Here, we present the calculations for assessing the coverage probabilities of the constructed confidence intervals under various scenarios.
library(ASSISTant)
## Various settings
settings <- list(setting1 = list(N = c(250, 400, 550), type1Error = 0.025,
eps = 1/2, type2Error = 0.1),
setting2 = list(N = c(250, 400, 550), type1Error = 0.05,
eps = 1/2, type2Error = 0.1),
setting3 = list(N = c(250, 400, 550), type1Error = 0.1,
eps = 1/2, type2Error = 0.2),
setting4 = list(N = c(250, 400, 550), type1Error = 0.2,
eps = 1/2, type2Error = 0.3))
The design parameters are the following for various scenarios.
scenarios <- list(
scenario0 = list(prevalence = rep(1/6, 6), mean = matrix(0, 2, 6),
sd = matrix(1, 2, 6)),
scenario1 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.5, 0.4, 0.3, 0, 0, 0)),
sd = matrix(1, 2, 6)),
scenario2 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.3, 0.3, 0, 0, 0, 0)),
sd = matrix(1, 2, 6)),
scenario3 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6), rep(0.3, 6)),
sd = matrix(1, 2, 6)),
scenario4 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.4, 0.3, 0.2, 0, 0, 0)),
sd = matrix(1, 2, 6)),
scenario5 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.5, 0.5, 0.3, 0.3, 0.1, 0.1)),
sd = matrix(1, 2, 6)),
scenario6 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.6, 0.6, -0.3, -0.3, -0.3, -0.3)),
sd = matrix(1, 2, 6)),
scenario7 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6), rep(0.01, 6)),
sd = matrix(1, 2, 6)), ## very small effect
scenario8 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6), rep(0.3, 6)),
sd = matrix(1, 2, 6)), ## moderate negative effect
scenario9 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.9, 0.3, 0, -0.1, -0.4, -0.7)),
sd = matrix(1, 2, 6)), ## single strong effect with negatives thrown in
scenario10 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6), rep(-0.01, 6)),
sd = matrix(1, 2, 6)) ## very small negative effect
)
rngSeed <- 2128783
set.seed(rngSeed)
for (setting in names(settings)) {
trialParameters <- settings[[setting]]
for (scenario in names(scenarios)) {
designParameters <- scenarios[[scenario]]
cat("##############################\n")
print(sprintf("%s/%s", setting, scenario))
cat("##############################\n")
designA <- ASSISTDesign$new(trialParameters = trialParameters,
designParameters = designParameters)
print(designA)
result <- designA$explore(numberOfSimulations = 5000,
rngSeed = rngSeed,
showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
rngSeed <- floor(runif(100000 * runif(1)))
}
}
## ##############################
## [1] "setting1/scenario0"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98fc94780>
## P(Reject H0_ITT) = 0.009600; P(Reject H0_subgp) = 0.011000; P(Reject H0) = 0.020600
## P(Early stop for efficacy [futility]) = 0.012800 [0.559000]
## Mean [SD] Randomized N = 442.300000 [105.531689]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1462
## 2 0.4256
## 3 0.4282
##
## Mean [SD] Lost N = 171.411400 [94.641016]
## Mean [SD] Analyzed N = 270.888600 [103.834586]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.51814 6.021910
## 1 2 166.76557 7.485671
## 1 3 125.19417 8.354445
## 1 4 83.59091 7.732183
## 1 5 41.93206 5.801655
## 2 1 333.69424 7.132326
## 2 2 266.06311 9.570835
## 2 3 199.93902 9.523426
## 2 4 133.81250 9.387777
## 2 5 66.55056 7.719730
## 3 1 457.29752 9.232772
## 3 2 365.79091 11.497184
## 3 3 276.26549 11.080080
## 3 4 182.44172 11.017998
## 3 5 91.40000 8.994861
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 22 0.0044
## 2 11 0.0022
## 3 8 0.0016
## 4 8 0.0016
## 5 6 0.0012
## 6 48 0.0096
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- ---- ----
## 1 1185 610 412 396 471
## 2 278 206 164 176 267
## 3 121 110 113 163 280
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9794 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9861111 1584 22
## 0.9881210 926 11
## 0.9883890 689 8
## 0.9891156 735 8
## 0.9941061 1018 6
## 0.0000000 48 48
## NULL
## ##############################
## [1] "setting1/scenario1"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb990c22358>
## P(Reject H0_ITT) = 0.366000; P(Reject H0_subgp) = 0.497800; P(Reject H0) = 0.863800
## P(Early stop for efficacy [futility]) = 0.377800 [0.003600]
## Mean [SD] Randomized N = 471.580000 [109.447245]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1414
## 2 0.2400
## 3 0.6186
##
## Mean [SD] Lost N = 169.659400 [149.102289]
## Mean [SD] Analyzed N = 301.920600 [117.347704]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.30556 5.713776
## 1 2 167.11299 6.650248
## 1 3 127.33537 8.124248
## 1 4 85.05405 7.706224
## 1 5 41.06250 6.526548
## 2 1 334.12360 7.449558
## 2 2 267.28431 9.431753
## 2 3 200.96992 9.563932
## 2 4 137.87500 7.969030
## 2 5 71.80000 7.496666
## 3 1 457.15385 7.730071
## 3 2 366.05405 10.987939
## 3 3 275.81206 11.829540
## 3 4 184.24034 11.100742
## 3 5 91.54237 8.665329
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 368 0.0736
## 2 747 0.1494
## 3 1146 0.2292
## 4 189 0.0378
## 5 39 0.0078
## 6 1830 0.3660
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ----- ---- ----
## 1 144 177 164 37 16
## 2 89 102 133 24 5
## 3 208 592 1128 233 118
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9962 0.9956008
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 441 368
## 1.0000000 871 747
## 1.0000000 1425 1146
## 1.0000000 294 189
## 1.0000000 139 39
## 0.9896175 1830 1830
## NULL
## ##############################
## [1] "setting1/scenario2"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98f96efc8>
## P(Reject H0_ITT) = 0.083600; P(Reject H0_subgp) = 0.473000; P(Reject H0) = 0.556600
## P(Early stop for efficacy [futility]) = 0.241600 [0.036800]
## Mean [SD] Randomized N = 500.680000 [85.058713]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.0504
## 2 0.2280
## 3 0.7216
##
## Mean [SD] Lost N = 223.482200 [121.339012]
## Mean [SD] Analyzed N = 277.197800 [108.876607]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.69215 6.136206
## 1 2 167.12518 7.130362
## 1 3 125.75862 7.783455
## 1 4 83.75728 7.581538
## 1 5 42.29412 6.093938
## 2 1 333.83193 7.041552
## 2 2 266.09375 9.364436
## 2 3 200.53077 10.387969
## 2 4 134.20225 9.134326
## 2 5 67.50877 7.418902
## 3 1 457.40891 8.780915
## 3 2 366.16484 11.501819
## 3 3 274.59649 10.948067
## 3 4 182.86695 10.620587
## 3 5 91.58367 9.114826
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 662 0.1324
## 2 1350 0.2700
## 3 237 0.0474
## 4 76 0.0152
## 5 40 0.0080
## 6 418 0.0836
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 497 711 232 103 68
## 2 238 480 130 89 57
## 3 247 910 342 233 245
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9916 0.9849084
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9959267 982 662
## 0.9966683 2101 1350
## 0.9971591 704 237
## 1.0000000 425 76
## 1.0000000 370 40
## 0.9306220 418 418
## NULL
## ##############################
## [1] "setting1/scenario3"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb994d4f750>
## P(Reject H0_ITT) = 0.778600; P(Reject H0_subgp) = 0.049400; P(Reject H0) = 0.828000
## P(Early stop for efficacy [futility]) = 0.639800 [0.004600]
## Mean [SD] Randomized N = 397.840000 [127.767755]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3700
## 2 0.2744
## 3 0.3556
##
## Mean [SD] Lost N = 39.291600 [89.840394]
## Mean [SD] Analyzed N = 358.548400 [114.479422]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.58824 5.292176
## 1 2 166.33333 7.327503
## 1 3 127.44444 7.374218
## 1 4 82.83333 7.895146
## 1 5 42.89474 4.965377
## 2 1 332.41667 8.511579
## 2 2 267.31250 10.964906
## 2 3 199.37500 7.249384
## 2 4 131.00000 9.290193
## 2 5 66.70588 7.895922
## 3 1 458.16327 9.186373
## 3 2 366.68367 11.295101
## 3 3 273.46429 12.716541
## 3 4 181.04103 10.443187
## 3 5 91.65336 8.624787
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 40 0.0080
## 2 59 0.0118
## 3 52 0.0104
## 4 47 0.0094
## 5 49 0.0098
## 6 3893 0.7786
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- ---- ---- ----
## 1 34 27 18 12 19
## 2 12 16 8 14 17
## 3 49 98 112 195 476
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9968 0.9961353
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 95 40
## 0.9929078 141 59
## 1.0000000 138 52
## 1.0000000 221 47
## 1.0000000 512 49
## 0.9961469 3893 3893
## NULL
## ##############################
## [1] "setting1/scenario4"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.4 0 0.3 0 0.2 0 0 0 0 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98f598bc0>
## P(Reject H0_ITT) = 0.193000; P(Reject H0_subgp) = 0.504600; P(Reject H0) = 0.697600
## P(Early stop for efficacy [futility]) = 0.295200 [0.012400]
## Mean [SD] Randomized N = 491.650000 [94.934609]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.0814
## 2 0.2262
## 3 0.6924
##
## Mean [SD] Lost N = 204.924200 [137.168770]
## Mean [SD] Analyzed N = 286.725800 [114.992854]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.29086 5.720446
## 1 2 167.84375 7.171850
## 1 3 126.15812 7.136664
## 1 4 83.92857 7.086022
## 1 5 42.35135 6.876757
## 2 1 332.62319 8.236648
## 2 2 267.35749 9.217845
## 2 3 201.01523 10.112872
## 2 4 132.11864 9.645590
## 2 5 68.18519 7.359123
## 3 1 458.66254 8.322352
## 3 2 366.14416 11.465642
## 3 3 274.82943 12.134243
## 3 4 184.35621 10.756953
## 3 5 92.19266 8.157411
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 651 0.1302
## 2 821 0.1642
## 3 809 0.1618
## 4 178 0.0356
## 5 64 0.0128
## 6 965 0.1930
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 361 288 234 84 37
## 2 138 207 197 59 27
## 3 323 659 897 306 218
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9936 0.9908257
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9987835 822 651
## 0.9965338 1154 821
## 0.9992470 1328 809
## 1.0000000 449 178
## 1.0000000 282 64
## 0.9730570 965 965
## NULL
## ##############################
## [1] "setting1/scenario5"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.5 0 0.5 0 0.3 0 0.3 0 0.1 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98faee000>
## P(Reject H0_ITT) = 0.766800; P(Reject H0_subgp) = 0.164600; P(Reject H0) = 0.931400
## P(Early stop for efficacy [futility]) = 0.638000 [0.000600]
## Mean [SD] Randomized N = 400.930000 [126.987638]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3552
## 2 0.2834
## 3 0.3614
##
## Mean [SD] Lost N = 55.709400 [113.437725]
## Mean [SD] Analyzed N = 345.220600 [116.406307]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.26923 5.618239
## 1 2 168.63043 7.196785
## 1 3 127.42105 6.914685
## 1 4 83.48148 9.099325
## 1 5 41.25000 7.135592
## 2 1 335.83333 5.455884
## 2 2 264.88000 9.799320
## 2 3 199.55556 12.400717
## 2 4 133.53846 9.597008
## 2 5 67.75000 10.719919
## 3 1 456.70000 7.903112
## 3 2 367.01487 11.806263
## 3 3 275.31553 11.360713
## 3 4 184.52881 11.328356
## 3 5 92.10778 8.286315
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 65 0.0130
## 2 281 0.0562
## 3 181 0.0362
## 4 217 0.0434
## 5 79 0.0158
## 6 3834 0.7668
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- ---- ---- ---- ----
## 1 26 46 19 27 4
## 2 6 25 9 13 4
## 3 50 269 206 295 167
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9972 0.9969938
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 82 65
## 1.0000000 340 281
## 1.0000000 234 181
## 1.0000000 335 217
## 1.0000000 175 79
## 0.9963485 3834 3834
## NULL
## ##############################
## [1] "setting1/scenario6"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.6 0 0.6 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb994c4c670>
## P(Reject H0_ITT) = 0.009000; P(Reject H0_subgp) = 0.983400; P(Reject H0) = 0.992400
## P(Early stop for efficacy [futility]) = 0.811800 [0.001200]
## Mean [SD] Randomized N = 392.620000 [97.310994]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.2362
## 2 0.5768
## 3 0.1870
##
## Mean [SD] Lost N = 220.468400 [76.317103]
## Mean [SD] Analyzed N = 172.151600 [72.884977]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 208.4572 5.948180
## 1 2 167.4858 7.241291
## 1 3 127.8370 8.120354
## 1 4 86.0000 10.862780
## 1 5 40.5000 7.778175
## 2 1 332.1341 7.607278
## 2 2 265.7067 9.331848
## 2 3 201.1333 9.448104
## 2 4 127.0000 11.313709
## 3 1 460.2381 6.371066
## 3 2 363.5560 11.077348
## 3 3 266.4286 13.758114
## 3 4 193.0000 7.071068
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 639 0.1278
## 2 4178 0.8356
## 3 95 0.0190
## 4 5 0.0010
## 6 45 0.0090
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- --- --- ---
## 1 538 2501 92 5 2
## 2 82 992 15 2 0
## 3 21 696 7 2 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9904 0.9903265
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 641 639
## 0.9995226 4189 4178
## 0.9912281 114 95
## 1.0000000 9 5
## 1.0000000 2 0
## 0.0000000 45 45
## NULL
## ##############################
## [1] "setting1/scenario7"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.01 0 0.01 0 0.01 0 0.01 0 0.01 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb991e9bbf8>
## P(Reject H0_ITT) = 0.011800; P(Reject H0_subgp) = 0.012400; P(Reject H0) = 0.024200
## P(Early stop for efficacy [futility]) = 0.014400 [0.519000]
## Mean [SD] Randomized N = 451.330000 [103.270829]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1244
## 2 0.4090
## 3 0.4666
##
## Mean [SD] Lost N = 169.514400 [94.831484]
## Mean [SD] Analyzed N = 281.815600 [104.862054]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.29747 5.789453
## 1 2 166.96795 7.517487
## 1 3 124.72026 8.329245
## 1 4 83.49471 7.437893
## 1 5 41.34831 5.957245
## 2 1 333.84502 7.426053
## 2 2 267.60000 9.908696
## 2 3 201.08383 10.629247
## 2 4 134.85427 8.978868
## 2 5 67.14737 7.325388
## 3 1 459.45528 8.711451
## 3 2 368.08824 10.385732
## 3 3 276.25714 11.943736
## 3 4 184.31169 10.986932
## 3 5 92.21981 9.431577
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 26 0.0052
## 2 15 0.0030
## 3 8 0.0016
## 4 8 0.0016
## 5 5 0.0010
## 6 59 0.0118
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- ---- ----
## 1 1106 624 454 378 445
## 2 271 170 167 199 285
## 3 123 102 140 154 323
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9814 0.231405
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9860000 1500 26
## 0.9866071 896 15
## 0.9934297 761 8
## 0.9931601 731 8
## 0.9971510 1053 5
## 0.2033898 59 59
## NULL
## ##############################
## [1] "setting1/scenario8"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98ee23268>
## P(Reject H0_ITT) = 0.778600; P(Reject H0_subgp) = 0.049400; P(Reject H0) = 0.828000
## P(Early stop for efficacy [futility]) = 0.639800 [0.004600]
## Mean [SD] Randomized N = 397.840000 [127.767755]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3700
## 2 0.2744
## 3 0.3556
##
## Mean [SD] Lost N = 39.291600 [89.840394]
## Mean [SD] Analyzed N = 358.548400 [114.479422]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.58824 5.292176
## 1 2 166.33333 7.327503
## 1 3 127.44444 7.374218
## 1 4 82.83333 7.895146
## 1 5 42.89474 4.965377
## 2 1 332.41667 8.511579
## 2 2 267.31250 10.964906
## 2 3 199.37500 7.249384
## 2 4 131.00000 9.290193
## 2 5 66.70588 7.895922
## 3 1 458.16327 9.186373
## 3 2 366.68367 11.295101
## 3 3 273.46429 12.716541
## 3 4 181.04103 10.443187
## 3 5 91.65336 8.624787
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 40 0.0080
## 2 59 0.0118
## 3 52 0.0104
## 4 47 0.0094
## 5 49 0.0098
## 6 3893 0.7786
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- ---- ---- ----
## 1 34 27 18 12 19
## 2 12 16 8 14 17
## 3 49 98 112 195 476
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9968 0.9961353
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 95 40
## 0.9929078 141 59
## 1.0000000 138 52
## 1.0000000 221 47
## 1.0000000 512 49
## 0.9961469 3893 3893
## NULL
## ##############################
## [1] "setting1/scenario9"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.9 0 0.3 0 0 0 -0.1 0 -0.4 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb9964c8bc8>
## P(Reject H0_ITT) = 0.008400; P(Reject H0_subgp) = 0.984400; P(Reject H0) = 0.992800
## P(Early stop for efficacy [futility]) = 0.830200 [0.000400]
## Mean [SD] Randomized N = 376.150000 [103.120339]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3284
## 2 0.5022
## 3 0.1694
##
## Mean [SD] Lost N = 236.279200 [87.881897]
## Mean [SD] Analyzed N = 139.870800 [85.944984]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.84950 5.689130
## 1 2 167.82227 7.278408
## 1 3 127.09125 8.276659
## 1 4 85.93846 7.260503
## 1 5 46.00000 NA
## 2 1 332.36380 7.521295
## 2 2 266.34653 9.419304
## 2 3 200.81522 10.083094
## 2 4 133.88235 7.809308
## 3 1 455.30986 8.788189
## 3 2 363.90208 11.358048
## 3 3 272.67647 11.377434
## 3 4 184.05000 11.047624
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 2664 0.5328
## 2 1764 0.3528
## 3 413 0.0826
## 4 80 0.0160
## 5 1 0.0002
## 6 42 0.0084
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ----- ---- --- ---
## 1 1814 1024 263 65 1
## 2 569 404 92 17 0
## 3 284 337 68 20 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9914 0.9913376
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 2667 2664
## 1.0000000 1765 1764
## 0.9976359 423 413
## 1.0000000 102 80
## 1.0000000 1 1
## 0.0000000 42 42
## NULL
## ##############################
## [1] "setting1/scenario10"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 -0.01 0 -0.01 0 -0.01 0 -0.01 0 -0.01 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.0798
## Boundaries:
## Named num [1:3] -1.85 2.64 2.77
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb994f661b8>
## P(Reject H0_ITT) = 0.007400; P(Reject H0_subgp) = 0.007600; P(Reject H0) = 0.015000
## P(Early stop for efficacy [futility]) = 0.009600 [0.611200]
## Mean [SD] Randomized N = 434.230000 [103.730223]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1510
## 2 0.4698
## 3 0.3792
##
## Mean [SD] Lost N = 168.268400 [88.873459]
## Mean [SD] Analyzed N = 265.961600 [101.643691]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.41595 5.833817
## 1 2 166.56153 7.153722
## 1 3 125.48374 7.926196
## 1 4 83.62871 7.654497
## 1 5 41.51203 6.070164
## 2 1 333.37255 7.664626
## 2 2 266.40000 9.221423
## 2 3 199.19868 9.907586
## 2 4 133.23392 10.546994
## 2 5 66.76271 7.190038
## 3 1 458.39130 8.689967
## 3 2 367.08750 10.344929
## 3 3 274.50526 11.751753
## 3 4 182.01835 11.238971
## 3 5 92.10588 8.541271
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 14 0.0028
## 2 10 0.0020
## 3 7 0.0014
## 4 6 0.0012
## 5 1 0.0002
## 6 37 0.0074
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- ---- ----
## 1 1279 707 492 404 457
## 2 255 180 151 171 236
## 3 92 80 95 109 255
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9834 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9895449 1626 14
## 0.9896587 967 10
## 0.9905149 738 7
## 0.9868421 684 6
## 0.9968354 948 1
## 0.0000000 37 37
## NULL
## ##############################
## [1] "setting2/scenario0"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb993789788>
## P(Reject H0_ITT) = 0.018200; P(Reject H0_subgp) = 0.022800; P(Reject H0) = 0.041000
## P(Early stop for efficacy [futility]) = 0.023400 [0.462000]
## Mean [SD] Randomized N = 459.850000 [102.954346]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1156
## 2 0.3698
## 3 0.5146
##
## Mean [SD] Lost N = 181.095800 [101.835259]
## Mean [SD] Analyzed N = 278.754200 [108.522283]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.52480 6.005305
## 1 2 166.77972 7.117016
## 1 3 125.04926 8.340444
## 1 4 83.16766 7.494264
## 1 5 41.90859 5.919831
## 2 1 333.61538 7.327841
## 2 2 267.19598 9.364493
## 2 3 199.49669 9.053084
## 2 4 133.22699 8.596080
## 2 5 67.26809 7.902210
## 3 1 457.63536 8.789493
## 3 2 366.26543 11.601453
## 3 3 274.95833 11.267259
## 3 4 182.44086 10.971671
## 3 5 90.60405 8.702283
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 46 0.0092
## 2 26 0.0052
## 3 22 0.0044
## 4 10 0.0020
## 5 10 0.0020
## 6 91 0.0182
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- ---- ----
## 1 1109 572 406 334 361
## 2 312 199 151 163 235
## 3 181 162 192 186 346
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.959 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9712859 1602 46
## 0.9721329 933 26
## 0.9706275 749 22
## 0.9853587 683 10
## 0.9893843 942 10
## 0.0000000 91 91
## NULL
## ##############################
## [1] "setting2/scenario1"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb990bcddf8>
## P(Reject H0_ITT) = 0.478200; P(Reject H0_subgp) = 0.430200; P(Reject H0) = 0.908400
## P(Early stop for efficacy [futility]) = 0.455400 [0.001400]
## Mean [SD] Randomized N = 450.130000 [120.059843]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.2090
## 2 0.2478
## 3 0.5432
##
## Mean [SD] Lost N = 144.040000 [154.165700]
## Mean [SD] Analyzed N = 306.090000 [118.335049]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.99029 4.999010
## 1 2 168.72000 7.265251
## 1 3 126.84553 8.225343
## 1 4 84.71429 7.210369
## 1 5 41.14286 7.690439
## 2 1 333.90909 7.370015
## 2 2 266.06494 8.313492
## 2 3 200.94949 10.058374
## 2 4 132.47059 9.676761
## 2 5 68.25000 8.301606
## 3 1 458.02857 8.605058
## 3 2 366.54775 11.210288
## 3 3 276.04894 11.379772
## 3 4 184.83871 11.063249
## 3 5 90.52747 8.000473
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 309 0.0618
## 2 672 0.1344
## 3 975 0.1950
## 4 159 0.0318
## 5 36 0.0072
## 6 2391 0.4782
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ---
## 1 103 125 123 28 7
## 2 44 77 99 17 4
## 3 210 555 940 186 91
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9906 0.9896521
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9971989 357 309
## 1.0000000 757 672
## 1.0000000 1162 975
## 1.0000000 231 159
## 1.0000000 102 36
## 0.9807612 2391 2391
## NULL
## ##############################
## [1] "setting2/scenario2"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb990ce03f0>
## P(Reject H0_ITT) = 0.129600; P(Reject H0_subgp) = 0.490600; P(Reject H0) = 0.620200
## P(Early stop for efficacy [futility]) = 0.278200 [0.026200]
## Mean [SD] Randomized N = 493.330000 [92.702372]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.0734
## 2 0.2310
## 3 0.6956
##
## Mean [SD] Lost N = 224.347200 [132.432259]
## Mean [SD] Analyzed N = 268.982800 [111.736350]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.96622 5.569283
## 1 2 167.35009 7.305972
## 1 3 125.83957 8.068653
## 1 4 83.61333 8.200022
## 1 5 40.68852 6.257105
## 2 1 333.35354 7.693115
## 2 2 266.39667 9.253411
## 2 3 200.38000 9.133997
## 2 4 134.13115 10.179187
## 2 5 67.12195 7.877802
## 3 1 457.40678 8.638072
## 3 2 366.12442 11.604131
## 3 3 274.31081 11.126674
## 3 4 185.47368 10.637984
## 3 5 92.77778 8.844613
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 670 0.1340
## 2 1383 0.2766
## 3 264 0.0528
## 4 99 0.0198
## 5 37 0.0074
## 6 648 0.1296
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- ---- ---- ----
## 1 444 577 187 75 61
## 2 198 421 100 61 41
## 3 295 1069 370 228 225
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9866 0.9783941
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9882604 937 670
## 0.9970972 2067 1383
## 0.9969559 657 264
## 1.0000000 364 99
## 1.0000000 327 37
## 0.9259259 648 648
## NULL
## ##############################
## [1] "setting2/scenario3"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98ffa49c8>
## P(Reject H0_ITT) = 0.855400; P(Reject H0_subgp) = 0.036000; P(Reject H0) = 0.891400
## P(Early stop for efficacy [futility]) = 0.739400 [0.002000]
## Mean [SD] Randomized N = 366.760000 [124.584135]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.4802
## 2 0.2612
## 3 0.2586
##
## Mean [SD] Lost N = 26.924200 [79.727487]
## Mean [SD] Analyzed N = 339.835800 [110.942436]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.59091 5.234129
## 1 2 166.07692 9.322567
## 1 3 121.00000 8.185353
## 1 4 85.80000 8.134972
## 1 5 40.00000 5.722762
## 2 1 334.07692 9.250780
## 2 2 267.66667 5.773503
## 2 3 195.50000 11.030261
## 2 4 135.66667 16.072751
## 2 5 68.00000 5.000000
## 3 1 458.16000 9.590301
## 3 2 366.86567 12.052782
## 3 3 275.32927 11.728466
## 3 4 182.47619 9.752806
## 3 5 91.13253 8.503806
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 39 0.0078
## 2 30 0.0060
## 3 27 0.0054
## 4 34 0.0068
## 5 50 0.0100
## 6 4277 0.8554
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- ---- ----
## 1 22 13 3 10 9
## 2 13 3 4 3 7
## 3 50 67 82 105 332
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9954 0.9948396
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 85 39
## 1.0000000 83 30
## 1.0000000 89 27
## 1.0000000 118 34
## 1.0000000 348 50
## 0.9946224 4277 4277
## NULL
## ##############################
## [1] "setting2/scenario4"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.4 0 0.3 0 0.2 0 0 0 0 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb992839670>
## P(Reject H0_ITT) = 0.275800; P(Reject H0_subgp) = 0.485600; P(Reject H0) = 0.761400
## P(Early stop for efficacy [futility]) = 0.342000 [0.007200]
## Mean [SD] Randomized N = 478.990000 [105.831564]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1242
## 2 0.2250
## 3 0.6508
##
## Mean [SD] Lost N = 192.834600 [149.471900]
## Mean [SD] Analyzed N = 286.155400 [121.026526]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.46237 5.756246
## 1 2 167.66537 7.172872
## 1 3 125.91477 8.115495
## 1 4 86.10638 7.664810
## 1 5 39.47368 5.699595
## 2 1 333.31667 7.053199
## 2 2 268.17901 9.071082
## 2 3 202.03906 10.374410
## 2 4 133.15217 8.692187
## 2 5 66.88235 8.999183
## 3 1 457.66053 8.870693
## 3 2 367.09495 10.668608
## 3 3 275.39019 11.586929
## 3 4 183.04626 10.798214
## 3 5 93.02000 8.773510
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 610 0.1220
## 2 821 0.1642
## 3 776 0.1552
## 4 177 0.0354
## 5 44 0.0088
## 6 1379 0.2758
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 279 257 176 47 19
## 2 120 162 128 46 17
## 3 380 653 856 281 200
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9938 0.9918571
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9961489 779 610
## 0.9972015 1072 821
## 1.0000000 1160 776
## 1.0000000 374 177
## 1.0000000 236 44
## 0.9818709 1379 1379
## NULL
## ##############################
## [1] "setting2/scenario5"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.5 0 0.5 0 0.3 0 0.3 0 0.1 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb992bf86d0>
## P(Reject H0_ITT) = 0.854800; P(Reject H0_subgp) = 0.110800; P(Reject H0) = 0.965600
## P(Early stop for efficacy [futility]) = 0.737600 [0.000600]
## Mean [SD] Randomized N = 367.990000 [124.743625]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.4752
## 2 0.2630
## 3 0.2618
##
## Mean [SD] Lost N = 37.217400 [98.974211]
## Mean [SD] Analyzed N = 330.772600 [111.756768]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 207.25000 2.895922
## 1 2 168.03704 7.683556
## 1 3 120.22222 8.437680
## 1 4 84.57143 2.760262
## 1 5 48.40000 5.412947
## 2 1 337.00000 5.099019
## 2 2 269.17647 8.669164
## 2 3 193.14286 3.670993
## 2 4 142.25000 7.041543
## 2 5 66.00000 8.755950
## 3 1 458.47619 8.854482
## 3 2 367.46701 10.636632
## 3 3 274.38583 10.549992
## 3 4 184.55670 11.226790
## 3 5 92.79710 8.935356
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 46 0.0092
## 2 209 0.0418
## 3 112 0.0224
## 4 158 0.0316
## 5 29 0.0058
## 6 4274 0.8548
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- ---- ---- ---- ---
## 1 12 27 9 7 5
## 2 5 17 7 4 4
## 3 42 197 127 194 69
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9964 0.9962717
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 59 46
## 1.0000000 241 209
## 1.0000000 143 112
## 1.0000000 205 158
## 1.0000000 78 29
## 0.9957885 4274 4274
## NULL
## ##############################
## [1] "setting2/scenario6"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.6 0 0.6 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98f92cc60>
## P(Reject H0_ITT) = 0.016200; P(Reject H0_subgp) = 0.979000; P(Reject H0) = 0.995200
## P(Early stop for efficacy [futility]) = 0.760400 [0.000400]
## Mean [SD] Randomized N = 396.460000 [106.229588]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.2628
## 2 0.4980
## 3 0.2392
##
## Mean [SD] Lost N = 231.999800 [84.262760]
## Mean [SD] Analyzed N = 164.460200 [71.212897]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 208.2769 6.125820
## 1 2 167.4275 7.157558
## 1 3 127.9595 8.885018
## 1 4 90.8000 7.463243
## 1 5 40.0000 NA
## 2 1 333.3448 7.839713
## 2 2 266.5435 9.324497
## 2 3 201.2105 10.008768
## 3 1 454.9630 7.949269
## 3 2 363.4251 11.313607
## 3 3 271.6364 12.855137
## 3 4 183.6667 10.503967
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 598 0.1196
## 2 4195 0.8390
## 3 98 0.0196
## 4 4 0.0008
## 6 81 0.0162
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- --- --- ---
## 1 484 2180 74 5 1
## 2 87 1047 19 0 0
## 3 27 981 11 3 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.983 0.982918
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9966555 598 598
## 0.9997624 4208 4195
## 0.9903846 104 98
## 1.0000000 8 4
## 1.0000000 1 0
## 0.0000000 81 81
## NULL
## ##############################
## [1] "setting2/scenario7"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.01 0 0.01 0 0.01 0 0.01 0 0.01 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98fefdf78>
## P(Reject H0_ITT) = 0.022800; P(Reject H0_subgp) = 0.022000; P(Reject H0) = 0.044800
## P(Early stop for efficacy [futility]) = 0.025800 [0.424400]
## Mean [SD] Randomized N = 465.730000 [102.777331]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1116
## 2 0.3386
## 3 0.5498
##
## Mean [SD] Lost N = 180.061600 [102.733684]
## Mean [SD] Analyzed N = 285.668400 [109.965552]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.58440 5.892652
## 1 2 166.91373 7.101776
## 1 3 125.26566 7.837841
## 1 4 83.96310 7.660778
## 1 5 42.16435 5.793780
## 2 1 333.52090 7.300821
## 2 2 266.78899 9.275679
## 2 3 200.21605 9.316864
## 2 4 133.41341 9.332018
## 2 5 67.29960 7.481095
## 3 1 457.88202 8.178283
## 3 2 365.90960 11.016659
## 3 3 274.07222 11.401769
## 3 4 184.43069 11.003737
## 3 5 91.59242 8.424584
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 37 0.0074
## 2 26 0.0052
## 3 26 0.0052
## 4 11 0.0022
## 5 10 0.0020
## 6 114 0.0228
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- ---- ----
## 1 1013 568 399 271 359
## 2 311 218 162 179 247
## 3 178 177 180 202 422
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9654 0.2276786
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9786951 1502 37
## 0.9792316 963 26
## 0.9703104 741 26
## 0.9877301 652 11
## 0.9931907 1028 10
## 0.2631579 114 114
## NULL
## ##############################
## [1] "setting2/scenario8"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98ee82230>
## P(Reject H0_ITT) = 0.855400; P(Reject H0_subgp) = 0.036000; P(Reject H0) = 0.891400
## P(Early stop for efficacy [futility]) = 0.739400 [0.002000]
## Mean [SD] Randomized N = 366.760000 [124.584135]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.4802
## 2 0.2612
## 3 0.2586
##
## Mean [SD] Lost N = 26.924200 [79.727487]
## Mean [SD] Analyzed N = 339.835800 [110.942436]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.59091 5.234129
## 1 2 166.07692 9.322567
## 1 3 121.00000 8.185353
## 1 4 85.80000 8.134972
## 1 5 40.00000 5.722762
## 2 1 334.07692 9.250780
## 2 2 267.66667 5.773503
## 2 3 195.50000 11.030261
## 2 4 135.66667 16.072751
## 2 5 68.00000 5.000000
## 3 1 458.16000 9.590301
## 3 2 366.86567 12.052782
## 3 3 275.32927 11.728466
## 3 4 182.47619 9.752806
## 3 5 91.13253 8.503806
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 39 0.0078
## 2 30 0.0060
## 3 27 0.0054
## 4 34 0.0068
## 5 50 0.0100
## 6 4277 0.8554
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- ---- ----
## 1 22 13 3 10 9
## 2 13 3 4 3 7
## 3 50 67 82 105 332
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9954 0.9948396
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 85 39
## 1.0000000 83 30
## 1.0000000 89 27
## 1.0000000 118 34
## 1.0000000 348 50
## 0.9946224 4277 4277
## NULL
## ##############################
## [1] "setting2/scenario9"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.9 0 0.3 0 0 0 -0.1 0 -0.4 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb992893118>
## P(Reject H0_ITT) = 0.017200; P(Reject H0_subgp) = 0.978800; P(Reject H0) = 0.996000
## P(Early stop for efficacy [futility]) = 0.763800 [0.000200]
## Mean [SD] Randomized N = 382.750000 [113.633270]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.351
## 2 0.413
## 3 0.236
##
## Mean [SD] Lost N = 250.977600 [98.929123]
## Mean [SD] Analyzed N = 131.772400 [83.356907]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 208.9210 5.762072
## 1 2 167.9169 7.298724
## 1 3 127.4392 7.819285
## 1 4 86.4000 8.553043
## 2 1 333.3963 6.849915
## 2 2 266.9693 9.705425
## 2 3 201.2500 10.706085
## 2 4 134.0000 7.615773
## 3 1 455.3398 8.754840
## 3 2 363.9262 10.849857
## 3 3 272.6053 11.459524
## 3 4 184.3684 12.544191
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 2630 0.5260
## 2 1814 0.3628
## 3 378 0.0756
## 4 72 0.0144
## 6 86 0.0172
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- --- ---
## 1 1633 903 189 45 0
## 2 535 424 80 19 0
## 3 465 488 114 19 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9816 0.9815261
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 2633 2630
## 0.9988981 1815 1814
## 0.9921671 383 378
## 0.9879518 83 72
## 0.0000000 86 86
## NULL
## ##############################
## [1] "setting2/scenario10"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 -0.01 0 -0.01 0 -0.01 0 -0.01 0 -0.01 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.05
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.072
## Boundaries:
## Named num [1:3] -1.85 2.36 2.49
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb996380698>
## P(Reject H0_ITT) = 0.014800; P(Reject H0_subgp) = 0.018200; P(Reject H0) = 0.033000
## P(Early stop for efficacy [futility]) = 0.019800 [0.493600]
## Mean [SD] Randomized N = 453.940000 [104.396629]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1270
## 2 0.3864
## 3 0.4866
##
## Mean [SD] Lost N = 180.894800 [101.114526]
## Mean [SD] Analyzed N = 273.045200 [107.137788]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.57823 5.765842
## 1 2 167.30000 7.421190
## 1 3 124.61111 8.091582
## 1 4 84.21296 7.476756
## 1 5 41.20312 6.109565
## 2 1 334.05797 7.464809
## 2 2 266.13260 9.651372
## 2 3 200.22485 9.738686
## 2 4 133.72671 8.560073
## 2 5 66.87448 7.888465
## 3 1 458.07568 9.611175
## 3 2 367.09774 10.837550
## 3 3 274.05839 12.337036
## 3 4 183.16561 10.581701
## 3 5 91.30091 8.974423
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 45 0.0090
## 2 18 0.0036
## 3 13 0.0026
## 4 6 0.0012
## 5 9 0.0018
## 6 74 0.0148
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- ---- ----
## 1 1176 610 396 324 384
## 2 345 181 169 161 239
## 3 185 133 137 157 329
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9634 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9701055 1706 45
## 0.9772727 924 18
## 0.9786325 702 13
## 0.9875389 642 6
## 0.9852941 952 9
## 0.0000000 74 74
## NULL
## ##############################
## [1] "setting3/scenario0"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb990cdd150>
## P(Reject H0_ITT) = 0.039600; P(Reject H0_subgp) = 0.042600; P(Reject H0) = 0.082200
## P(Early stop for efficacy [futility]) = 0.050800 [0.346400]
## Mean [SD] Randomized N = 471.940000 [105.649746]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1232
## 2 0.2740
## 3 0.6028
##
## Mean [SD] Lost N = 187.931800 [111.661551]
## Mean [SD] Analyzed N = 284.008200 [114.900098]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.50725 5.415909
## 1 2 167.26275 7.553190
## 1 3 124.98438 8.135399
## 1 4 83.53925 7.039711
## 1 5 41.74558 5.785676
## 2 1 333.14148 6.751290
## 2 2 266.75122 8.728563
## 2 3 200.20000 9.882745
## 2 4 133.63433 9.227730
## 2 5 66.77778 7.889515
## 3 1 458.72563 8.260511
## 3 2 366.26341 11.091371
## 3 3 274.82787 11.028353
## 3 4 183.24046 10.570299
## 3 5 92.15844 8.653085
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 80 0.0160
## 2 59 0.0118
## 3 40 0.0080
## 4 19 0.0038
## 5 15 0.0030
## 6 198 0.0396
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 966 510 320 293 283
## 2 311 205 135 134 171
## 3 277 205 244 262 486
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9178 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9485199 1554 80
## 0.9358696 920 59
## 0.9427754 699 40
## 0.9724238 689 19
## 0.9840426 940 15
## 0.0000000 198 198
## NULL
## ##############################
## [1] "setting3/scenario1"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb994de6d78>
## P(Reject H0_ITT) = 0.595200; P(Reject H0_subgp) = 0.350200; P(Reject H0) = 0.945400
## P(Early stop for efficacy [futility]) = 0.546800 [0.000600]
## Mean [SD] Randomized N = 421.330000 [129.289885]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3104
## 2 0.2370
## 3 0.4526
##
## Mean [SD] Lost N = 117.152200 [154.136303]
## Mean [SD] Analyzed N = 304.177800 [119.781725]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.66667 5.601625
## 1 2 169.47368 6.818064
## 1 3 127.30120 7.542942
## 1 4 85.40000 9.856752
## 1 5 45.66667 5.859465
## 2 1 334.90909 7.186635
## 2 2 265.61364 8.978569
## 2 3 202.68182 10.591292
## 2 4 129.60000 4.505552
## 2 5 72.00000 9.000000
## 3 1 458.16895 9.220228
## 3 2 366.92157 11.081790
## 3 3 275.81673 11.559209
## 3 4 185.23016 11.075857
## 3 5 92.57143 8.009576
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 323 0.0646
## 2 538 0.1076
## 3 769 0.1538
## 4 100 0.0200
## 5 21 0.0042
## 6 2976 0.5952
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ---
## 1 105 95 83 10 3
## 2 33 44 44 5 3
## 3 219 459 753 126 42
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9874 0.9866723
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9943978 357 323
## 1.0000000 598 538
## 1.0000000 880 769
## 1.0000000 141 100
## 1.0000000 48 21
## 0.9795027 2976 2976
## NULL
## ##############################
## [1] "setting3/scenario2"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb9929df190>
## P(Reject H0_ITT) = 0.218800; P(Reject H0_subgp) = 0.483600; P(Reject H0) = 0.702400
## P(Early stop for efficacy [futility]) = 0.320800 [0.012600]
## Mean [SD] Randomized N = 481.690000 [105.225750]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1220
## 2 0.2114
## 3 0.6666
##
## Mean [SD] Lost N = 219.498400 [151.232660]
## Mean [SD] Analyzed N = 262.191600 [117.297687]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.58309 5.969558
## 1 2 167.12927 7.211128
## 1 3 125.44444 7.743442
## 1 4 83.51064 6.560330
## 1 5 41.88571 4.843257
## 2 1 332.99259 7.643646
## 2 2 266.92830 9.881042
## 2 3 199.50877 11.299688
## 2 4 137.16129 8.741078
## 2 5 67.43750 8.702251
## 3 1 458.50125 8.777219
## 3 2 366.11183 11.031628
## 3 3 275.27411 12.629421
## 3 4 184.87037 11.775491
## 3 5 92.20106 8.569602
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 632 0.1264
## 2 1379 0.2758
## 3 274 0.0548
## 4 95 0.0190
## 5 38 0.0076
## 6 1094 0.2188
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- ---- ---- ----
## 1 343 410 126 47 35
## 2 135 265 57 31 16
## 3 399 1243 394 216 189
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9694 0.9564351
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9817560 877 632
## 0.9927007 1918 1379
## 0.9965338 577 274
## 0.9965986 294 95
## 1.0000000 240 38
## 0.8903108 1094 1094
## NULL
## ##############################
## [1] "setting3/scenario3"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb990c4c508>
## P(Reject H0_ITT) = 0.914600; P(Reject H0_subgp) = 0.028200; P(Reject H0) = 0.942800
## P(Early stop for efficacy [futility]) = 0.834400 [0.001400]
## Mean [SD] Randomized N = 334.150000 [113.722751]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.6032
## 2 0.2326
## 3 0.1642
##
## Mean [SD] Lost N = 15.987200 [61.964255]
## Mean [SD] Analyzed N = 318.162800 [100.907883]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 209.92308 4.212314
## 1 2 164.53846 8.588902
## 1 3 124.33333 5.085928
## 1 4 86.40000 10.469002
## 1 5 42.50000 7.489386
## 2 1 337.50000 8.812869
## 2 2 273.00000 10.583005
## 2 3 193.00000 15.874508
## 2 4 133.50000 2.121320
## 2 5 73.00000 NA
## 3 1 458.64286 9.699997
## 3 2 361.42857 13.120002
## 3 3 273.25000 13.789560
## 3 4 181.69512 11.671099
## 3 5 93.61963 8.929220
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 25 0.0050
## 2 26 0.0052
## 3 26 0.0052
## 4 36 0.0072
## 5 28 0.0056
## 6 4573 0.9146
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ----
## 1 13 13 6 10 12
## 2 4 3 3 2 1
## 3 28 35 52 82 163
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9894 0.9887569
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 45 25
## 1.0000000 51 26
## 1.0000000 61 26
## 1.0000000 94 36
## 1.0000000 176 28
## 0.9884102 4573 4573
## NULL
## ##############################
## [1] "setting3/scenario4"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.4 0 0.3 0 0.2 0 0 0 0 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98f638b78>
## P(Reject H0_ITT) = 0.399600; P(Reject H0_subgp) = 0.431600; P(Reject H0) = 0.831200
## P(Early stop for efficacy [futility]) = 0.419400 [0.003000]
## Mean [SD] Randomized N = 458.260000 [117.735062]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1892
## 2 0.2332
## 3 0.5776
##
## Mean [SD] Lost N = 169.367200 [161.015060]
## Mean [SD] Analyzed N = 288.892800 [123.115614]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 209.16176 5.928832
## 1 2 168.81215 7.974826
## 1 3 126.19328 7.631644
## 1 4 86.08000 8.845526
## 1 5 42.81818 6.060303
## 2 1 333.02083 6.949410
## 2 2 268.46154 8.814518
## 2 3 201.19767 11.145898
## 2 4 134.05000 9.219402
## 2 5 66.72727 10.555481
## 3 1 457.90201 8.402228
## 3 2 366.15944 10.590224
## 3 3 275.22342 11.413032
## 3 4 183.46667 10.986057
## 3 5 92.30000 9.015952
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 544 0.1088
## 2 724 0.1448
## 3 711 0.1422
## 4 143 0.0286
## 5 36 0.0072
## 6 1998 0.3996
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 204 181 119 25 22
## 2 96 91 86 20 11
## 3 398 646 743 240 120
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9798 0.9756978
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9871060 698 544
## 0.9956427 918 724
## 1.0000000 948 711
## 1.0000000 285 143
## 1.0000000 153 36
## 0.9559560 1998 1998
## NULL
## ##############################
## [1] "setting3/scenario5"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.5 0 0.5 0 0.3 0 0.3 0 0.1 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb99630d990>
## P(Reject H0_ITT) = 0.914400; P(Reject H0_subgp) = 0.070600; P(Reject H0) = 0.985000
## P(Early stop for efficacy [futility]) = 0.832200 [0.000000]
## Mean [SD] Randomized N = 337.930000 [114.067600]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.5816
## 2 0.2506
## 3 0.1678
##
## Mean [SD] Lost N = 22.757000 [80.903037]
## Mean [SD] Analyzed N = 315.173000 [101.489376]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- -----------
## 1 1 209.16667 8.3102711
## 1 2 166.50000 7.8450911
## 1 3 128.25000 9.8814400
## 1 4 78.00000 5.2915026
## 1 5 43.33333 0.5773503
## 2 1 340.66667 3.7859389
## 2 2 266.00000 4.2426407
## 2 3 191.50000 2.1213203
## 2 4 136.66667 6.5064071
## 3 1 461.03030 9.8154370
## 3 2 368.21600 10.5315073
## 3 3 276.44286 11.5189016
## 3 4 184.50420 10.6880846
## 3 5 90.66667 7.2872606
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 40 0.0080
## 2 129 0.0258
## 3 72 0.0144
## 4 94 0.0188
## 5 18 0.0036
## 6 4572 0.9144
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- ---- --- ---- ---
## 1 12 12 8 3 3
## 2 3 2 2 3 0
## 3 33 125 70 119 33
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9842 0.9839594
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 48 40
## 1.0000000 139 129
## 1.0000000 80 72
## 1.0000000 125 94
## 1.0000000 36 18
## 0.9827209 4572 4572
## NULL
## ##############################
## [1] "setting3/scenario6"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.6 0 0.6 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98f473958>
## P(Reject H0_ITT) = 0.035400; P(Reject H0_subgp) = 0.961400; P(Reject H0) = 0.996800
## P(Early stop for efficacy [futility]) = 0.691200 [0.000000]
## Mean [SD] Randomized N = 399.010000 [118.517210]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3154
## 2 0.3758
## 3 0.3088
##
## Mean [SD] Lost N = 242.099000 [97.059850]
## Mean [SD] Analyzed N = 156.911000 [73.600664]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- --------- ----------
## 1 1 208.6629 5.681771
## 1 2 167.8563 7.289131
## 1 3 127.6000 7.072835
## 1 4 80.0000 NA
## 1 5 47.0000 NA
## 2 1 332.3053 6.681307
## 2 2 266.8128 9.558984
## 2 3 199.6667 11.793864
## 3 1 455.6800 9.615973
## 3 2 365.2894 10.990155
## 3 3 275.9474 16.008587
## 3 4 183.0000 7.071068
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 588 0.1176
## 2 4124 0.8248
## 3 93 0.0186
## 4 2 0.0004
## 6 177 0.0354
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- --- --- ---
## 1 445 1921 65 1 1
## 2 95 844 15 0 0
## 3 50 1365 19 2 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9604 0.9602729
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9949153 590 588
## 0.9963680 4130 4124
## 0.9797980 99 93
## 0.6666667 3 2
## 1.0000000 1 0
## 0.0000000 177 177
## NULL
## ##############################
## [1] "setting3/scenario7"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.01 0 0.01 0 0.01 0 0.01 0 0.01 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98f2b6720>
## P(Reject H0_ITT) = 0.037400; P(Reject H0_subgp) = 0.040600; P(Reject H0) = 0.078000
## P(Early stop for efficacy [futility]) = 0.042400 [0.318800]
## Mean [SD] Randomized N = 479.800000 [102.029613]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1068
## 2 0.2544
## 3 0.6388
##
## Mean [SD] Lost N = 189.078600 [113.992660]
## Mean [SD] Analyzed N = 290.721400 [116.993973]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.31286 5.707463
## 1 2 167.12222 7.334556
## 1 3 125.18788 7.851655
## 1 4 83.97119 7.499531
## 1 5 41.64041 5.748821
## 2 1 334.10561 7.345003
## 2 2 266.22340 8.503732
## 2 3 200.33803 10.830668
## 2 4 134.87413 8.455240
## 2 5 66.40278 7.336420
## 3 1 458.43836 9.307627
## 3 2 366.83402 11.158958
## 3 3 274.78986 11.432937
## 3 4 183.73883 10.603212
## 3 5 91.57875 8.371880
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 69 0.0138
## 2 50 0.0100
## 3 43 0.0086
## 4 23 0.0046
## 5 18 0.0036
## 6 187 0.0374
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 879 450 330 243 292
## 2 303 188 142 143 216
## 3 292 241 276 291 527
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9408 0.2410256
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9592944 1474 69
## 0.9544937 879 50
## 0.9518717 748 43
## 0.9793205 677 23
## 0.9884058 1035 18
## 0.2834225 187 187
## NULL
## ##############################
## [1] "setting3/scenario8"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb9949e6b18>
## P(Reject H0_ITT) = 0.914600; P(Reject H0_subgp) = 0.028200; P(Reject H0) = 0.942800
## P(Early stop for efficacy [futility]) = 0.834400 [0.001400]
## Mean [SD] Randomized N = 334.150000 [113.722751]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.6032
## 2 0.2326
## 3 0.1642
##
## Mean [SD] Lost N = 15.987200 [61.964255]
## Mean [SD] Analyzed N = 318.162800 [100.907883]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 209.92308 4.212314
## 1 2 164.53846 8.588902
## 1 3 124.33333 5.085928
## 1 4 86.40000 10.469002
## 1 5 42.50000 7.489386
## 2 1 337.50000 8.812869
## 2 2 273.00000 10.583005
## 2 3 193.00000 15.874508
## 2 4 133.50000 2.121320
## 2 5 73.00000 NA
## 3 1 458.64286 9.699997
## 3 2 361.42857 13.120002
## 3 3 273.25000 13.789560
## 3 4 181.69512 11.671099
## 3 5 93.61963 8.929220
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 25 0.0050
## 2 26 0.0052
## 3 26 0.0052
## 4 36 0.0072
## 5 28 0.0056
## 6 4573 0.9146
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ----
## 1 13 13 6 10 12
## 2 4 3 3 2 1
## 3 28 35 52 82 163
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9894 0.9887569
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 45 25
## 1.0000000 51 26
## 1.0000000 61 26
## 1.0000000 94 36
## 1.0000000 176 28
## 0.9884102 4573 4573
## NULL
## ##############################
## [1] "setting3/scenario9"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.9 0 0.3 0 0 0 -0.1 0 -0.4 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98e724270>
## P(Reject H0_ITT) = 0.039400; P(Reject H0_subgp) = 0.958800; P(Reject H0) = 0.998200
## P(Early stop for efficacy [futility]) = 0.700000 [0.000000]
## Mean [SD] Randomized N = 388.570000 [122.828631]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3762
## 2 0.3238
## 3 0.3000
##
## Mean [SD] Lost N = 262.956800 [112.918125]
## Mean [SD] Analyzed N = 125.613200 [84.560190]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 209.46268 5.831618
## 1 2 168.02681 7.667369
## 1 3 128.31737 7.196125
## 1 4 86.82759 6.319296
## 2 1 332.53420 7.300002
## 2 2 266.98711 8.883823
## 2 3 204.26984 9.476978
## 2 4 134.30769 9.303983
## 3 1 456.28134 8.327485
## 3 2 365.91156 10.780559
## 3 3 272.49254 12.518105
## 3 4 188.07143 9.467013
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 2646 0.5292
## 2 1722 0.3444
## 3 363 0.0726
## 4 63 0.0126
## 6 197 0.0394
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- --- ---
## 1 1420 746 167 29 0
## 2 541 388 63 13 0
## 3 686 588 134 28 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9556 0.9555199
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9992444 2647 2646
## 0.9936121 1722 1722
## 0.9725275 364 363
## 0.9714286 70 63
## 0.0000000 197 197
## NULL
## ##############################
## [1] "setting3/scenario10"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 -0.01 0 -0.01 0 -0.01 0 -0.01 0 -0.01 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.1
## $ eps : num 0.5
## $ type2Error: num 0.2
## $ effectSize: num 0.0523
## Boundaries:
## Named num [1:3] -1.5 2.04 2.17
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb99103c958>
## P(Reject H0_ITT) = 0.030800; P(Reject H0_subgp) = 0.033800; P(Reject H0) = 0.064600
## P(Early stop for efficacy [futility]) = 0.041600 [0.376400]
## Mean [SD] Randomized N = 470.050000 [103.815476]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.115
## 2 0.303
## 3 0.582
##
## Mean [SD] Lost N = 191.750600 [108.822676]
## Mean [SD] Analyzed N = 278.299400 [112.276641]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.59777 5.780727
## 1 2 166.62632 7.344570
## 1 3 124.33724 7.839233
## 1 4 84.41696 7.262748
## 1 5 41.61111 5.930880
## 2 1 333.52174 7.835606
## 2 2 266.14141 8.577518
## 2 3 199.65823 9.874223
## 2 4 132.88806 9.508730
## 2 5 65.60795 7.494741
## 3 1 458.26740 8.694462
## 3 2 366.77551 11.656213
## 3 3 274.28689 11.533797
## 3 4 183.73950 10.279193
## 3 5 90.99458 8.679372
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 73 0.0146
## 2 41 0.0082
## 3 25 0.0050
## 4 17 0.0034
## 5 13 0.0026
## 6 154 0.0308
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- ---- ----
## 1 1074 570 341 283 270
## 2 322 198 158 134 176
## 3 273 196 244 238 369
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9284 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9532654 1669 73
## 0.9460581 964 41
## 0.9569314 743 25
## 0.9618321 655 17
## 0.9791411 815 13
## 0.0000000 154 154
## NULL
## ##############################
## [1] "setting4/scenario0"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98ee210e0>
## P(Reject H0_ITT) = 0.082600; P(Reject H0_subgp) = 0.082200; P(Reject H0) = 0.164800
## P(Early stop for efficacy [futility]) = 0.098400 [0.218400]
## Mean [SD] Randomized N = 483.100000 [106.656763]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1292
## 2 0.1876
## 3 0.6832
##
## Mean [SD] Lost N = 201.568400 [130.621152]
## Mean [SD] Analyzed N = 281.531600 [123.421382]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.56545 6.129204
## 1 2 166.74083 7.762486
## 1 3 124.98374 7.881245
## 1 4 83.28856 7.348219
## 1 5 41.37017 5.916173
## 2 1 334.18467 7.432026
## 2 2 265.56944 9.017196
## 2 3 201.09565 9.100775
## 2 4 134.20690 9.166595
## 2 5 67.91791 6.669478
## 3 1 458.40964 9.203319
## 3 2 366.89124 10.565823
## 3 3 275.26791 11.505292
## 3 4 182.09202 11.194125
## 3 5 91.74586 8.658009
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 181 0.0362
## 2 97 0.0194
## 3 62 0.0124
## 4 43 0.0086
## 5 28 0.0056
## 6 413 0.0826
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 764 409 246 201 181
## 2 287 144 115 87 134
## 3 498 331 321 326 543
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.8352 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.8831504 1549 181
## 0.8902715 884 97
## 0.9090909 682 62
## 0.9299674 614 43
## 0.9673660 858 28
## 0.0000000 413 413
## NULL
## ##############################
## [1] "setting4/scenario1"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98eec1118>
## P(Reject H0_ITT) = 0.745600; P(Reject H0_subgp) = 0.230200; P(Reject H0) = 0.975800
## P(Early stop for efficacy [futility]) = 0.679600 [0.000200]
## Mean [SD] Randomized N = 380.800000 [130.091294]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.4482
## 2 0.2316
## 3 0.3202
##
## Mean [SD] Lost N = 75.822800 [138.519306]
## Mean [SD] Analyzed N = 304.977200 [114.140487]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 209.74603 5.535715
## 1 2 168.03448 7.887288
## 1 3 126.69048 7.093412
## 1 4 85.22222 6.942222
## 1 5 42.00000 NA
## 2 1 333.00000 7.123903
## 2 2 269.30435 11.347546
## 2 3 202.13333 9.326358
## 2 4 135.00000 NA
## 3 1 458.69231 9.151503
## 3 2 367.49169 11.352713
## 3 3 275.88793 11.528552
## 3 4 186.02703 11.434115
## 3 5 89.85185 9.126056
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 243 0.0486
## 2 359 0.0718
## 3 470 0.0940
## 4 65 0.0130
## 5 14 0.0028
## 6 3728 0.7456
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- --- ---
## 1 63 58 42 9 1
## 2 25 23 15 1 0
## 3 169 301 464 74 27
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9584 0.9573683
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9688716 257 243
## 0.9947644 382 359
## 1.0000000 521 470
## 1.0000000 84 65
## 1.0000000 28 14
## 0.9468884 3728 3728
## NULL
## ##############################
## [1] "setting4/scenario2"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98f4a8b08>
## P(Reject H0_ITT) = 0.348000; P(Reject H0_subgp) = 0.452200; P(Reject H0) = 0.800200
## P(Early stop for efficacy [futility]) = 0.406400 [0.007000]
## Mean [SD] Randomized N = 458.680000 [118.972638]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1954
## 2 0.2180
## 3 0.5866
##
## Mean [SD] Lost N = 193.431200 [166.496675]
## Mean [SD] Analyzed N = 265.248800 [122.619692]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.63910 6.265013
## 1 2 167.70000 7.102627
## 1 3 125.42222 7.954898
## 1 4 83.93548 6.727731
## 1 5 42.80000 6.235841
## 2 1 334.13000 7.288645
## 2 2 267.91975 9.719020
## 2 3 205.17241 7.426155
## 2 4 133.20000 14.394443
## 2 5 68.75000 9.516732
## 3 1 458.40385 8.383598
## 3 2 366.39211 10.933561
## 3 3 274.84795 12.571449
## 3 4 183.47024 9.352015
## 3 5 91.65359 8.590325
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 604 0.1208
## 2 1238 0.2476
## 3 294 0.0588
## 4 87 0.0174
## 5 38 0.0076
## 6 1740 0.3480
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- ---- ---- ----
## 1 266 280 90 31 15
## 2 100 162 29 5 12
## 3 416 1191 342 168 153
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.936 0.92002
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9590793 782 604
## 0.9816289 1633 1238
## 0.9913232 461 294
## 0.9901961 204 87
## 1.0000000 180 38
## 0.8551724 1740 1740
## NULL
## ##############################
## [1] "setting4/scenario3"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98f7a1a60>
## P(Reject H0_ITT) = 0.960000; P(Reject H0_subgp) = 0.017200; P(Reject H0) = 0.977200
## P(Early stop for efficacy [futility]) = 0.911000 [0.001000]
## Mean [SD] Randomized N = 303.280000 [95.472848]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.7328
## 2 0.1792
## 3 0.0880
##
## Mean [SD] Lost N = 8.758200 [50.974117]
## Mean [SD] Analyzed N = 294.521800 [86.831355]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 209.16667 5.419102
## 1 2 167.60000 7.765307
## 1 3 125.20000 7.854935
## 1 4 81.00000 9.899495
## 1 5 44.00000 5.773503
## 2 1 331.00000 NA
## 2 2 271.00000 1.414214
## 2 3 186.00000 NA
## 2 4 128.00000 9.899495
## 2 5 61.00000 5.656854
## 3 1 460.06250 10.286030
## 3 2 369.47059 10.595504
## 3 3 272.92308 11.996410
## 3 4 187.03846 10.592377
## 3 5 91.81159 8.833884
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 21 0.0042
## 2 11 0.0022
## 3 19 0.0038
## 4 18 0.0036
## 5 17 0.0034
## 6 4800 0.9600
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 6 5 5 2 4
## 2 1 2 1 2 2
## 3 32 17 26 26 69
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9636 0.9627507
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 39 21
## 1.0000000 24 11
## 1.0000000 32 19
## 1.0000000 30 18
## 1.0000000 75 17
## 0.9620833 4800 4800
## NULL
## ##############################
## [1] "setting4/scenario4"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.4 0 0.3 0 0.2 0 0 0 0 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb990e3ac30>
## P(Reject H0_ITT) = 0.554200; P(Reject H0_subgp) = 0.345000; P(Reject H0) = 0.899200
## P(Early stop for efficacy [futility]) = 0.533800 [0.001400]
## Mean [SD] Randomized N = 423.220000 [129.989273]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3100
## 2 0.2252
## 3 0.4648
##
## Mean [SD] Lost N = 130.634600 [162.032560]
## Mean [SD] Analyzed N = 292.585400 [120.103817]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.65185 5.934114
## 1 2 166.85437 7.767968
## 1 3 127.08955 7.813608
## 1 4 80.23529 8.961929
## 1 5 41.25000 6.798109
## 2 1 333.35088 7.783892
## 2 2 268.03390 9.951548
## 2 3 203.91667 12.122264
## 2 4 132.87500 7.079901
## 2 5 53.00000 NA
## 3 1 458.15727 8.803183
## 3 2 366.67164 10.646417
## 3 3 275.26138 11.147694
## 3 4 184.62712 10.559730
## 3 5 92.90654 8.854732
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 450 0.0900
## 2 588 0.1176
## 3 521 0.1042
## 4 125 0.0250
## 5 41 0.0082
## 6 2771 0.5542
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 135 103 67 17 8
## 2 57 59 24 8 1
## 3 337 536 593 177 107
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9534 0.9481762
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9621928 529 450
## 0.9899713 698 588
## 1.0000000 684 521
## 1.0000000 202 125
## 1.0000000 116 41
## 0.9256586 2771 2771
## NULL
## ##############################
## [1] "setting4/scenario5"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.5 0 0.5 0 0.3 0 0.3 0 0.1 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb992a93c00>
## P(Reject H0_ITT) = 0.962600; P(Reject H0_subgp) = 0.032600; P(Reject H0) = 0.995200
## P(Early stop for efficacy [futility]) = 0.904600 [0.000000]
## Mean [SD] Randomized N = 304.780000 [97.524632]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.7302
## 2 0.1744
## 3 0.0954
##
## Mean [SD] Lost N = 9.910800 [54.420371]
## Mean [SD] Analyzed N = 294.869200 [88.041544]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 198.33333 11.372481
## 1 2 170.50000 1.290994
## 1 3 130.00000 7.549834
## 1 4 79.66667 1.154700
## 1 5 39.00000 NA
## 2 1 333.00000 4.242641
## 2 2 261.00000 NA
## 2 3 199.00000 NA
## 2 4 129.00000 NA
## 3 1 457.57143 6.034698
## 3 2 365.83333 9.933268
## 3 3 276.31429 10.246295
## 3 4 182.98000 8.911103
## 3 5 91.53333 6.289068
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 18 0.0036
## 2 56 0.0112
## 3 37 0.0074
## 4 44 0.0088
## 5 8 0.0016
## 6 4813 0.9626
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 3 4 3 3 1
## 2 2 1 1 1 0
## 3 14 54 35 50 15
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9644 0.9642283
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 19 18
## 1.0000000 59 56
## 1.0000000 39 37
## 1.0000000 54 44
## 1.0000000 16 8
## 0.9630168 4813 4813
## NULL
## ##############################
## [1] "setting4/scenario6"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.6 0 0.6 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb995d8b578>
## P(Reject H0_ITT) = 0.077400; P(Reject H0_subgp) = 0.919400; P(Reject H0) = 0.996800
## P(Early stop for efficacy [futility]) = 0.587600 [0.000200]
## Mean [SD] Randomized N = 415.510000 [126.432341]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3088
## 2 0.2790
## 3 0.4122
##
## Mean [SD] Lost N = 252.655000 [113.625121]
## Mean [SD] Analyzed N = 162.855000 [82.723833]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.86717 5.681664
## 1 2 168.38958 7.423291
## 1 3 127.65116 9.268183
## 1 4 82.66667 6.506407
## 2 1 332.48387 7.114915
## 2 2 266.56528 9.918661
## 2 3 204.00000 9.000000
## 3 1 456.39286 8.121098
## 3 2 365.19492 10.940995
## 3 3 275.68421 12.763022
## 3 4 197.00000 NA
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 574 0.1148
## 2 3956 0.7912
## 3 65 0.0130
## 4 2 0.0004
## 6 387 0.0774
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ----- --- --- ---
## 1 399 1440 43 3 0
## 2 93 674 5 0 0
## 3 84 1852 19 1 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9104 0.9101124
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9670139 576 574
## 0.9904186 3966 3956
## 0.9402985 67 65
## 1.0000000 4 2
## 0.0000000 387 387
## NULL
## ##############################
## [1] "setting4/scenario7"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.01 0 0.01 0 0.01 0 0.01 0 0.01 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb9910e8778>
## P(Reject H0_ITT) = 0.102000; P(Reject H0_subgp) = 0.085800; P(Reject H0) = 0.187800
## P(Early stop for efficacy [futility]) = 0.110800 [0.189000]
## Mean [SD] Randomized N = 485.920000 [106.023591]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1274
## 2 0.1724
## 3 0.7002
##
## Mean [SD] Lost N = 197.404600 [130.963477]
## Mean [SD] Analyzed N = 288.515400 [123.060680]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.88608 5.824157
## 1 2 166.31105 7.305443
## 1 3 124.57692 7.069585
## 1 4 83.22599 6.416846
## 1 5 41.82209 5.755213
## 2 1 333.73790 7.841539
## 2 2 267.64641 9.059486
## 2 3 199.57522 11.868179
## 2 4 133.19355 9.787146
## 2 5 67.34951 7.690979
## 3 1 458.36384 8.958768
## 3 2 367.17618 11.750568
## 3 3 274.10063 11.931558
## 3 4 183.68997 10.576143
## 3 5 91.62267 9.274976
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 165 0.0330
## 2 121 0.0242
## 3 69 0.0138
## 4 40 0.0080
## 5 34 0.0068
## 6 510 0.1020
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 711 389 234 177 163
## 2 248 181 113 93 103
## 3 437 403 318 329 591
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.8468 0.1842386
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.8939828 1396 165
## 0.8890031 973 121
## 0.9233083 665 69
## 0.9515860 599 40
## 0.9766628 857 34
## 0.1960784 510 510
## NULL
## ##############################
## [1] "setting4/scenario8"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ 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 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb98e598c70>
## P(Reject H0_ITT) = 0.960000; P(Reject H0_subgp) = 0.017200; P(Reject H0) = 0.977200
## P(Early stop for efficacy [futility]) = 0.911000 [0.001000]
## Mean [SD] Randomized N = 303.280000 [95.472848]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.7328
## 2 0.1792
## 3 0.0880
##
## Mean [SD] Lost N = 8.758200 [50.974117]
## Mean [SD] Analyzed N = 294.521800 [86.831355]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 209.16667 5.419102
## 1 2 167.60000 7.765307
## 1 3 125.20000 7.854935
## 1 4 81.00000 9.899495
## 1 5 44.00000 5.773503
## 2 1 331.00000 NA
## 2 2 271.00000 1.414214
## 2 3 186.00000 NA
## 2 4 128.00000 9.899495
## 2 5 61.00000 5.656854
## 3 1 460.06250 10.286030
## 3 2 369.47059 10.595504
## 3 3 272.92308 11.996410
## 3 4 187.03846 10.592377
## 3 5 91.81159 8.833884
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 21 0.0042
## 2 11 0.0022
## 3 19 0.0038
## 4 18 0.0036
## 5 17 0.0034
## 6 4800 0.9600
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- --- --- --- --- ---
## 1 6 5 5 2 4
## 2 1 2 1 2 2
## 3 32 17 26 26 69
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9636 0.9627507
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 1.0000000 39 21
## 1.0000000 24 11
## 1.0000000 32 19
## 1.0000000 30 18
## 1.0000000 75 17
## 0.9620833 4800 4800
## NULL
## ##############################
## [1] "setting4/scenario9"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0.9 0 0.3 0 0 0 -0.1 0 -0.4 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb994d9c750>
## P(Reject H0_ITT) = 0.079800; P(Reject H0_subgp) = 0.919800; P(Reject H0) = 0.999600
## P(Early stop for efficacy [futility]) = 0.598800 [0.000000]
## Mean [SD] Randomized N = 406.060000 [130.811692]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.3608
## 2 0.2380
## 3 0.4012
##
## Mean [SD] Lost N = 275.854600 [131.759551]
## Mean [SD] Analyzed N = 130.205400 [93.860871]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 209.01885 5.671056
## 1 2 168.11052 7.462184
## 1 3 127.20175 7.119933
## 1 4 89.38095 5.074211
## 2 1 333.95158 7.437771
## 2 2 267.61594 9.445208
## 2 3 201.34091 10.211583
## 2 4 135.16667 5.706721
## 3 1 457.02616 8.841067
## 3 2 365.75320 10.874289
## 3 3 275.48175 12.099527
## 3 4 185.70833 9.331942
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 2635 0.5270
## 2 1619 0.3238
## 3 294 0.0588
## 4 51 0.0102
## 6 399 0.0798
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ----- ---- ---- --- ---
## 1 1167 561 114 21 0
## 2 475 276 44 6 0
## 3 994 782 137 24 0
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.9078 0.9077631
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9954476 2636 2635
## 0.9814700 1619 1619
## 0.9457627 295 294
## 0.9215686 51 51
## 0.0000000 399 399
## NULL
## ##############################
## [1] "setting4/scenario10"
## ##############################
## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 -0.01 0 -0.01 0 -0.01 0 -0.01 0 -0.01 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 250 400 550
## $ type1Error: num 0.2
## $ eps : num 0.5
## $ type2Error: num 0.3
## $ effectSize: num 0.0336
## Boundaries:
## Named num [1:3] -1.26 1.67 1.79
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence, N, mean, sd)
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb9963c5440>
## P(Reject H0_ITT) = 0.067800; P(Reject H0_subgp) = 0.063600; P(Reject H0) = 0.131400
## P(Early stop for efficacy [futility]) = 0.079400 [0.246200]
## Mean [SD] Randomized N = 481.960000 [106.483924]
##
## Stage at exit (proportion)
##
##
## exitStage proportion
## ---------- -----------
## 1 0.1280
## 2 0.1976
## 3 0.6744
##
## Mean [SD] Lost N = 201.089200 [124.869146]
## Mean [SD] Analyzed N = 280.870800 [122.898113]
##
## Mean loss by futility stage and subgroup
##
##
## FutilityStage selectedGroup mean sd
## -------------- -------------- ---------- ----------
## 1 1 208.69658 5.776268
## 1 2 166.80045 7.201629
## 1 3 125.31579 8.189149
## 1 4 83.78537 7.019076
## 1 5 41.32984 5.655095
## 2 1 333.21203 7.897517
## 2 2 265.50265 9.238923
## 2 3 199.24590 10.709779
## 2 4 132.13889 9.996690
## 2 5 67.07018 6.985091
## 3 1 458.43632 8.612801
## 3 2 366.80896 10.882851
## 3 3 273.73818 10.594233
## 3 4 182.96181 10.813042
## 3 5 91.50280 8.847622
##
## Chance of each subpopulation rejected
##
##
## group count proportion
## ------ ------ -----------
## 1 121 0.0242
## 2 94 0.0188
## 3 50 0.0100
## 4 34 0.0068
## 5 19 0.0038
## 6 339 0.0678
##
## Counts by futility stage and subgroup choice
##
##
## FutilityStage G1 G2 G3 G4 G5
## -------------- ---- ---- ---- ---- ----
## 1 847 446 266 205 191
## 2 316 189 122 108 114
## 3 424 335 275 288 535
##
## CI Statistics:
## Overall coverage and coverage for rejections:
##
## overall rejection
## -------- ----------
## 0.8584 0
##
## P(theta_test is in the confidence interval)
##
##
## coverage selectedCount rejectedCount
## ---------- -------------- --------------
## 0.9136736 1587 121
## 0.8948454 970 94
## 0.9095023 663 50
## 0.9301165 601 34
## 0.9666667 840 19
## 0.0000000 339 339
## NULL