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Returns the simulated power, stopping probabilities, conditional power, and expected sample size for testing rates in a one or two treatment groups testing situation.
getSimulationRates(
design = NULL,
...,
groups = 2L,
normalApproximation = TRUE,
riskRatio = FALSE,
thetaH0 = ifelse(riskRatio, 1, 0),
pi1 = seq(0.2, 0.5, 0.1),
pi2 = NA_real_,
plannedSubjects = NA_real_,
directionUpper = TRUE,
allocationRatioPlanned = NA_real_,
minNumberOfSubjectsPerStage = NA_real_,
maxNumberOfSubjectsPerStage = NA_real_,
conditionalPower = NA_real_,
pi1H1 = NA_real_,
pi2H1 = NA_real_,
maxNumberOfIterations = 1000L,
seed = NA_real_,
calcSubjectsFunction = NULL,
showStatistics = FALSE
)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.
The number of treatment groups (1 or 2), default is 2.
The type of computation of the p-values. Default is FALSE for
testing means (i.e., the t test is used) and TRUE for testing rates and the hazard ratio.
For testing rates, if normalApproximation = FALSE is specified, the binomial test
(one sample) or the exact test of Fisher (two samples) is used for calculating the p-values.
In the survival setting normalApproximation = FALSE has no effect.
If TRUE, the design characteristics for
one-sided testing of H0: pi1 / pi2 = thetaH0 are simulated, default is FALSE.
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.
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.
A numeric value or vector that represents the assumed probability in
the active treatment group if two treatment groups
are considered, or the alternative probability for a one treatment group design,
default is seq(0.2, 0.5, 0.1) (power calculations and simulations) or
seq(0.4, 0.6, 0.1) (sample size calculations).
A numeric value that represents the assumed probability in the reference group if two treatment
groups are considered, default is 0.2.
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.
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.
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.
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.
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.
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.
If specified, the assumed probability in the active treatment group if two treatment groups are considered, or the assumed probability for a one treatment group design, for which the conditional power was calculated.
If specified, the assumed probability in the reference group if two treatment groups are considered, for which the conditional power was calculated.
The number of simulation iterations, default is 1000.
The seed to reproduce the simulation, default is a random seed.
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).
If TRUE, summary statistics of the simulated data
are displayed for the print command, otherwise the output is suppressed, default
is FALSE.
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,
The summary statistics "Simulated data" contains the following parameters: median [range]; mean +/-sd
$show(showStatistics = FALSE) or $setShowStatistics(FALSE) can be used to disable
the output of the aggregated simulated data.
Example 1:
simulationResults <- getSimulationRates(plannedSubjects = 40)
simulationResults$show(showStatistics = FALSE)
Example 2:
simulationResults <- getSimulationRates(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:
iterationNumber: The number of the simulation iteration.
stageNumber: The stage.
pi1: The assumed or derived event rate in the treatment group (if available).
pi2: The assumed or derived event rate in the control group (if available).
numberOfSubjects: The number of subjects under consideration when the
(interim) analysis takes place.
rejectPerStage: 1 if null hypothesis can be rejected, 0 otherwise.
futilityPerStage: 1 if study should be stopped for futility, 0 otherwise.
testStatistic: The test statistic that is used for the test decision,
depends on which design was chosen (group sequential, inverse normal,
or Fisher combination test)'
testStatisticsPerStage: The test statistic for each stage if only data from
the considered stage is taken into account.
overallRate1: The cumulative rate in treatment group 1.
overallRate2: The cumulative rate in treatment group 2.
stagewiseRates1: The stage-wise rate in treatment group 1.
stagewiseRates2: The stage-wise rate in treatment group 2.
sampleSizesPerStage1: The stage-wise sample size in treatment group 1.
sampleSizesPerStage2: The stage-wise sample size in treatment group 2.
trialStop: TRUE if study should be stopped for efficacy or futility or final stage, FALSE otherwise.
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 pi1H1 and pi2H1.
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.
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 pi1H1 and/or pi2H1 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,
riskRatio,
thetaH0,
groups,
plannedSubjects,
sampleSizesPerStage,
directionUpper,
allocationRatioPlanned,
minNumberOfSubjectsPerStage,
maxNumberOfSubjectsPerStage,
conditionalPower,
conditionalCriticalValue,
overallRate,
farringtonManningValue1, and farringtonManningValue2.
The function has to contain the three-dots argument '...' (see examples).
# NOT RUN {
# Fixed sample size design (two groups) with total sample
# size 120, pi1 = (0.3,0.4,0.5,0.6) and pi2 = 0.3
getSimulationRates(pi1 = seq(0.3, 0.6, 0.1), pi2 = 0.3,
plannedSubjects = 120, maxNumberOfIterations = 10)
# }
# NOT RUN {
# Increase number of simulation iterations and compare results with power calculator
getSimulationRates(pi1 = seq(0.3, 0.6, 0.1), pi2 = 0.3,
plannedSubjects = 120, maxNumberOfIterations = 50)
getPowerRates(pi1 = seq(0.3, 0.6, 0.1), pi2 = 0.3, maxNumberOfSubjects = 120)
# Do the same for a two-stage Pocock inverse normal group sequential
# design with non-binding futility stops
designIN <- getDesignInverseNormal(typeOfDesign = "P", futilityBounds = c(0))
getSimulationRates(designIN, pi1 = seq(0.3, 0.6, 0.1), pi2 = 0.3,
plannedSubjects = c(40, 80), maxNumberOfIterations = 50)
getPowerRates(designIN, pi1 = seq(0.3, 0.6, 0.1), pi2 = 0.3, maxNumberOfSubjects = 80)
# Assess power and average sample size if a sample size reassessment is
# foreseen at conditional power 80% for the subsequent stage (decrease and increase)
# based on observed overall rates and specified minNumberOfSubjectsPerStage
# and maxNumberOfSubjectsPerStage
# Do the same under the assumption that a sample size increase only takes place
# if the rate difference exceeds the value 0.1 at interim. For this, the sample
# size recalculation method needs to be redefined:
mySampleSizeCalculationFunction <- function(..., stage,
plannedSubjects,
minNumberOfSubjectsPerStage,
maxNumberOfSubjectsPerStage,
conditionalPower,
conditionalCriticalValue,
overallRate) {
if (overallRate[1] - overallRate[2] < 0.1) {
return(plannedSubjects[stage] - plannedSubjects[stage - 1])
} else {
rateUnderH0 <- (overallRate[1] + overallRate[2]) / 2
stageSubjects <- 2 * (max(0, conditionalCriticalValue *
sqrt(2 * rateUnderH0 * (1 - rateUnderH0)) +
stats::qnorm(conditionalPower) * sqrt(overallRate[1] *
(1 - overallRate[1]) + overallRate[2] * (1 - overallRate[2]))))^2 /
(max(1e-12, (overallRate[1] - overallRate[2])))^2
stageSubjects <- ceiling(min(max(
minNumberOfSubjectsPerStage[stage],
stageSubjects), maxNumberOfSubjectsPerStage[stage]))
return(stageSubjects)
}
}
getSimulationRates(designIN, pi1 = seq(0.3, 0.6, 0.1), pi2 = 0.3,
plannedSubjects = c(40, 80), minNumberOfSubjectsPerStage = c(40, 20),
maxNumberOfSubjectsPerStage = c(40, 160), conditionalPower = 0.8,
calcSubjectsFunction = mySampleSizeCalculationFunction, maxNumberOfIterations = 50)
# }
# NOT RUN {
# }
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