Get Simulation Multi-Arm Survival — getSimulationMultiArmSurvival • rpact

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

Depending on simulationType, either a patient-wise survival simulation is performed, a patient-wise basic approximation is used, or normally distributed log-rank test statistics are simulated. The default simulationType = "auto" chooses the simulation approach automatically based on the explicitly specified arguments.

Usage

getSimulationMultiArmSurvival(
  design = NULL,
  ...,
  simulationType = c("auto", "patientWise", "testStatisticBased", "patientWiseBasic"),
  activeArms = NA_integer_,
  piControl = 0.2,
  effectMatrix = NULL,
  typeOfShape = c("linear", "sigmoidEmax", "userDefined"),
  omegaMaxVector = seq(1, 2.6, 0.4),
  kappa = 1,
  gED50 = NA_real_,
  slope = 1,
  doseLevels = NA_real_,
  eventTime = 12,
  accrualTime = c(0, 12),
  accrualIntensity = 0.1,
  accrualIntensityType = c("auto", "absolute", "relative"),
  dropoutRate1 = 0,
  dropoutRate2 = 0,
  dropoutTime = 12,
  maxNumberOfSubjects = NA_real_,
  intersectionTest = c("Dunnett", "Bonferroni", "Simes", "Sidak", "Hierarchical"),
  directionUpper = NA,
  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.
simulationType: Character value specifying the simulation approach: "auto", "patientWise", "testStatisticBased", or "patientWiseBasic". If "auto" is specified, the simulation type is selected automatically based on the explicitly specified arguments. If patient-wise-specific arguments such as piControl, eventTime, accrualTime, accrualIntensity, accrualIntensityType, dropoutRate1, dropoutRate2, dropoutTime, maxNumberOfSubjects, or kappa are provided, a patient-wise simulation approach is used; otherwise the test-statistic-based simulation is used for backward compatibility.
activeArms: The number of active treatment arms to be compared with control, default is 3.
piControl: The assumed probability in the control arm, default is 0.2.
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", omegaMaxVector 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", omegaMaxVector 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.
omegaMaxVector: Range of hazard ratios with highest response for "linear" and "sigmoidEmax" model, default is seq(1, 2.6, 0.4).
kappa: A numeric value > 0. A kappa != 1 will be used for the specification of the shape of the Weibull distribution. Default is 1, i.e., the exponential survival distribution is used instead of the Weibull distribution. Note that the Weibull distribution cannot be used for the piecewise definition of the survival time distribution, i.e., only piecewiselambda (as a single value) and kappa can be specified. This function is equivalent to pweibull(t, shape = kappa, scale = 1 / lambda) of the stats package, i.e., the scale parameter is 1 / 'hazard rate'.
For example, getPiecewiseExponentialDistribution(time = 130, piecewiseLambda = 0.01, kappa = 4.2) and pweibull(q = 130, shape = 4.2, scale = 1 / 0.01) provide the same result.
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.
doseLevels: The dose levels for the dose response relationship. If not specified, these dose levels are 1,...,activeArms.
eventTime: The assumed time under which the event rates are calculated, default is 12.
accrualTime: The assumed accrual time intervals for the study, default is c(0, 12) (for details see getAccrualTime()).
accrualIntensity: A numeric vector of accrual intensities, default is the relative intensity 0.1 (for details see getAccrualTime()).
accrualIntensityType: A character value specifying the accrual intensity input type. Must be one of "auto", "absolute", or "relative"; default is "auto", i.e., if all values are < 1 the type is "relative", otherwise it is "absolute".
dropoutRate1: The assumed drop-out rate in the treatment group, default is 0.
dropoutRate2: The assumed drop-out rate in the control group, default is 0.
dropoutTime: The assumed time for drop-out rates in the control and the treatment group, default is 12.
maxNumberOfSubjects: maxNumberOfSubjects > 0 needs to be specified. If accrual time and accrual intensity are specified, this will be calculated. Must be a positive integer of length 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".
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.
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".
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 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.
plannedEvents: plannedEvents is a numeric 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. 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.
minNumberOfEventsPerStage: When performing a data driven sample size recalculation, the numeric 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 numeric 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. Must be a 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.
calcEventsFunction: Optionally, a function can be entered that defines the way of performing the sample size recalculation. By default, event number recalculation is performed with conditional power and 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 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 (see 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.

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.

Details

At given design the function simulates the analysis times, power, stopping probabilities, expected sample size and events, and selection probabilities, at given number of subjects, events, parameter configuration, and treatment arm selection rule in the multi-arm survival design 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.

If simulationType = "patientWise", patient-wise survival data are simulated based on the specified accrual, event-time, and dropout assumptions. If simulationType = "patientWiseBasic", a simplified patient-wise survival approach is used. If simulationType = "testStatisticBased", normally distributed log-rank test statistics are simulated instead. The default simulationType = "auto" selects the simulation approach automatically based on the explicitly specified arguments and uses the legacy test-statistic-based approach for backward compatibility if no patient-wise-specific arguments are provided.

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).

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

if (FALSE) { # \dontrun{
# 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.
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 = 50, 
    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 = 50, 
     plannedEvents = c(75, 120))

y1$effectMatrix

y1$rejectAtLeastOne
y2$rejectAtLeastOne

y1$selectedArms
y2$selectedArms
} # }