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Introduction

We simulate data from a discrete distribution for the Rankin scores, which are ordinal integers from 0 to 6 in the following simulations. So we define a few scenarios.

library(ASSISTant)
null.uniform <- rep(1, 7L) ## uniform on 7 support points
hourglass <- c(1, 2, 2, 1, 2, 2, 1)
inverted.hourglass <- c(2, 1, 1, 2, 1, 1, 2)
bottom.heavy <- c(2, 2, 2, 1, 1, 1, 1)
bottom.heavier <- c(3, 3, 2, 2, 1, 1, 1)
top.heavy <- c(1, 1, 1, 1, 2, 2, 2)
top.heavier <- c(1, 1, 1, 2, 2, 3, 3)
ctlDist <- null.uniform
trtDist <- cbind(null.uniform, null.uniform, null.uniform,
                 hourglass, hourglass, hourglass)

##d <- generateDiscreteRankinScores(rep(1, 6), 10, ctlDist, trtDist)

Scenario S0

This is the null setting.

data(LLL.SETTINGS)
designParameters <- list(prevalence = rep(1/6, 6),
                         ctlDist = ctlDist,
                         trtDist = trtDist)

designA <- ASSISTDesign$new(trialParameters = LLL.SETTINGS$trialParameters,
                            designParameters = designParameters, discreteData = TRUE)
print(designA)
## Design Parameters:
##  Number of Groups: 6
##  Prevalence:
## 
## |    Group1|    Group2|    Group3|    Group4|    Group5|    Group6|
## |---------:|---------:|---------:|---------:|---------:|---------:|
## | 0.1666667| 0.1666667| 0.1666667| 0.1666667| 0.1666667| 0.1666667|
## 
##  Using Discrete Rankin scores? TRUE
## 
##  Null Rankin Distribution:
## 
## |   |    Group1|    Group2|    Group3|    Group4|    Group5|    Group6|
## |:--|---------:|---------:|---------:|---------:|---------:|---------:|
## |0  | 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571|
## |1  | 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571|
## |2  | 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571|
## |3  | 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571|
## |4  | 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571|
## |5  | 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571|
## |6  | 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571| 0.1428571|
##  Null Mean and SD
## 
## |     | Group1| Group2| Group3| Group4| Group5| Group6|
## |:----|------:|------:|------:|------:|------:|------:|
## |mean |      3|      3|      3|      3|      3|      3|
## |sd   |      2|      2|      2|      2|      2|      2|
##  Alternative Rankin Distribution:
## 
## 
## |   |    Group1|    Group2|    Group3|    Group4|    Group5|    Group6|
## |:--|---------:|---------:|---------:|---------:|---------:|---------:|
## |0  | 0.1428571| 0.1428571| 0.1428571| 0.0909091| 0.0909091| 0.0909091|
## |1  | 0.1428571| 0.1428571| 0.1428571| 0.1818182| 0.1818182| 0.1818182|
## |2  | 0.1428571| 0.1428571| 0.1428571| 0.1818182| 0.1818182| 0.1818182|
## |3  | 0.1428571| 0.1428571| 0.1428571| 0.0909091| 0.0909091| 0.0909091|
## |4  | 0.1428571| 0.1428571| 0.1428571| 0.1818182| 0.1818182| 0.1818182|
## |5  | 0.1428571| 0.1428571| 0.1428571| 0.1818182| 0.1818182| 0.1818182|
## |6  | 0.1428571| 0.1428571| 0.1428571| 0.0909091| 0.0909091| 0.0909091|
##  Alternative Mean and SD
## 
## |     | Group1| Group2| Group3|   Group4|   Group5|   Group6|
## |:----|------:|------:|------:|--------:|--------:|--------:|
## |mean |      3|      3|      3| 3.000000| 3.000000| 3.000000|
## |sd   |      2|      2|      2| 1.858641| 1.858641| 1.858641|
## 
## Trial Parameters:
## List of 5
##  $ N         : num [1:3] 300 400 500
##  $ type1Error: num 0.05
##  $ eps       : num 0.5
##  $ type2Error: num 0.2
##  $ effectSize: num 0.0642
## 
## Boundaries:
## 
## 
## |    btilde|        b|        c|
## |---------:|--------:|--------:|
## | -1.460993| 2.390404| 2.491775|
result <- designA$explore(numberOfSimulations = 5000, showProgress = FALSE)
analysis <- designA$analyze(result)
print(designA$summary(analysis))
## P(Reject H0_ITT) = 0.017200; P(Reject H0_subgp) = 0.021800; P(Reject H0) = 0.039000
## P(Early stop for efficacy [futility]) = 0.024400 [0.568800]
## Mean [SD] Randomized N = 419.620000 [76.093453]
## 
## Stage at exit (proportion)
## 
## 
## | exitStage| proportion|
## |---------:|----------:|
## |         1|     0.2106|
## |         2|     0.3826|
## |         3|     0.4068|
## 
## Mean [SD] Lost N = 183.574400 [92.930368]
## Mean [SD] Analyzed N = 236.045600 [97.620219]
## 
## Mean loss by futility stage and subgroup
## 
## 
## | FutilityStage| selectedGroup|      mean|        sd|
## |-------------:|-------------:|---------:|---------:|
## |             1|             1| 250.28419|  6.348342|
## |             1|             2| 200.61538|  8.317006|
## |             1|             3| 150.09895|  8.528229|
## |             1|             4| 100.22222|  8.528198|
## |             1|             5|  50.00383|  6.256512|
## |             2|             1| 332.21970|  6.692042|
## |             2|             2| 266.84762|  9.663354|
## |             2|             3| 201.28723| 10.548019|
## |             2|             4| 132.33628|  9.354726|
## |             2|             5|  66.10778|  7.323037|
## |             3|             1| 416.92357|  8.126832|
## |             3|             2| 332.46825|  9.598072|
## |             3|             3| 249.78462| 10.513177|
## |             3|             4| 166.63415| 10.659841|
## |             3|             5|  82.41924|  8.427552|
## 
## Chance of each subpopulation rejected
## 
## 
## | group| count| proportion|
## |-----:|-----:|----------:|
## |     1|    40|     0.0080|
## |     2|    30|     0.0060|
## |     3|    18|     0.0036|
## |     4|    13|     0.0026|
## |     5|     8|     0.0016|
## |     6|    86|     0.0172|
## 
## Counts by futility stage and subgroup choice
## 
## 
## | FutilityStage|   G1|  G2|  G3|  G4|  G5|
## |-------------:|----:|---:|---:|---:|---:|
## |             1| 1309| 715| 475| 414| 522|
## |             2|  132| 105|  94| 113| 167|
## |             3|  157| 126| 130| 164| 291|
## 
## CI Statistics:
## Overall coverage and coverage for rejections:
## 
## | overall| rejection|
## |-------:|---------:|
## |       1|         1|
## 
## P(theta_test is in the confidence interval)
## 
## 
## | coverage| selectedCount| rejectedCount|
## |--------:|-------------:|-------------:|
## |        1|          1598|            40|
## |        1|           946|            30|
## |        1|           699|            18|
## |        1|           691|            13|
## |        1|           980|             8|
## |        1|            86|            86|
## NULL

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They may not be fully stable and should be used with caution. We make no claims about them.