.708876]
## Mean [SD] Analyzed N = 314.720000 [98.752430]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 237.0000 5.244044
## 1 2 215.0000 8.869423
## 1 5 56.5000 7.148426
## 2 1 325.0000 NA
## 2 5 84.0000 NA
## 3 1 400.0000 NA
## 3 2 359.0000 NA
## 3 5 100.7059 10.042190
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 5 1 0.02
## 6 14 0.28
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 5 4 0 0 6
## 2 1 0 0 0 1
## 3 1 1 0 0 17
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.7 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 7 0
## 1.0000000 5 0
## 0.9583333 24 1
## 0.0000000 14 14
## NULLLai, Tze Leung, Philip W. Lavori, and Olivia Yueh-Wen Liao. 2014. “Adaptive Choice of Patient Subgroup for Comparing Two Treatments.” Contemporary Clinical Trials 39 (2): 191–200. doi:10.1016/j.cct.2014.09.001.