rpact (version 3.2.1)

getSimulationMultiArmMeans: Get Simulation Multi-Arm Means

Description

Returns the simulated power, stopping and selection probabilities, conditional power, and expected sample size for testing means in a multi-arm treatment groups testing situation.

Usage

getSimulationMultiArmMeans(
  design = NULL,
  ...,
  activeArms = 3L,
  effectMatrix = NULL,
  typeOfShape = c("linear", "sigmoidEmax", "userDefined"),
  muMaxVector = seq(0, 1, 0.2),
  gED50 = NA_real_,
  slope = 1,
  intersectionTest = c("Dunnett", "Bonferroni", "Simes", "Sidak", "Hierarchical"),
  stDev = 1,
  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,
  selectArmsFunction = 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.

activeArms

The number of active treatment arms to be compared with control, default is 3.

effectMatrix

Matrix of effect sizes with activeArms columns and number of rows reflecting the different situations to consider.

typeOfShape

The shape of the dose-response relationship over the treatment groups. This can be either "linear", "sigmoidEmax", or "userDefined". If "sigmoidEmax" is selected, "gED50" and "slope" has to be entered to specify the ED50 and the slope of the sigmoid Emax model. For "linear" and "sigmoidEmax", "muMaxVector" specifies the range of effect sizes for the treatment group with highest response. If "userDefined" is selected, "effectMatrix" has to be entered.

muMaxVector

Range of effect sizes for the treatment group with highest response for "linear" and "sigmoidEmax" model, default is seq(0, 1, 0.2).

gED50

If typeOfShape = "sigmoidEmax" is selected, "gED50" has to be entered to specify the ED50 of the sigmoid Emax model.

slope

If typeOfShape = "sigmoidEmax" is selected, "slope" can be entered to specify the slope of the sigmoid Emax model, default is 1.

intersectionTest

Defines the multiple test for the intersection hypotheses in the closed system of hypotheses. Five options are available in multi-arm designs: "Dunnett", "Bonferroni", "Simes", "Sidak", and "Hierarchical", default is "Dunnett".

stDev

The standard deviation under which the data is simulated, default is 1. If meanRatio = TRUE is specified, stDev defines the coefficient of variation sigma / mu2.

adaptations

A 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.

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 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.

minNumberOfSubjectsPerStage

When performing a data driven sample size recalculation, the 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 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.

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.

maxNumberOfIterations

The number of simulation iterations, default is 1000.

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 with specified minNumberOfSubjectsPerStage and maxNumberOfSubjectsPerStage (see details and examples).

selectArmsFunction

Optionally, a function can be entered that defines the way of how treatment arms are selected. This function is allowed to depend on effectVector with length activeArms and stage (see examples).

showStatistics

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.

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.

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 treatment arm selection rule in the multi-arm 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, selectedArms, plannedSubjects, allocationRatioPlanned, minNumberOfSubjectsPerStage, maxNumberOfSubjectsPerStage, conditionalPower, conditionalCriticalValue, overallEffects, and stDevH1. The function has to contain the three-dots argument '...' (see examples).

Examples

# NOT RUN {
# Assess a treatment-arm selection strategy with three active arms, 
# if the better of the arms is selected for the second stage, and 
# compare it with the no-selection case. 
# Assume a linear dose-response relationship 
maxNumberOfIterations <- 100
designIN <- getDesignInverseNormal(typeOfDesign = "OF", kMax = 2)
sim <- getSimulationMultiArmMeans(design = designIN,
    activeArms = 3, typeOfShape = "linear",
    muMaxVector = seq(0,0.8,0.2),
    intersectionTest = "Simes",
    typeOfSelection = "best",
    plannedSubjects = c(30,60),
    maxNumberOfIterations = maxNumberOfIterations)

sim0 <- getSimulationMultiArmMeans(design = designIN,
    activeArms = 3, typeOfShape = "linear",
    muMaxVector = seq(0,0.8,0.2),
    intersectionTest = "Simes",
    typeOfSelection = "all",
    plannedSubjects = c(30,60),
    maxNumberOfIterations = maxNumberOfIterations)

sim$rejectAtLeastOne
sim$expectedNumberOfSubjects

sim0$rejectAtLeastOne
sim0$expectedNumberOfSubjects

# Compare the power of the conditional Dunnett test with the power of the 
# combination test using Dunnett's intersection tests if no treatment arm 
# selection takes place. Asseume a linear dose-response relationship.
maxNumberOfIterations <- 100
designIN <- getDesignInverseNormal(typeOfDesign = "asUser", 
    userAlphaSpending = c(0, 0.025))
designCD <- getDesignConditionalDunnett(secondStageConditioning = TRUE)

index <- 1
for (design in c(designIN, designCD)) {
    results <- getSimulationMultiArmMeans(design, activeArms = 3, 
        muMaxVector = seq(0, 1, 0.2), typeOfShape = "linear", 
        plannedSubjects = cumsum(rep(20, 2)), 
        intersectionTest = "Dunnett", 
        typeOfSelection = "all", maxNumberOfIterations = maxNumberOfIterations)
    if (index == 1) {
        drift <- results$effectMatrix[nrow(results$effectMatrix), ]
        plot(drift,results$rejectAtLeastOne, type = "l", lty = 1, 
            lwd = 3, col = "black", ylab = "Power")
    } else {
        lines(drift,results$rejectAtLeastOne, type = "l", 
            lty = index, lwd = 3, col = "red")
    }
    index <- index + 1
}
legend("topleft", legend=c("Combination Dunnett", "Conditional Dunnett"),
    col=c("black", "red"), lty = (1:2), cex = 0.8)

# Assess the design characteristics of a user defined selection
# strategy in a two-stage design using the inverse normal method
# with constant bounds. Stopping for futility due to
# de-selection of all treatment arms.
designIN <- getDesignInverseNormal(typeOfDesign = "P", kMax = 2)

mySelection <- function(effectVector) {
    selectedArms <- (effectVector >= c(0, 0.1, 0.3))
    return(selectedArms)
}

results <- getSimulationMultiArmMeans(designIN, activeArms = 3, 
    muMaxVector = seq(0, 1, 0.2), 
    typeOfShape = "linear", 
    plannedSubjects = c(30,60), 
    intersectionTest = "Dunnett", 
    typeOfSelection = "userDefined",
    selectArmsFunction = mySelection,
    maxNumberOfIterations = 100)

options(rpact.summary.output.size = "medium")         
summary(results)
plot(results, type = c(5,3,9), grid = 4)
# }
# NOT RUN {
# }