Introduction

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
)

The Results

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