Get Simulation Enrichment Means — getSimulationEnrichmentMeans • rpact

Returns the simulated power, stopping and selection probabilities, conditional power, and expected sample size or testing means in an enrichment design testing situation.

Usage

getSimulationEnrichmentMeans(
  design = NULL,
  ...,
  effectList = NULL,
  intersectionTest = c("Simes", "SpiessensDebois", "Bonferroni", "Sidak"),
  stratifiedAnalysis = TRUE,
  adaptations = NA,
  typeOfSelection = c("best", "rBest", "epsilon", "all", "userDefined"),
  effectMeasure = c("effectEstimate", "testStatistic"),
  successCriterion = c("all", "atLeastOne"),
  epsilonValue = NA_real_,
  rValue = NA_real_,
  threshold = -Inf,
  plannedSubjects = NA_integer_,
  allocationRatioPlanned = NA_real_,
  minNumberOfSubjectsPerStage = NA_real_,
  maxNumberOfSubjectsPerStage = NA_real_,
  conditionalPower = NA_real_,
  thetaH1 = NA_real_,
  stDevH1 = NA_real_,
  maxNumberOfIterations = 1000L,
  seed = NA_real_,
  calcSubjectsFunction = NULL,
  selectPopulationsFunction = NULL,
  showStatistics = FALSE
)

Arguments

design: The trial design. If no trial design is specified, a fixed sample size design is used. In this case, Type I error rate alpha, Type II error rate beta, twoSidedPower, and sided can be directly entered as argument where necessary.
...: Ensures that all arguments (starting from the "...") are to be named and that a warning will be displayed if unknown arguments are passed.
effectList: List of subsets, prevalences, and effect sizes with columns and number of rows reflecting the different situations to consider (see examples).
intersectionTest: Defines the multiple test for the intersection hypotheses in the closed system of hypotheses. Four options are available in enrichment designs: "SpiessensDebois", "Bonferroni", "Simes", and "Sidak", default is "Simes".
stratifiedAnalysis: Logical. For enrichment designs, typically a stratified analysis should be chosen. For testing rates, also a non-stratified analysis based on overall data can be performed. For survival data, only a stratified analysis is possible (see Brannath et al., 2009), default is TRUE.
adaptations: A logical vector of length kMax - 1 indicating whether or not an adaptation takes place at interim k, default is rep(TRUE, kMax - 1).
typeOfSelection: The way the treatment arms or populations are selected at interim. Five options are available: "best", "rbest", "epsilon", "all", and "userDefined", default is "best".
For "rbest" (select the rValue best treatment arms/populations), the parameter rValue has to be specified, for "epsilon" (select treatment arm/population not worse than epsilon compared to the best), the parameter epsilonValue has to be specified. If "userDefined" is selected, "selectArmsFunction" or "selectPopulationsFunction" has to be specified.
effectMeasure: Criterion for treatment arm/population selection, either based on test statistic ("testStatistic") or effect estimate (difference for means and rates or ratio for survival) ("effectEstimate"), default is "effectEstimate".
successCriterion: Defines when the study is stopped for efficacy at interim. Two options are available: "all" stops the trial if the efficacy criterion is fulfilled for all selected treatment arms/populations, "atLeastOne" stops if at least one of the selected treatment arms/populations is shown to be superior to control at interim, default is "all".
epsilonValue: For typeOfSelection = "epsilon" (select treatment arm / population not worse than epsilon compared to the best), the parameter epsilonValue has to be specified. Must be a numeric of length 1.
rValue: For typeOfSelection = "rbest" (select the rValue best treatment arms / populations), the parameter rValue has to be specified.
threshold: Selection criterion: treatment arm / population is selected only if effectMeasure exceeds threshold, default is -Inf. threshold can also be a vector of length activeArms referring to a separate threshold condition over the treatment arms.
plannedSubjects: plannedSubjects is a numeric vector of length kMax (the number of stages of the design) that determines the number of cumulated (overall) subjects when the interim stages are planned. For two treatment arms, it is the number of subjects for both treatment arms. For multi-arm designs, plannedSubjects refers to the number of subjects per selected active arm.
allocationRatioPlanned: The planned allocation ratio n1 / n2 for a two treatment groups design, default is 1. For multi-arm designs, it is the allocation ratio relating the active arm(s) to the control. For simulating means and rates for a two treatment groups design, it can be a vector of length kMax, the number of stages. It can be a vector of length kMax, too, for multi-arm and enrichment designs. In these cases, a change of allocating subjects to treatment groups over the stages can be assessed. Note that internally allocationRatioPlanned is treated as a vector of length kMax, not a scalar.
minNumberOfSubjectsPerStage: When performing a data driven sample size recalculation, the numeric vector minNumberOfSubjectsPerStage with length kMax determines the minimum number of subjects per stage (i.e., not cumulated), the first element is not taken into account. For two treatment arms, it is the number of subjects for both treatment arms. For multi-arm designs minNumberOfSubjectsPerStage refers to the minimum number of subjects per selected active arm.
maxNumberOfSubjectsPerStage: When performing a data driven sample size recalculation, the numeric vector maxNumberOfSubjectsPerStage with length kMax determines the maximum number of subjects per stage (i.e., not cumulated), the first element is not taken into account. For two treatment arms, it is the number of subjects for both treatment arms. For multi-arm designs maxNumberOfSubjectsPerStage refers to the maximum number of subjects per selected active arm.
conditionalPower: If conditionalPower together with minNumberOfSubjectsPerStage and maxNumberOfSubjectsPerStage (or minNumberOfEventsPerStage and maxNumberOfEventsPerStage for survival designs) is specified, a sample size recalculation based on the specified conditional power is performed. It is defined as the power for the subsequent stage given the current data. By default, the conditional power will be calculated under the observed effect size. Optionally, you can also specify thetaH1 and stDevH1 (for simulating means), pi1H1 and pi2H1 (for simulating rates), or thetaH1 (for simulating hazard ratios) as parameters under which it is calculated and the sample size recalculation is performed.
thetaH1: If specified, the value of the alternative under which the conditional power or sample size recalculation calculation is performed. Must be a numeric of length 1.
stDevH1: If specified, the value of the standard deviation under which the conditional power or sample size recalculation calculation is performed, default is the value of stDev. Must be a positive numeric of length 1.
maxNumberOfIterations: The number of simulation iterations, default is 1000. Must be a positive integer of length 1.
seed: The seed to reproduce the simulation, default is a random seed.
calcSubjectsFunction: Optionally, a function can be entered that defines the way of performing the sample size recalculation. By default, sample size recalculation is performed with conditional power and specified minNumberOfSubjectsPerStage and maxNumberOfSubjectsPerStage (see details and examples).
selectPopulationsFunction: Optionally, a function can be entered that defines the way of how populations are selected. This function is allowed to depend on effectVector with length populations stage, conditionalPower, conditionalCriticalValue, plannedSubjects/plannedEvents, allocationRatioPlanned, selectedPopulations, thetaH1 (for means and survival), stDevH1 (for means), overallEffects, and for rates additionally: piTreatmentsH1, piControlH1, overallRates, and overallRatesControl (see examples).
showStatistics: Logical. If TRUE, summary statistics of the simulated data are displayed for the print command, otherwise the output is suppressed, default is FALSE.

Value

Returns a SimulationResults object. The following generics (R generic functions) are available for this object:

names() to obtain the field names,
print() to print the object,
summary() to display a summary of the object,
plot() to plot the object,
as.data.frame() to coerce the object to a data.frame,
as.matrix() to coerce the object to a matrix.

Details

At given design the function simulates the power, stopping probabilities, selection probabilities, and expected sample size at given number of subjects, parameter configuration, and population selection rule in the enrichment situation. An allocation ratio can be specified referring to the ratio of number of subjects in the active treatment groups as compared to the control group.

The definition of thetaH1 and/or stDevH1 makes only sense if kMax > 1 and if conditionalPower, minNumberOfSubjectsPerStage, and maxNumberOfSubjectsPerStage (or calcSubjectsFunction) are defined.

calcSubjectsFunction
This function returns the number of subjects at given conditional power and conditional critical value for specified testing situation. The function might depend on the variables stage, selectedPopulations, plannedSubjects, allocationRatioPlanned, minNumberOfSubjectsPerStage, maxNumberOfSubjectsPerStage, conditionalPower, conditionalCriticalValue, overallEffects, and stDevH1. The function has to contain the three-dots argument '...' (see examples).

How to get help for generic functions

Click on the link of a generic in the list above to go directly to the help documentation of the rpact specific implementation of the generic. Note that you can use the R function methods to get all the methods of a generic and to identify the object specific name of it, e.g., use methods("plot") to get all the methods for the plot generic. There you can find, e.g., plot.AnalysisResults and obtain the specific help documentation linked above by typing ?plot.AnalysisResults.

Examples

if (FALSE) { # \dontrun{
# Assess a population selection strategy with one subset population.
# If the subset is better than the full population, then the subset
# is selected for the second stage, otherwise the full. Print and plot
# design characteristics.

# Define design
designIN <- getDesignInverseNormal(kMax = 2)

# Define subgroups and their prevalences
subGroups <- c("S", "R") # fixed names!
prevalences <- c(0.2, 0.8)

# Define effect matrix and variability
effectR <- 0.2
m <- c()
for (effectS in seq(0, 0.5, 0.25)) {
    m <- c(m, effectS, effectR)
}
effects <- matrix(m, byrow = TRUE, ncol = 2)
stDev <- c(0.4, 0.8)

# Define effect list
effectList <- list(subGroups=subGroups, prevalences=prevalences, stDevs = stDev, effects = effects)

# Perform simulation
simResultsPE <- getSimulationEnrichmentMeans(design = designIN,
    effectList = effectList, plannedSubjects = c(50, 100),
    maxNumberOfIterations = 100)
print(simResultsPE)

# Assess the design characteristics of a user defined selection
# strategy in a three-stage design with no interim efficacy stop
# using the inverse normal method for combining the stages.
# Only the second interim is used for a selecting of a study
# population. There is a small probability for stopping the trial
# at the first interim.

# Define design
designIN2 <- getDesignInverseNormal(typeOfDesign = "noEarlyEfficacy", kMax = 3)

# Define selection function
mySelection <- function(effectVector, stage) {
    selectedPopulations <- rep(TRUE, 3)
    if (stage == 2) {
        selectedPopulations <- (effectVector >= c(1, 2, 3))
    }
    return(selectedPopulations)
}

# 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, 1)) {
    for (effectS2 in seq(0, 5, 1)) {
        m <- c(m, effectS1, effectS12, effectS2, effectR)
    }
}
effects <- matrix(m, byrow = TRUE, ncol = 4)
stDev <- 10

# Define effect list
effectList <- list(subGroups=subGroups, prevalences=prevalences, stDevs = stDev, effects = effects)

# Perform simulation
simResultsPE <- getSimulationEnrichmentMeans(
    design = designIN2,
    effectList = effectList,
    typeOfSelection = "userDefined",
    selectPopulationsFunction = mySelection,
    intersectionTest = "Simes",
    plannedSubjects = c(50, 100, 150),
    maxNumberOfIterations = 100)
print(simResultsPE)
if (require(ggplot2)) plot(simResultsPE, type = 3)
} # }