Adaptive Subgroup Selection in Sequential Trials

Introduction

ASSISTant is an R package for Adaptive Subgroup Selection In Sequential Trials. This vignette reproduces all the simulations in the original paper of Lai, Lavori and Liao [-@Lai2014191].

NOTE The number of simulations has been drastically reduced in this vignette in order to avoid taxing CRAN servers. The full_doc sources contain the complete sources and output; see files in the directory

system.file("full_doc", package="ASSISTant")

library(ASSISTant)
data(LLL.SETTINGS)
str(LLL.SETTINGS)

## List of 3
##  $ trialParameters:List of 4
##   ..$ N         : num [1:3] 300 400 500
##   ..$ type1Error: num 0.05
##   ..$ eps       : num 0.5
##   ..$ type2Error: num 0.2
##  $ scenarios      :List of 11
##   ..$ S0 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0 0 0 0 0 0 0 0 0 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ S1 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0.3 0 0.3 0 0.3 0 0.3 0 0.3 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ S2 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0.3 0 0.3 0 0.3 0 0.3 0 0.3 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ S3 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0.3 0 0.3 0 0 0 0 0 0 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ S4 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0 0 0 0 0.3 0 0.3 0 0 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ S5 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0.6 0 0 0 0 0 0 0 0 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ S6 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0.5 0 0 0 0 0 0 0 0 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ S7 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0.5 0 0.4 0 0.3 0 0 0 0 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ S8 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0.5 0 0.4 0 0.3 0 0 0 0 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 2 1 1.5 1 1 1 0.5 1 0.5 ...
##   ..$ S9 :List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0.5 0 0.4 0 0.3 0 0 0 0 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 0.5 1 1 1 1.5 1 2 1 2 ...
##   ..$ S10:List of 2
##   .. ..$ mean: num [1:2, 1:6] 0 0 0 0 0 0 0 0.3 0 0.4 ...
##   .. ..$ sd  : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##  $ prevalences    :List of 2
##   ..$ table1: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
##   ..$ table2: num [1:6] 0.2 0.1 0.3 0.1 0.1 0.2

The LLL.SETTINGS list contains all the scenarios described in the paper.

Table 1 Results

Scenario S0

This is the null setting.

scenario <- LLL.SETTINGS$scenarios$S0
designParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
designA <- ASSISTDesign$new(trialParameters = LLL.SETTINGS$trialParameters,
                            designParameters = designParameters)
print(designA)

## Design Parameters:
## 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] 300 400 500
##  $ type1Error: num 0.05
##  $ eps       : num 0.5
##  $ type2Error: num 0.2
##  $ effectSize: num 0.0642
## Boundaries:
##  Named num [1:3] -1.46 2.39 2.31
##  - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence = rep(1/6, 6), N, mean = matrix(0, 2, 6), 
##     sd = matrix(1, 2, 6)) 
## {
##     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: 0x7fd45d3bef78>

result <- designA$explore(numberOfSimulations = 50, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.040000; P(Reject H0_subgp) = 0.000000; P(Reject H0) = 0.040000
## P(Early stop for efficacy [futility]) = 0.040000 [0.480000]
## Mean [SD] Randomized N = 428.000000 [78.350338]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.20 0.32 0.48 
## 
## Mean [SD] Lost N = 194.300000 [91.615490]
## Mean [SD] Analyzed N = 233.700000 [94.038258]
## 
## Chance of each subpopulation rejected
## 
##    6 
## 0.04 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0  2  0  0  0  0  0
##   1  0 16  5  3  5  4
##   2  0  1  4  1  0  0
##   3  0  0  3  2  1  3
## 
## Mean loss by futility stage and subgroup
##    0        1        2   3   4        5
## 0  0       NA       NA  NA  NA       NA
## 1 NA 251.5625 201.6000 155 101 45.25000
## 2 NA 325.0000 277.2500 203  NA       NA
## 3 NA       NA 326.6667 250 179 78.33333
## 
## SD loss by futility stage and subgroup
##    0        1        2        3        4         5
## 0  0       NA       NA       NA       NA        NA
## 1 NA 7.685213 8.049845 6.557439 5.612486  4.193249
## 2 NA       NA 9.639329       NA       NA        NA
## 3 NA       NA 5.773503 2.828427       NA 10.692677
##    0        1        2        3        4         5
## 0  0       NA       NA       NA       NA        NA
## 1 NA 7.685213 8.049845 6.557439 5.612486  4.193249
## 2 NA       NA 9.639329       NA       NA        NA
## 3 NA       NA 5.773503 2.828427       NA 10.692677

Alternative Scenario S1

scenario <- LLL.SETTINGS$scenarios$S1
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.740000; P(Reject H0_subgp) = 0.100000; P(Reject H0) = 0.840000
## P(Early stop for efficacy [futility]) = 0.640000 [0.040000]
## Mean [SD] Randomized N = 378.000000 [91.003476]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.54 0.14 0.32 
## 
## Mean [SD] Lost N = 33.940000 [68.316613]
## Mean [SD] Analyzed N = 344.060000 [83.644391]
## 
## Chance of each subpopulation rejected
## 
##    1    2    4    5    6 
## 0.02 0.02 0.02 0.04 0.74 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0 37  0  0  0  0  0
##   1  0  1  1  0  0  2
##   3  0  0  0  1  3  5
## 
## Mean loss by futility stage and subgroup
##    0   1   2   3   4    5
## 0  0  NA  NA  NA  NA   NA
## 1 NA 253 195  NA  NA 41.0
## 3 NA  NA  NA 246 169 82.8
## 
## SD loss by futility stage and subgroup
##    0  1  2  3        4         5
## 0  0 NA NA NA       NA        NA
## 1 NA NA NA NA       NA 14.142136
## 3 NA NA NA NA 4.582576  6.534524
##    0  1  2  3        4         5
## 0  0 NA NA NA       NA        NA
## 1 NA NA NA NA       NA 14.142136
## 3 NA NA NA NA 4.582576  6.534524

Alternative Scenario S2

scenario <- LLL.SETTINGS$scenarios$S2
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.680000; P(Reject H0_subgp) = 0.180000; P(Reject H0) = 0.860000
## P(Early stop for efficacy [futility]) = 0.560000 [0.000000]
## Mean [SD] Randomized N = 404.000000 [92.493795]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.40 0.16 0.44 
## 
## Mean [SD] Lost N = 51.140000 [93.683795]
## Mean [SD] Analyzed N = 352.860000 [85.513100]
## 
## Chance of each subpopulation rejected
## 
##    2    4    5    6 
## 0.04 0.02 0.12 0.68 
## 
## Counts by futility stage and subgroup choice
##    
##      0  2  3  4  5
##   0 34  0  0  0  0
##   1  0  1  0  0  0
##   3  0  3  1  2  9
## 
## Mean loss by futility stage and subgroup
##    0   2   3     4        5
## 0  0  NA  NA    NA       NA
## 1 NA 198  NA    NA       NA
## 3 NA 331 262 173.5 84.11111
## 
## SD loss by futility stage and subgroup
##    0  2  3         4        5
## 0  0 NA NA        NA       NA
## 1 NA NA NA        NA       NA
## 3 NA  7 NA 0.7071068 6.273843
##    0  2  3         4        5
## 0  0 NA NA        NA       NA
## 1 NA NA NA        NA       NA
## 3 NA  7 NA 0.7071068 6.273843

Alternative Scenario S3

scenario <- LLL.SETTINGS$scenarios$S3
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.040000; P(Reject H0_subgp) = 0.580000; P(Reject H0) = 0.620000
## P(Early stop for efficacy [futility]) = 0.200000 [0.040000]
## Mean [SD] Randomized N = 472.000000 [53.604752]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.04 0.20 0.76 
## 
## Mean [SD] Lost N = 224.720000 [95.940041]
## Mean [SD] Analyzed N = 247.280000 [97.164292]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    4    5    6 
## 0.04 0.42 0.08 0.02 0.02 0.04 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0  2  0  0  0  0  0
##   1  0  2 10  2  2  1
##   2  0  0  5  0  1  0
##   3  0  1 12  6  3  3
## 
## Mean loss by futility stage and subgroup
##    0     1        2        3   4        5
## 0  0    NA       NA       NA  NA       NA
## 1 NA 249.5 201.0000 153.5000 109 56.00000
## 2 NA    NA 264.4000       NA 128       NA
## 3 NA 413.0 336.3333 248.6667 168 83.66667
## 
## SD loss by futility stage and subgroup
##    0        1        2        3        4        5
## 0  0       NA       NA       NA       NA       NA
## 1 NA 3.535534 6.128259 16.26346 1.414214       NA
## 2 NA       NA 9.208692       NA       NA       NA
## 3 NA       NA 7.923880 14.50057 5.291503 6.027714
##    0        1        2        3        4        5
## 0  0       NA       NA       NA       NA       NA
## 1 NA 3.535534 6.128259 16.26346 1.414214       NA
## 2 NA       NA 9.208692       NA       NA       NA
## 3 NA       NA 7.923880 14.50057 5.291503 6.027714

Alternative Scenario S4

scenario <- LLL.SETTINGS$scenarios$S4
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.120000; P(Reject H0_subgp) = 0.060000; P(Reject H0) = 0.180000
## P(Early stop for efficacy [futility]) = 0.080000 [0.180000]
## Mean [SD] Randomized N = 464.000000 [66.270934]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.10 0.16 0.74 
## 
## Mean [SD] Lost N = 122.300000 [75.176866]
## Mean [SD] Analyzed N = 341.700000 [85.074577]
## 
## Chance of each subpopulation rejected
## 
##    3    4    6 
## 0.02 0.04 0.12 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0  6  0  0  0  0  0
##   1  0  2  0  4  7  3
##   2  0  0  1  0  3  4
##   3  0  0  0  4 10  6
## 
## Mean loss by futility stage and subgroup
##    0     1   2      3         4        5
## 0  0    NA  NA     NA        NA       NA
## 1 NA 252.5  NA 149.50  98.42857 59.33333
## 2 NA    NA 262     NA 128.33333 66.50000
## 3 NA    NA  NA 249.75 173.10000 83.66667
## 
## SD loss by futility stage and subgroup
##    0        1  2        3         4         5
## 0  0       NA NA       NA        NA        NA
## 1 NA 7.778175 NA 7.047458  6.629659  6.658328
## 2 NA       NA NA       NA 11.718931 10.878113
## 3 NA       NA NA 9.069179 10.082438  7.312090
##    0        1  2        3         4         5
## 0  0       NA NA       NA        NA        NA
## 1 NA 7.778175 NA 7.047458  6.629659  6.658328
## 2 NA       NA NA       NA 11.718931 10.878113
## 3 NA       NA NA 9.069179 10.082438  7.312090

Alternative Scenario S5

scenario <- LLL.SETTINGS$scenarios$S5
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.240000; P(Reject H0_subgp) = 0.700000; P(Reject H0) = 0.940000
## P(Early stop for efficacy [futility]) = 0.420000 [0.000000]
## Mean [SD] Randomized N = 440.000000 [78.246080]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.18 0.24 0.58 
## 
## Mean [SD] Lost N = 235.380000 [154.285171]
## Mean [SD] Analyzed N = 204.620000 [148.262851]
## 
## Chance of each subpopulation rejected
## 
##    1    2    4    6 
## 0.58 0.10 0.02 0.24 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4
##   0 12  0  0  0  0
##   1  0 13  2  0  1
##   2  0  3  1  0  1
##   3  0 13  3  1  0
## 
## Mean loss by futility stage and subgroup
##    0        1     2   3   4
## 0  0       NA    NA  NA  NA
## 1 NA 250.7692 201.5  NA 100
## 2 NA 333.6667 263.0  NA 130
## 3 NA 412.0769 335.0 250  NA
## 
## SD loss by futility stage and subgroup
##    0        1         2  3  4
## 0  0       NA        NA NA NA
## 1 NA 4.710871 0.7071068 NA NA
## 2 NA 2.516611        NA NA NA
## 3 NA 8.025600 6.0827625 NA NA
##    0        1         2  3  4
## 0  0       NA        NA NA NA
## 1 NA 4.710871 0.7071068 NA NA
## 2 NA 2.516611        NA NA NA
## 3 NA 8.025600 6.0827625 NA NA

Alternative Scenario S6

scenario <- LLL.SETTINGS$scenarios$S6
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.120000; P(Reject H0_subgp) = 0.640000; P(Reject H0) = 0.760000
## P(Early stop for efficacy [futility]) = 0.400000 [0.060000]
## Mean [SD] Randomized N = 438.000000 [75.295337]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.16 0.30 0.54 
## 
## Mean [SD] Lost N = 261.200000 [129.838675]
## Mean [SD] Analyzed N = 176.800000 [98.540989]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    6 
## 0.56 0.06 0.02 0.12 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0  6  0  0  0  0  0
##   1  0 14  3  1  1  0
##   2  0  4  1  1  0  0
##   3  0 13  3  2  0  1
## 
## Mean loss by futility stage and subgroup
##    0        1        2   3   4  5
## 0  0       NA       NA  NA  NA NA
## 1 NA 250.2143 197.6667 138 100 NA
## 2 NA 332.0000 271.0000 188  NA NA
## 3 NA 411.6154 324.6667 260  NA 94
## 
## SD loss by futility stage and subgroup
##    0        1        2        3  4  5
## 0  0       NA       NA       NA NA NA
## 1 NA 5.885818 12.09683       NA NA NA
## 2 NA 6.683313       NA       NA NA NA
## 3 NA 6.801207 17.47379 4.242641 NA NA
##    0        1        2        3  4  5
## 0  0       NA       NA       NA NA NA
## 1 NA 5.885818 12.09683       NA NA NA
## 2 NA 6.683313       NA       NA NA NA
## 3 NA 6.801207 17.47379 4.242641 NA NA

Alternative Scenario S7

scenario <- LLL.SETTINGS$scenarios$S7
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.520000; P(Reject H0_subgp) = 0.440000; P(Reject H0) = 0.960000
## P(Early stop for efficacy [futility]) = 0.560000 [0.000000]
## Mean [SD] Randomized N = 414.000000 [85.738092]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.30 0.26 0.44 
## 
## Mean [SD] Lost N = 112.460000 [126.492431]
## Mean [SD] Analyzed N = 301.540000 [94.530032]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    4    6 
## 0.02 0.14 0.24 0.04 0.52 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0 26  0  0  0  0  0
##   1  0  1  2  4  0  0
##   2  0  0  1  1  0  0
##   3  0  0  4  8  2  1
## 
## Mean loss by futility stage and subgroup
##    0   1      2       3   4  5
## 0  0  NA     NA      NA  NA NA
## 1 NA 257 203.50 160.000  NA NA
## 2 NA  NA 271.00 202.000  NA NA
## 3 NA  NA 328.25 262.625 171 90
## 
## SD loss by futility stage and subgroup
##    0  1         2         3        4  5
## 0  0 NA        NA        NA       NA NA
## 1 NA NA  7.778175  4.966555       NA NA
## 2 NA NA        NA        NA       NA NA
## 3 NA NA 12.971122 10.689614 8.485281 NA
##    0  1         2         3        4  5
## 0  0 NA        NA        NA       NA NA
## 1 NA NA  7.778175  4.966555       NA NA
## 2 NA NA        NA        NA       NA NA
## 3 NA NA 12.971122 10.689614 8.485281 NA

Alternative Scenario S8

scenario <- LLL.SETTINGS$scenarios$S8
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.400000; P(Reject H0_subgp) = 0.320000; P(Reject H0) = 0.720000
## P(Early stop for efficacy [futility]) = 0.360000 [0.000000]
## Mean [SD] Randomized N = 450.000000 [73.540215]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.14 0.22 0.64 
## 
## Mean [SD] Lost N = 149.840000 [140.310786]
## Mean [SD] Analyzed N = 300.160000 [116.642548]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    4    6 
## 0.06 0.08 0.14 0.04 0.40 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0 20  0  0  0  0  0
##   1  0  2  1  1  2  0
##   2  0  0  1  1  0  0
##   3  0  3  4 11  3  1
## 
## Mean loss by futility stage and subgroup
##    0        1     2        3        4  5
## 0  0       NA    NA       NA       NA NA
## 1 NA 249.0000 198.0 148.0000 109.0000 NA
## 2 NA       NA 285.0 208.0000       NA NA
## 3 NA 413.6667 332.5 253.9091 164.6667 79
## 
## SD loss by futility stage and subgroup
##    0         1        2        3        4  5
## 0  0        NA       NA       NA       NA NA
## 1 NA  1.414214       NA       NA 11.31371 NA
## 2 NA        NA       NA       NA       NA NA
## 3 NA 12.096832 7.141428 8.251722 12.50333 NA
##    0         1        2        3        4  5
## 0  0        NA       NA       NA       NA NA
## 1 NA  1.414214       NA       NA 11.31371 NA
## 2 NA        NA       NA       NA       NA NA
## 3 NA 12.096832 7.141428 8.251722 12.50333 NA

Alternative Scenario S9

scenario <- LLL.SETTINGS$scenarios$S9
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.380000; P(Reject H0_subgp) = 0.540000; P(Reject H0) = 0.920000
## P(Early stop for efficacy [futility]) = 0.440000 [0.000000]
## Mean [SD] Randomized N = 428.000000 [88.155706]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.28 0.16 0.56 
## 
## Mean [SD] Lost N = 180.840000 [161.409652]
## Mean [SD] Analyzed N = 247.160000 [127.419660]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    5    6 
## 0.16 0.22 0.14 0.02 0.38 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  5
##   0 19  0  0  0  0
##   1  0  3  1  2  0
##   2  0  0  1  2  0
##   3  0  6 10  4  2
## 
## Mean loss by futility stage and subgroup
##    0        1     2     3  5
## 0  0       NA    NA    NA NA
## 1 NA 254.3333 198.0 156.5 NA
## 2 NA       NA 273.0 214.0 NA
## 3 NA 416.6667 339.5 252.5 81
## 
## SD loss by futility stage and subgroup
##    0        1        2         3        5
## 0  0       NA       NA        NA       NA
## 1 NA 6.429101       NA 12.020815       NA
## 2 NA       NA       NA  0.000000       NA
## 3 NA 6.772493 6.786424  4.203173 7.071068
##    0        1        2         3        5
## 0  0       NA       NA        NA       NA
## 1 NA 6.429101       NA 12.020815       NA
## 2 NA       NA       NA  0.000000       NA
## 3 NA 6.772493 6.786424  4.203173 7.071068

Alternative Scenario S10

scenario <- LLL.SETTINGS$scenarios$S10
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table1,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50,
                          trueParameters = trueParameters, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.540000; P(Reject H0_subgp) = 0.000000; P(Reject H0) = 0.540000
## P(Early stop for efficacy [futility]) = 0.440000 [0.140000]
## Mean [SD] Randomized N = 400.000000 [92.582010]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.42 0.16 0.42 
## 
## Mean [SD] Lost N = 75.140000 [120.881796]
## Mean [SD] Analyzed N = 324.860000 [116.619740]
## 
## Chance of each subpopulation rejected
## 
##    6 
## 0.54 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0 27  0  0  0  0  0
##   1  0  2  1  0  1  3
##   3  0  4  0  1  0 11
## 
## Mean loss by futility stage and subgroup
##    0      1   2   3   4        5
## 0  0     NA  NA  NA  NA       NA
## 1 NA 246.50 198  NA 114 48.66667
## 3 NA 411.25  NA 252  NA 82.63636
## 
## SD loss by futility stage and subgroup
##    0        1  2  3  4        5
## 0  0       NA NA NA NA       NA
## 1 NA  2.12132 NA NA NA 15.69501
## 3 NA 10.87428 NA NA NA 12.24968
##    0        1  2  3  4        5
## 0  0       NA NA NA NA       NA
## 1 NA  2.12132 NA NA NA 15.69501
## 3 NA 10.87428 NA NA NA 12.24968

Table 2 Results

Scenario S0

scenario <- LLL.SETTINGS$scenarios$S0
designParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
designA <- ASSISTDesign$new(trialParameters = LLL.SETTINGS$trialParameters,
                            designParameters = designParameters)
print(designA)

## Design Parameters:
## List of 4
##  $ prevalence: num [1:6] 0.2 0.1 0.3 0.1 0.1 0.2
##  $ mean      : num [1:2, 1:6] 0 0 0 0 0 0 0 0 0 0 ...
##  $ sd        : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
##  $ J         : int 6
## Trial Parameters:
## List of 5
##  $ N         : num [1:3] 300 400 500
##  $ type1Error: num 0.05
##  $ eps       : num 0.5
##  $ type2Error: num 0.2
##  $ effectSize: num 0.0642
## Boundaries:
##  Named num [1:3] -1.46 2.37 2.28
##  - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence = rep(1/6, 6), N, mean = matrix(0, 2, 6), 
##     sd = matrix(1, 2, 6)) 
## {
##     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: 0x7fd45e031698>

result <- designA$explore(numberOfSimulations = 50, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.000000; P(Reject H0_subgp) = 0.060000; P(Reject H0) = 0.060000
## P(Early stop for efficacy [futility]) = 0.060000 [0.400000]
## Mean [SD] Randomized N = 440.000000 [72.843136]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.14 0.32 0.54 
## 
## Mean [SD] Lost N = 210.980000 [93.765337]
## Mean [SD] Analyzed N = 229.020000 [102.968688]
## 
## Chance of each subpopulation rejected
## 
##    1    2 
## 0.04 0.02 
## 
## Counts by futility stage and subgroup choice
##    
##      1  2  3  4  5
##   1 14  9  2  3  3
##   2  2  2  3  1  1
##   3  4  2  1  0  3
## 
## Mean loss by futility stage and subgroup
##          1        2        3         4        5
## 1 236.7143 209.5556 121.0000  83.66667 59.00000
## 2 325.0000 277.0000 161.3333 140.00000 88.00000
## 3 402.7500 342.5000 183.0000        NA 94.66667
## 
## SD loss by futility stage and subgroup
##           1         2         3       4        5
## 1  8.099654  5.246692  4.242641 4.50925 1.732051
## 2 15.556349  1.414214 13.868429      NA       NA
## 3  6.946222 12.020815        NA      NA 1.527525
##           1         2         3       4        5
## 1  8.099654  5.246692  4.242641 4.50925 1.732051
## 2 15.556349  1.414214 13.868429      NA       NA
## 3  6.946222 12.020815        NA      NA 1.527525

Alternative Scenario S1

scenario <- LLL.SETTINGS$scenarios$S1
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.880000; P(Reject H0_subgp) = 0.020000; P(Reject H0) = 0.900000
## P(Early stop for efficacy [futility]) = 0.720000 [0.020000]
## Mean [SD] Randomized N = 370.000000 [86.307471]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.56 0.18 0.26 
## 
## Mean [SD] Lost N = 21.720000 [71.888530]
## Mean [SD] Analyzed N = 348.280000 [85.889117]
## 
## Chance of each subpopulation rejected
## 
##    5    6 
## 0.02 0.88 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  3  5
##   0 44  0  0  0
##   1  0  1  0  1
##   3  0  1  1  2
## 
## Mean loss by futility stage and subgroup
##    0   1   3    5
## 0  0  NA  NA   NA
## 1 NA 244  NA 64.0
## 3 NA 399 190 94.5
## 
## SD loss by futility stage and subgroup
##    0  1  3        5
## 0  0 NA NA       NA
## 1 NA NA NA       NA
## 3 NA NA NA 4.949747
##    0  1  3        5
## 0  0 NA NA       NA
## 1 NA NA NA       NA
## 3 NA NA NA 4.949747

Alternative Scenario S2

scenario <- LLL.SETTINGS$scenarios$S2
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.700000; P(Reject H0_subgp) = 0.180000; P(Reject H0) = 0.880000
## P(Early stop for efficacy [futility]) = 0.500000 [0.000000]
## Mean [SD] Randomized N = 412.000000 [93.982195]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.38 0.12 0.50 
## 
## Mean [SD] Lost N = 45.820000 [84.837826]
## Mean [SD] Analyzed N = 366.180000 [95.368178]
## 
## Chance of each subpopulation rejected
## 
##    1    2    4    5    6 
## 0.02 0.02 0.06 0.08 0.70 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0 35  0  0  0  0  0
##   1  0  1  0  0  1  0
##   2  0  0  1  0  0  0
##   3  0  1  0  1  3  7
## 
## Mean loss by futility stage and subgroup
##    0   1   2   3        4        5
## 0  0  NA  NA  NA       NA       NA
## 1 NA 235  NA  NA  82.0000       NA
## 2 NA  NA 279  NA       NA       NA
## 3 NA 390  NA 185 146.3333 97.28571
## 
## SD loss by futility stage and subgroup
##    0  1  2  3        4        5
## 0  0 NA NA NA       NA       NA
## 1 NA NA NA NA       NA       NA
## 2 NA NA NA NA       NA       NA
## 3 NA NA NA NA 10.78579 11.61485
##    0  1  2  3        4        5
## 0  0 NA NA NA       NA       NA
## 1 NA NA NA NA       NA       NA
## 2 NA NA NA NA       NA       NA
## 3 NA NA NA NA 10.78579 11.61485

Alternative Scenario S3

scenario <- LLL.SETTINGS$scenarios$S3
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.060000; P(Reject H0_subgp) = 0.560000; P(Reject H0) = 0.620000
## P(Early stop for efficacy [futility]) = 0.340000 [0.060000]
## Mean [SD] Randomized N = 452.000000 [64.649763]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.08 0.32 0.60 
## 
## Mean [SD] Lost N = 213.040000 [99.616809]
## Mean [SD] Analyzed N = 238.960000 [109.326316]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    4    5    6 
## 0.14 0.34 0.04 0.02 0.02 0.06 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0  3  0  0  0  0  0
##   1  0  4 16  1  2  2
##   2  0  2  3  0  0  1
##   3  0  3  4  6  2  1
## 
## Mean loss by futility stage and subgroup
##    0      1        2   3     4   5
## 0  0     NA       NA  NA    NA  NA
## 1 NA 235.75 211.3125 123  98.0  61
## 2 NA 316.50 291.0000  NA    NA  85
## 3 NA 407.00 354.5000 202 166.5 112
## 
## SD loss by futility stage and subgroup
##    0         1         2        3        4        5
## 0  0        NA        NA       NA       NA       NA
## 1 NA  5.560276  8.631097       NA 0.000000 1.414214
## 2 NA 13.435029 14.000000       NA       NA       NA
## 3 NA  7.549834  7.937254 12.91511 6.363961       NA
##    0         1         2        3        4        5
## 0  0        NA        NA       NA       NA       NA
## 1 NA  5.560276  8.631097       NA 0.000000 1.414214
## 2 NA 13.435029 14.000000       NA       NA       NA
## 3 NA  7.549834  7.937254 12.91511 6.363961       NA

Alternative Scenario S4

scenario <- LLL.SETTINGS$scenarios$S4
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.100000; P(Reject H0_subgp) = 0.200000; P(Reject H0) = 0.300000
## P(Early stop for efficacy [futility]) = 0.120000 [0.200000]
## Mean [SD] Randomized N = 456.000000 [70.450446]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.12 0.20 0.68 
## 
## Mean [SD] Lost N = 125.700000 [75.198038]
## Mean [SD] Analyzed N = 330.300000 [69.693571]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    4    5    6 
## 0.02 0.02 0.06 0.04 0.06 0.10 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0  5  0  0  0  0  0
##   1  0  2  0  3  6  4
##   2  0  0  0  4  5  0
##   3  0  1  1  3 10  6
## 
## Mean loss by futility stage and subgroup
##    0   1   2        3         4      5
## 0  0  NA  NA       NA        NA     NA
## 1 NA 235  NA 122.3333  89.66667  59.75
## 2 NA  NA  NA 153.2500 117.00000     NA
## 3 NA 385 344 206.0000 149.60000 105.00
## 
## SD loss by futility stage and subgroup
##    0        1  2        3        4        5
## 0  0       NA NA       NA       NA       NA
## 1 NA 1.414214 NA 1.527525 12.17648 7.632169
## 2 NA       NA NA 7.932003 10.95445       NA
## 3 NA       NA NA 8.185353 11.42317 5.138093
##    0        1  2        3        4        5
## 0  0       NA NA       NA       NA       NA
## 1 NA 1.414214 NA 1.527525 12.17648 7.632169
## 2 NA       NA NA 7.932003 10.95445       NA
## 3 NA       NA NA 8.185353 11.42317 5.138093

Alternative Scenario S5

scenario <- LLL.SETTINGS$scenarios$S5
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.180000; P(Reject H0_subgp) = 0.760000; P(Reject H0) = 0.940000
## P(Early stop for efficacy [futility]) = 0.440000 [0.000000]
## Mean [SD] Randomized N = 438.000000 [77.958649]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.18 0.26 0.56 
## 
## Mean [SD] Lost N = 264.200000 [145.644801]
## Mean [SD] Analyzed N = 173.800000 [117.296763]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    6 
## 0.64 0.10 0.02 0.18 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  5
##   0  9  0  0  0  0
##   1  0 12  2  0  0
##   2  0  3  0  0  0
##   3  0 18  4  1  1
## 
## Mean loss by futility stage and subgroup
##    0        1      2   3  5
## 0  0       NA     NA  NA NA
## 1 NA 243.6667 211.50  NA NA
## 2 NA 322.3333     NA  NA NA
## 3 NA 398.7222 353.25 210 96
## 
## SD loss by futility stage and subgroup
##    0        1         2  3  5
## 0  0       NA        NA NA NA
## 1 NA 6.169328 10.606602 NA NA
## 2 NA 7.371115        NA NA NA
## 3 NA 7.759666  5.678908 NA NA
##    0        1         2  3  5
## 0  0       NA        NA NA NA
## 1 NA 6.169328 10.606602 NA NA
## 2 NA 7.371115        NA NA NA
## 3 NA 7.759666  5.678908 NA NA

Alternative Scenario S6

scenario <- LLL.SETTINGS$scenarios$S6
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.100000; P(Reject H0_subgp) = 0.700000; P(Reject H0) = 0.800000
## P(Early stop for efficacy [futility]) = 0.360000 [0.000000]
## Mean [SD] Randomized N = 458.000000 [60.911445]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.06 0.30 0.64 
## 
## Mean [SD] Lost N = 257.000000 [123.352821]
## Mean [SD] Analyzed N = 201.000000 [127.133226]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    6 
## 0.50 0.16 0.04 0.10 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0  5  0  0  0  0  0
##   1  0 10  4  0  1  0
##   2  0  6  2  0  0  0
##   3  0 11  5  3  0  3
## 
## Mean loss by futility stage and subgroup
##    0        1     2        3  4        5
## 0  0       NA    NA       NA NA       NA
## 1 NA 241.2000 211.5       NA 99       NA
## 2 NA 320.5000 283.5       NA NA       NA
## 3 NA 397.3636 352.0 193.3333 NA 97.33333
## 
## SD loss by futility stage and subgroup
##    0         1         2        3  4        5
## 0  0        NA        NA       NA NA       NA
## 1 NA  6.232531  9.000000       NA NA       NA
## 2 NA  5.612486  4.949747       NA NA       NA
## 3 NA 11.775166 11.768602 13.57694 NA 14.57166
##    0         1         2        3  4        5
## 0  0        NA        NA       NA NA       NA
## 1 NA  6.232531  9.000000       NA NA       NA
## 2 NA  5.612486  4.949747       NA NA       NA
## 3 NA 11.775166 11.768602 13.57694 NA 14.57166

Alternative Scenario S7

scenario <- LLL.SETTINGS$scenarios$S7
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.640000; P(Reject H0_subgp) = 0.320000; P(Reject H0) = 0.960000
## P(Early stop for efficacy [futility]) = 0.540000 [0.000000]
## Mean [SD] Randomized N = 414.000000 [88.086229]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.32 0.22 0.46 
## 
## Mean [SD] Lost N = 84.740000 [123.778243]
## Mean [SD] Analyzed N = 329.260000 [114.318533]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    4    6 
## 0.08 0.04 0.18 0.02 0.64 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4
##   0 32  0  0  0  0
##   1  0  3  0  1  0
##   2  0  0  0  1  0
##   3  0  2  2  8  1
## 
## Mean loss by futility stage and subgroup
##    0   1     2       3   4
## 0  0  NA    NA      NA  NA
## 1 NA 242    NA 109.000  NA
## 2 NA  NA    NA 157.000  NA
## 3 NA 391 346.5 201.875 155
## 
## SD loss by futility stage and subgroup
##    0         1        2        3  4
## 0  0        NA       NA       NA NA
## 1 NA  6.244998       NA       NA NA
## 2 NA        NA       NA       NA NA
## 3 NA 11.313708 4.949747 14.05538 NA
##    0         1        2        3  4
## 0  0        NA       NA       NA NA
## 1 NA  6.244998       NA       NA NA
## 2 NA        NA       NA       NA NA
## 3 NA 11.313708 4.949747 14.05538 NA

Alternative Scenario S8

scenario <- LLL.SETTINGS$scenarios$S8
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.440000; P(Reject H0_subgp) = 0.360000; P(Reject H0) = 0.800000
## P(Early stop for efficacy [futility]) = 0.420000 [0.020000]
## Mean [SD] Randomized N = 432.000000 [84.370417]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.24 0.20 0.56 
## 
## Mean [SD] Lost N = 104.300000 [114.934276]
## Mean [SD] Analyzed N = 327.700000 [95.751006]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    4    5    6 
## 0.04 0.08 0.18 0.04 0.02 0.44 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0 22  0  0  0  0  0
##   1  0  1  2  3  0  3
##   2  0  0  2  1  0  0
##   3  0  1  2  8  2  3
## 
## Mean loss by futility stage and subgroup
##    0   1   2   3   4         5
## 0  0  NA  NA  NA  NA        NA
## 1 NA 245 212 120  NA  56.66667
## 2 NA  NA 285 165  NA        NA
## 3 NA 407 350 199 140 100.66667
## 
## SD loss by futility stage and subgroup
##    0  1         2       3        4        5
## 0  0 NA        NA      NA       NA       NA
## 1 NA NA  1.414214 16.0000       NA 7.023769
## 2 NA NA  4.242641      NA       NA       NA
## 3 NA NA 11.313708 10.5695 11.31371 5.507571
##    0  1         2       3        4        5
## 0  0 NA        NA      NA       NA       NA
## 1 NA NA  1.414214 16.0000       NA 7.023769
## 2 NA NA  4.242641      NA       NA       NA
## 3 NA NA 11.313708 10.5695 11.31371 5.507571

Alternative Scenario S9

scenario <- LLL.SETTINGS$scenarios$S9
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.640000; P(Reject H0_subgp) = 0.340000; P(Reject H0) = 0.980000
## P(Early stop for efficacy [futility]) = 0.540000 [0.000000]
## Mean [SD] Randomized N = 412.000000 [89.533941]
## 
## Stage at exit (proportion)
## 
##    1    2    3 
## 0.34 0.20 0.46 
## 
## Mean [SD] Lost N = 107.080000 [153.440122]
## Mean [SD] Analyzed N = 304.920000 [115.418111]
## 
## Chance of each subpopulation rejected
## 
##    1    2    3    6 
## 0.12 0.12 0.10 0.64 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  5
##   0 32  0  0  0  0
##   1  0  1  0  0  0
##   2  0  1  0  0  0
##   3  0  4  6  5  1
## 
## Mean loss by futility stage and subgroup
##    0   1   2     3   5
## 0  0  NA  NA    NA  NA
## 1 NA 243  NA    NA  NA
## 2 NA 315  NA    NA  NA
## 3 NA 399 343 206.4 110
## 
## SD loss by futility stage and subgroup
##    0       1        2        3  5
## 0  0      NA       NA       NA NA
## 1 NA      NA       NA       NA NA
## 2 NA      NA       NA       NA NA
## 3 NA 11.5181 8.809086 4.827007 NA
##    0       1        2        3  5
## 0  0      NA       NA       NA NA
## 1 NA      NA       NA       NA NA
## 2 NA      NA       NA       NA NA
## 3 NA 11.5181 8.809086 4.827007 NA

Alternative Scenario S10

scenario <- LLL.SETTINGS$scenarios$S10
trueParameters <- list(prevalence = LLL.SETTINGS$prevalences$table2,
                       mean = scenario$mean,
                       sd = scenario$sd)
result <- designA$explore(numberOfSimulations = 50, trueParameters = trueParameters,
                          showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))

## P(Reject H0_ITT) = 0.340000; P(Reject H0_subgp) = 0.000000; P(Reject H0) = 0.340000
## P(Early stop for efficacy [futility]) = 0.180000 [0.120000]
## Mean [SD] Randomized N = 460.000000 [67.005939]
## 
## Stage at exit (proportion)
## 
##   1   2   3 
## 0.1 0.2 0.7 
## 
## Mean [SD] Lost N = 121.720000 [130.210354]
## Mean [SD] Analyzed N = 338.280000 [127.607664]
## 
## Chance of each subpopulation rejected
## 
##    6 
## 0.34 
## 
## Counts by futility stage and subgroup choice
##    
##      0  1  2  3  4  5
##   0 17  0  0  0  0  0
##   1  0  4  0  0  0  0
##   2  0  0  0  0  1  1
##   3  0  5  2  1  2 17
## 
## Mean loss by futility stage and subgroup
##    0     1   2   3   4        5
## 0  0    NA  NA  NA  NA       NA
## 1 NA 240.0  NA  NA  NA       NA
## 2 NA    NA  NA  NA 123 87.00000
## 3 NA 403.8 349 211 153 98.94118
## 
## SD loss by futility stage and subgroup
##    0         1        2  3        4        5
## 0  0        NA       NA NA       NA       NA
## 1 NA  3.741657       NA NA       NA       NA
## 2 NA        NA       NA NA       NA       NA
## 3 NA 13.065221 5.656854 NA 7.071068 8.034851
##    0         1        2  3        4        5
## 0  0        NA       NA NA       NA       NA
## 1 NA  3.741657       NA NA       NA       NA
## 2 NA        NA       NA NA       NA       NA
## 3 NA 13.065221 5.656854 NA 7.071068 8.034851

Adaptive Subgroup Selection in Sequential Trials

Tze Leung Lai, Philip W. Lavori, Olivia Liao, Ka Wai Tsang and Balasubramanian Narasimhan

2016-05-02

Introduction

Table 1 Results

Scenario S0

Alternative Scenario S1

Alternative Scenario S2

Alternative Scenario S3

Alternative Scenario S4

Alternative Scenario S5

Alternative Scenario S6

Alternative Scenario S7

Alternative Scenario S8

Alternative Scenario S9

Alternative Scenario S10

Table 2 Results

Scenario S0

Alternative Scenario S1

Alternative Scenario S2

Alternative Scenario S3

Alternative Scenario S4

Alternative Scenario S5

Alternative Scenario S6

Alternative Scenario S7

Alternative Scenario S8

Alternative Scenario S9

Alternative Scenario S10