R: Get Simulation Multi-Arm Means

getSimulationMultiArmMeans {rpact}

R Documentation

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"`, default is `"linear"`. For `"linear"`, `"muMaxVector"` specifies the range of effect sizes for the treatment group with highest response. If `"sigmoidEmax"` is selected, `"gED50"` and `"slope"` has to be entered to specify the ED50 and the slope of the sigmoid Emax model. For `"sigmoidEmax"`, `"muMaxVector"` specifies the range of effect sizes for the treatment group with response according to infinite dose. 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`. Must be a positive numeric of length 1.
`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).
`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`, `stage`, `"conditionalPower"`, `"conditionalCriticalValue"`, `"plannedSubjects/plannedEvents"`, `"allocationRatioPlanned"`, `"selectedArms"`, `"thetaH1"` (for means and survival), `"stDevH1"` (for means), `"overallEffects"`, and for rates additionally: `"piTreatmentsH1"`, `"piControlH1"`, `"overallRates"`, and `"overallRatesControl"`.
`showStatistics`	Logical. If `TRUE`, summary statistics of the simulated data are displayed for the `print` command, otherwise the output is suppressed, default is `FALSE`.

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).

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.

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)
if (require(ggplot2)) plot(results, type = c(5,3,9), grid = 4)

## End(Not run)

[Package rpact version 4.0.0 Index]