getSimulationMultiArmSurvival: Get Simulation Multi-Arm Survival

Description

Returns the simulated power, stopping probabilities, conditional power, and expected sample size for testing survival in a multi-arm treatment groups testing situation. In contrast to getSimulationSurvival() (where survival times are simulated), normally distributed logrank test statistics are simulated.

Usage

getSimulationMultiArmSurvival(
  design = NULL,
  ...,
  activeArms = 3L,
  effectMatrix = NULL,
  typeOfShape = c("linear", "sigmoidEmax", "userDefined"),
  omegaMaxVector = seq(1, 2.6, 0.4),
  gED50 = NA_real_,
  slope = 1,
  intersectionTest = c("Dunnett", "Bonferroni", "Simes", "Sidak", "Hierarchical"),
  directionUpper = TRUE,
  adaptations = NA,
  typeOfSelection = c("best", "rBest", "epsilon", "all", "userDefined"),
  effectMeasure = c("effectEstimate", "testStatistic"),
  successCriterion = c("all", "atLeastOne"),
  correlationComputation = c("alternative", "null"),
  epsilonValue = NA_real_,
  rValue = NA_real_,
  threshold = -Inf,
  plannedEvents = NA_real_,
  allocationRatioPlanned = NA_real_,
  minNumberOfEventsPerStage = NA_real_,
  maxNumberOfEventsPerStage = NA_real_,
  conditionalPower = NA_real_,
  thetaH1 = NA_real_,
  maxNumberOfIterations = 1000L,
  seed = NA_real_,
  calcEventsFunction = 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.

omegaMaxVector

Range of hazard ratios with highest response for "linear" and "sigmoidEmax" model, default is seq(1, 2.6, 0.4).

gED50

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

slope

If "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: "Dunnett", "Bonferroni", "Simes", "Sidak", and "Hierarchical", default is "Dunnett".

directionUpper

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.

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 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), the parameter rValue has to be specified, for "epsilon" (select treatment arm not worse than epsilon compared to the best), the parameter epsilonValue has to be specified. If "userDefined" is selected, "selectArmsFunction" has to be specified.

effectMeasure

Criterion for treatment arm 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, "atLeastOne" stops if at least one of the selected treatment arms is shown to be superior to control at interim, default is "all".

correlationComputation

If correlationComputation = "alternative", for simulating log-rank statistics in the many-to-one design, a correlation matrix according to Deng et al. (Biometrics, 2019) accounting for the respective alternative is used; if correlationComputation = "null", a constant correlation matrix valid under the null, i.e., not accounting for the alternative is used, default is "alternative".

epsilonValue

For "epsilon" (select treatment arm not worse than epsilon compared to the best), the parameter epsilonValue has to be specified.

rValue

For "rbest" (select the rValue best treatment arms), the parameter rValue has to be specified.

threshold

Selection criterion: treatment arm 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.

plannedEvents

plannedEvents is a vector of length kMax (the number of stages of the design) that determines the number of cumulated (overall) events in survival designs when the interim stages are planned. For two treatment arms, it is the number of events for both treatment arms. For multi-arm designs, plannedEvents refers to the overall number of events for the selected arms plus control.

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.

minNumberOfEventsPerStage

When performing a data driven sample size recalculation, the vector minNumberOfEventsPerStage with length kMax determines the minimum number of events per stage (i.e., not cumulated), the first element is not taken into account.

maxNumberOfEventsPerStage

When performing a data driven sample size recalculation, the vector maxNumberOfEventsPerStage with length kMax determines the maximum number of events per stage (i.e., not cumulated), the first element is not taken into account.

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.

maxNumberOfIterations

The number of simulation iterations, default is 1000.

seed

The seed to reproduce the simulation, default is a random seed.

calcEventsFunction

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 minNumberOfEventsPerStage and maxNumberOfEventsPerStage (see details and examples).

selectArmsFunction

Optionally, a function can be entered that defines the way of how treatment arms are selected. This function has to depend on effectVector with length activeArms (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 makes only sense if kMax > 1 and if conditionalPower, minNumberOfEventsPerStage, and maxNumberOfEventsPerStage (or calcEventsFunction) are defined.

calcEventsFunction This function returns the number of events at given conditional power and conditional critical value for specified testing situation. The function might depend on the variables stage, selectedArms, plannedEvents, directionUpper, allocationRatioPlanned, minNumberOfEventsPerStage, maxNumberOfEventsPerStage, conditionalPower, conditionalCriticalValue, and overallEffects. The function has to contain the three-dots argument '...' (see examples).

Examples

Run this code

# NOT RUN {
# Assess different selection rules for a two-stage survival design with 
# O'Brien & Fleming alpha spending boundaries and (non-binding) stopping 
# for futility if the test statistic is negative. 
# Number of events at the second stage is adjusted based on conditional 
# power 80% and specified minimum and maximum number of Events.
maxNumberOfIterations <- 50
design <- getDesignInverseNormal(typeOfDesign = "asOF", futilityBounds = 0)

y1 <- getSimulationMultiArmSurvival(design = design, activeArms = 4, 
    intersectionTest = "Simes", typeOfShape = "sigmoidEmax", 
    omegaMaxVector = seq(1, 2, 0.5), gED50 = 2, slope = 4, 
    typeOfSelection = "best", conditionalPower = 0.8, 
    minNumberOfEventsPerStage = c(NA_real_, 30), 
    maxNumberOfEventsPerStage = c(NA_real_, 90),
    maxNumberOfIterations = maxNumberOfIterations, 
    plannedEvents = c(75, 120))

y2 <- getSimulationMultiArmSurvival(design = design, activeArms = 4, 
    intersectionTest = "Simes", typeOfShape = "sigmoidEmax", 
    omegaMaxVector = seq(1,2,0.5), gED50 = 2, slope = 4,
    typeOfSelection = "epsilon", epsilonValue = 0.2, 
    effectMeasure = "effectEstimate",
    conditionalPower = 0.8, minNumberOfEventsPerStage = c(NA_real_, 30), 
    maxNumberOfEventsPerStage = c(NA_real_, 90),
    maxNumberOfIterations = maxNumberOfIterations, 
	   plannedEvents = c(75, 120))

y1$effectMatrix

y1$rejectAtLeastOne
y2$rejectAtLeastOne

y1$selectedArms
y2$selectedArms
# }
# NOT RUN {
# }

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