How to Create One- and Multi-Arm Simulation Result Plots with rpact

Utilities
Power simulation
Multi-arm
This document provides many different examples for creating one- and multi-arm as well as enrichment simulation result plots with rpact and ggplot2.
Author

Friedrich Pahlke Gernot Wassmer

Published

October 28, 2024

Preparation

First, load the rpact package

library(rpact)
packageVersion("rpact") # version should be version 3.0 or later
[1] '4.1.0'

Simulation results base

Simulation results base - means

maxNumberOfSubjects <- 90
informationRates <- c(0.2, 0.5, 1)
plannedSubjects <- round(informationRates * maxNumberOfSubjects)

getDesignInverseNormal(
    futilityBounds = c(-0.5, 0.5),
    informationRates = informationRates
) |> 
  getSimulationMeans(
    groups = 2, 
    meanRatio = TRUE,
    thetaH0 = 0.4, 
    plannedSubjects = plannedSubjects,
    maxNumberOfIterations = 500, 
    allocationRatioPlanned = 3,
    stDev = 1.5, 
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

Simulation results base - rates

maxNumberOfSubjects <- 90
informationRates <- (1:3) / 3
plannedSubjects <- round(informationRates * maxNumberOfSubjects)

getDesignInverseNormal(
    futilityBounds = c(-0.5, 0.5),
    informationRates = informationRates
) |>
  getSimulationRates(
    groups = 2, 
    riskRatio = TRUE,
    thetaH0 = 0.8, 
    plannedSubjects = plannedSubjects,
    maxNumberOfIterations = 500, 
    allocationRatioPlanned = 3,
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

Simulation results base - survival

kMax <- 3
getDesignFisher(
  kMax = kMax, 
  alpha0Vec = c(0.5, 0.5)
) |> 
  getSimulationSurvival(
    pi2 = 0.6,
    pi1 = seq(0.3, 0.45, 0.05), 
    directionUpper = FALSE,
    maxNumberOfSubjects = 500, 
    plannedEvents = (1:kMax) * 20,
    allocation1 = 1, 
    allocation2 = 1, 
    accrualTime = c(0, 3, 6, 12),
    accrualIntensity = c(0.1, 0.2, 0.2), 
    dropoutRate1 = 0,
    dropoutRate2 = 0, 
    dropoutTime = 12, 
    conditionalPower = 0.8,
    minNumberOfEventsPerStage = c(NA_real_, 10, 10),
    maxNumberOfEventsPerStage = c(NA_real_, 100, 200),
    maxNumberOfIterations = 500, 
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

piecewiseSurvivalTime <- list(
    "<6" = 0.025,
    "6 - <9" = 0.04,
    "9 - <15" = 0.015,
    "15 - <21" = 0.01,
    ">=21" = 0.007
)

kMax <- 3
getDesignGroupSequential(
  kMax = kMax, 
  typeOfDesign = "WT", 
  deltaWT = 0.25
) |>
  getSimulationSurvival(
    directionUpper = TRUE, 
    maxNumberOfSubjects = 500,
    plannedEvents = (1:kMax) * 20, 
    allocation1 = 1,
    allocation2 = 1, 
    accrualTime = c(0, 3, 6, 12),
    piecewiseSurvivalTime = piecewiseSurvivalTime, 
    hazardRatio = 1.7,
    accrualIntensity = c(0.1, 0.2, 0.2), 
    dropoutRate1 = 0,
    dropoutRate2 = 0, 
    dropoutTime = 12, 
    conditionalPower = 0.8,
    minNumberOfEventsPerStage = c(NA_real_, 10, 10),
    maxNumberOfEventsPerStage = c(NA_real_, 100, 200),
    maxNumberOfIterations = 500, 
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

Simulation results multi-arm

Simulation results multi-arm - means

getDesignInverseNormal(
    informationRates = c(0.2, 0.6, 1),
    futilityBounds = c(-0.5, 0.5)
) |>
  getSimulationMultiArmMeans(
    typeOfShape = "linear",
    activeArms = 4, 
    plannedSubjects = c(10, 30, 50), 
    stDev = 1.2,
    muMaxVector = seq(0.3, 0.6, 0.1), 
    adaptations = rep(TRUE, 2),
    conditionalPower = 0.8, 
    minNumberOfSubjectsPerStage = c(10, 4, 4),
    maxNumberOfSubjectsPerStage = c(10, 100, 100),
    maxNumberOfIterations = 500, 
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

Simulation results multi-arm - rates

getDesignInverseNormal(
    informationRates = c(0.2, 0.6, 1),
    futilityBounds = c(-0.5, 0.5)
) |>
  getSimulationMultiArmRates(
    typeOfShape = "linear",
    activeArms = 4, 
    plannedSubjects = c(10, 30, 50),
    piControl = 0.3, 
    piMaxVector = seq(0.3, 0.6, 0.1),
    adaptations = rep(TRUE, 2), 
    conditionalPower = 0.8,
    minNumberOfSubjectsPerStage = c(10, 4, 4),
    maxNumberOfSubjectsPerStage = c(10, 100, 100),
    maxNumberOfIterations = 500, 
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

Simulation results multi-arm - survival

getDesignInverseNormal(
    informationRates = c(0.2, 0.6, 1),
    futilityBounds = c(-0.5, 0.5)
) |>
  getSimulationMultiArmSurvival(
    activeArms = 4,
    typeOfSelection = "rBest", 
    rValue = 2, 
    plannedEvents = c(10, 30, 50),
    omegaMaxVector = seq(1, 1.6, 0.2), 
    adaptations = rep(TRUE, 2),
    conditionalPower = 0.8, 
    minNumberOfEventsPerStage = c(10, 4, 4),
    maxNumberOfEventsPerStage = c(10, 100, 100),
    maxNumberOfIterations = 500, 
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

Simulation results enrichment

Simulation results enrichment - means

design <- getDesignInverseNormal(
    informationRates = c(0.2, 0.6, 1),
    futilityBounds = c(-0.5, 0.5)
)
# Define subgroups and their prevalences
subGroups <- c("S1", "S12", "S2", "R") # fixed names!
prevalences <- c(0.2, 0.3, 0.4, 0.1)

effectR <- 1.5
effectS12 <- 5
m <- c()
for (effectS1 in seq(0, 5, 5)) {
    for (effectS2 in seq(0, 5, 5)) {
        m <- c(m, effectS1, effectS12, effectS2, effectR)
    }
}
effects <- matrix(m, byrow = TRUE, ncol = 4)
stDev <- 10
# Define effect list
el <- list(
    subGroups = subGroups, prevalences = prevalences,
    stDevs = stDev, effects = effects
)

# Perform simulation
design |> 
  getSimulationEnrichmentMeans(
    plannedSubjects = c(10, 30, 50),
    effectList = el,
    adaptations = rep(TRUE, 2),
    conditionalPower = 0.8,
    minNumberOfSubjectsPerStage = c(10, 4, 4),
    maxNumberOfSubjectsPerStage = c(10, 100, 100),
    maxNumberOfIterations = 500,
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

Simulation results enrichment - rates

design <- getDesignInverseNormal(
    informationRates = c(0.2, 0.6, 1),
    futilityBounds = c(-0.5, 0.5)
)
# Define effect list
subGroups <- c("S", "R")
prevalences <- c(0.4, 0.6)
piControl <- c(0.1, 0.4)
range1 <- piControl[1] + seq(0.0, 0.2, 0.1)
range2 <- piControl[2] + seq(0.0, 0.2, 0.1)
piTreatments <- c()
for (x1 in range1) {
    for (x2 in range2) {
        piTreatments <- c(piTreatments, x1, x2)
    }
}
el <- list(
    subGroups = subGroups,
    prevalences = prevalences,
    piControl = piControl,
    piTreatments = matrix(piTreatments,
        byrow = TRUE, ncol = 2
    )
)

# Perform simulation
design |> 
  getSimulationEnrichmentRates(
    plannedSubjects = c(10, 30, 50),
    effectList = el,
    maxNumberOfIterations = 500,
    seed = 1234567890
) |>
  plot(type = "all", grid = 0)

Simulation results enrichment - survival

# Define subgroups and their prevalences
subGroups <- c("S1", "S2", "S12", "R") # fixed names!
prevalences <- c(0.2, 0.3, 0.4, 0.1)

piControls <- c(0.2, 0.4, 0.15, 0.3)
effect <- c(-0.05, -0.02, -0.10, -0.10)
piTreatments <- piControls + effect

hr <- log(1 - piTreatments) / log(1 - piControls)

# Define effect list
el <- list(
    subGroups = subGroups, prevalences = prevalences,
    piControls = piControls, hazardRatios = matrix(rep(hr, 3), nrow = 3)
)

# Perform simulation
getDesignInverseNormal(
    typeOfDesign = "noEarlyEfficacy") |>
  getSimulationEnrichmentSurvival(
    effectList = el,
    typeOfSelection = "rbest",
    rValue = 2,
    intersectionTest = "Simes",
    plannedEvents = c(30, 80, 120),
    maxNumberOfIterations = 500,
    directionUpper = FALSE
) |>
  plot(type = "all", grid = 0)

System: rpact 4.1.0, R version 4.3.3 (2024-02-29 ucrt), platform: x86_64-w64-mingw32

To cite R in publications use:

R Core Team (2024). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

To cite package ‘rpact’ in publications use:

Wassmer G, Pahlke F (2024). rpact: Confirmatory Adaptive Clinical Trial Design and Analysis. R package version 4.1.0, https://CRAN.R-project.org/package=rpact.