rpact (version 4.1.0)

getSimulationMeans: Get Simulation Means

Description

Returns the simulated power, stopping probabilities, conditional power, and expected sample size for testing means in a one or two treatment groups testing situation.

Usage

getSimulationMeans(
  design = NULL,
  ...,
  groups = 2L,
  normalApproximation = TRUE,
  meanRatio = FALSE,
  thetaH0 = ifelse(meanRatio, 1, 0),
  alternative = seq(0, 1, 0.2),
  stDev = 1,
  plannedSubjects = NA_real_,
  directionUpper = NA,
  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,
  showStatistics = 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.

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.

groups

The number of treatment groups (1 or 2), default is 2.

normalApproximation

The type of computation of the p-values. Default is TRUE, i.e., normally distributed test statistics are generated. If FALSE, the t test is used for calculating the p-values, i.e., t distributed test statistics are generated.

meanRatio

If TRUE, the design characteristics for one-sided testing of H0: mu1 / mu2 = thetaH0 are simulated, default is FALSE.

thetaH0

The null hypothesis value, default is 0 for the normal and the binary case (testing means and rates, respectively), it is 1 for the survival case (testing the hazard ratio).

For non-inferiority designs, thetaH0 is the non-inferiority bound. That is, in case of (one-sided) testing of

• means: a value != 0 (or a value != 1 for testing the mean ratio) can be specified.

• rates: a value != 0 (or a value != 1 for testing the risk ratio pi1 / pi2) can be specified.

• survival data: a bound for testing H0: hazard ratio = thetaH0 != 1 can be specified.

• count data: a bound for testing H0: lambda1 / lambda2 = thetaH0 != 1 can be specified.

For testing a rate in one sample, a value thetaH0 in (0, 1) has to be specified for defining the null hypothesis H0: pi = thetaH0.

alternative

The alternative hypothesis value for testing means under which the data is simulated. This can be a vector of assumed alternatives, default is seq(0, 1, 0.2).

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.

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.

directionUpper

Logical. Specifies the direction of the alternative, only applicable for one-sided testing; default is TRUE which means that larger values of the test statistics yield smaller p-values.

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).

showStatistics

Logical. If TRUE, summary statistics of the simulated data are displayed for the print command, otherwise the output is suppressed, default is FALSE.

Simulation Data

The summary statistics "Simulated data" contains the following parameters: median range; mean +/-sd

$show(showStatistics = FALSE) or $setShowStatistics(FALSE) can be used to disable the output of the aggregated simulated data.

Example 1:
simulationResults <- getSimulationMeans(plannedSubjects = 40)
simulationResults$show(showStatistics = FALSE)

Example 2:
simulationResults <- getSimulationMeans(plannedSubjects = 40)
simulationResults$setShowStatistics(FALSE)
simulationResults

getData() can be used to get the aggregated simulated data from the object as data.frame. The data frame contains the following columns:

1. iterationNumber: The number of the simulation iteration.

2. stageNumber: The stage.

3. alternative: The alternative hypothesis value.

4. numberOfSubjects: The number of subjects under consideration when the (interim) analysis takes place.

5. rejectPerStage: 1 if null hypothesis can be rejected, 0 otherwise.

6. futilityPerStage: 1 if study should be stopped for futility, 0 otherwise.

7. testStatistic: The test statistic that is used for the test decision, depends on which design was chosen (group sequential, inverse normal, or Fisher's combination test).

8. testStatisticsPerStage: The test statistic for each stage if only data from the considered stage is taken into account.

9. effectEstimate: Overall simulated standardized effect estimate.

10. trialStop: TRUE if study should be stopped for efficacy or futility or final stage, FALSE otherwise.

11. conditionalPowerAchieved: The conditional power for the subsequent stage of the trial for selected sample size and effect. The effect is either estimated from the data or can be user defined with thetaH1.

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, conditional power, and expected sample size at given number of subjects and parameter configuration. Additionally, an allocation ratio = n1/n2 can be specified where n1 and n2 are the number of subjects in the two treatment groups.

The definition of thetaH1 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 variables stage, meanRatio, thetaH0, groups, plannedSubjects, sampleSizesPerStage, directionUpper, allocationRatioPlanned, minNumberOfSubjectsPerStage, maxNumberOfSubjectsPerStage, conditionalPower, conditionalCriticalValue, thetaH1, and stDevH1. The function has to contain the three-dots argument '...' (see examples).

Examples

if (FALSE) {
# Fixed sample size design with two groups, total sample size 40,
# alternative = c(0, 0.2, 0.4, 0.8, 1), and standard deviation = 1 (the default)
getSimulationMeans(plannedSubjects = 40, maxNumberOfIterations = 10)

# Increase number of simulation iterations and compare results
# with power calculator using normal approximation
getSimulationMeans(
    alternative = 0:4, stDev = 5,
    plannedSubjects = 40, maxNumberOfIterations = 1000
)
getPowerMeans(
    alternative = 0:4, stDev = 5,
    maxNumberOfSubjects = 40, normalApproximation = TRUE
)

# Do the same for a three-stage O'Brien&Fleming inverse
# normal group sequential design with non-binding futility stops
designIN <- getDesignInverseNormal(typeOfDesign = "OF", futilityBounds = c(0, 0))
x <- getSimulationMeans(designIN,
    alternative = c(0:4), stDev = 5,
    plannedSubjects = c(20, 40, 60), maxNumberOfIterations = 1000
)
getPowerMeans(designIN,
    alternative = 0:4, stDev = 5,
    maxNumberOfSubjects = 60, normalApproximation = TRUE
)

# Assess power and average sample size if a sample size increase is foreseen
# at conditional power 80% for each subsequent stage based on observed overall
# effect and specified minNumberOfSubjectsPerStage and
# maxNumberOfSubjectsPerStage
getSimulationMeans(designIN,
    alternative = 0:4, stDev = 5,
    plannedSubjects = c(20, 40, 60),
    minNumberOfSubjectsPerStage = c(NA, 20, 20),
    maxNumberOfSubjectsPerStage = c(NA, 80, 80),
    conditionalPower = 0.8,
    maxNumberOfIterations = 50
)

# Do the same under the assumption that a sample size increase only takes
# place at the first interim. The sample size for the third stage is set equal
# to the second stage sample size.
mySampleSizeCalculationFunction <- function(..., stage,
        minNumberOfSubjectsPerStage,
        maxNumberOfSubjectsPerStage,
        sampleSizesPerStage,
        conditionalPower,
        conditionalCriticalValue,
        allocationRatioPlanned,
        thetaH1,
        stDevH1) {
    if (stage <= 2) {
        # Note that allocationRatioPlanned is as a vector of length kMax
        stageSubjects <- (1 + allocationRatioPlanned[stage])^2 / 
            allocationRatioPlanned[stage] *
            (max(0, conditionalCriticalValue + stats::qnorm(conditionalPower)))^2 /
            (max(1e-12, thetaH1 / stDevH1))^2
        stageSubjects <- min(max(
            minNumberOfSubjectsPerStage[stage],
            stageSubjects
        ), maxNumberOfSubjectsPerStage[stage])
    } else {
        stageSubjects <- sampleSizesPerStage[stage - 1]
    }
    return(stageSubjects)
}
getSimulationMeans(designIN,
    alternative = 0:4, stDev = 5,
    plannedSubjects = c(20, 40, 60),
    minNumberOfSubjectsPerStage = c(NA, 20, 20),
    maxNumberOfSubjectsPerStage = c(NA, 80, 80),
    conditionalPower = 0.8,
    calcSubjectsFunction = mySampleSizeCalculationFunction,
    maxNumberOfIterations = 50
)
}