kmpower: Power for Difference in Milestone Survival Probabilities

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Power for Difference in Milestone Survival Probabilities

Description

Estimates the power for testing the difference in milestone survival probabilities in a two-sample survival design.

Usage

kmpower(
  kMax = 1L,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  futilityStopping = NA_integer_,
  criticalValues = NA_real_,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NA_real_,
  typeBetaSpending = "none",
  parameterBetaSpending = NA_real_,
  milestone = NA_real_,
  survDiffH0 = 0,
  allocationRatioPlanned = 1,
  accrualTime = 0L,
  accrualIntensity = NA_real_,
  piecewiseSurvivalTime = 0L,
  stratumFraction = 1L,
  lambda1 = NA_real_,
  lambda2 = NA_real_,
  gamma1 = 0L,
  gamma2 = 0L,
  accrualDuration = NA_real_,
  followupTime = NA_real_,
  fixedFollowup = 0L,
  spendingTime = NA_real_,
  studyDuration = NA_real_
)

Arguments

kMax	The maximum number of stages.
informationRates	The information rates. Defaults to (1:kMax) / kMax if left unspecified.
efficacyStopping	Indicators of whether efficacy stopping is allowed at each stage. Defaults to true if left unspecified.
futilityStopping	Indicators of whether futility stopping is allowed at each stage. Defaults to true if left unspecified.
criticalValues	Upper boundaries on the z-test statistic scale for stopping for efficacy.
alpha	The significance level. Defaults to 0.025.
typeAlphaSpending	The type of alpha spending. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early efficacy stopping. Defaults to "sfOF".
parameterAlphaSpending	The parameter value for the alpha spending. Corresponds to Delta for "WT", rho for "sfKD", and gamma for "sfHSD".
userAlphaSpending	The user defined alpha spending. Cumulative alpha spent up to each stage.
futilityBounds	Lower boundaries on the z-test statistic scale for stopping for futility at stages 1, ..., kMax-1. Defaults to rep(-6, kMax-1) if left unspecified. The futility bounds are non-binding for the calculation of critical values.
typeBetaSpending	The type of beta spending. One of the following: "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, and "none" for no early futility stopping. Defaults to "none".
parameterBetaSpending	The parameter value for the beta spending. Corresponds to rho for "sfKD", and gamma for "sfHSD".
milestone	The milestone time at which to calculate the survival probability.
survDiffH0	The difference in milestone survival probabilities under the null hypothesis. Defaults to 0 for superiority test.
allocationRatioPlanned	Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization.
accrualTime	A vector that specifies the starting time of piecewise Poisson enrollment time intervals. Must start with 0, e.g., c(0, 3) breaks the time axis into 2 accrual intervals: [0, 3) and [3, Inf).
accrualIntensity	A vector of accrual intensities. One for each accrual time interval.
piecewiseSurvivalTime	A vector that specifies the starting time of piecewise exponential survival time intervals. Must start with 0, e.g., c(0, 6) breaks the time axis into 2 event intervals: [0, 6) and [6, Inf). Defaults to 0 for exponential distribution.
stratumFraction	A vector of stratum fractions that sum to 1. Defaults to 1 for no stratification.
lambda1	A vector of hazard rates for the event in each analysis time interval by stratum for the active treatment group.
lambda2	A vector of hazard rates for the event in each analysis time interval by stratum for the control group.
gamma1	The hazard rate for exponential dropout, a vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for the active treatment group.
gamma2	The hazard rate for exponential dropout, a vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for the control group.
accrualDuration	Duration of the enrollment period.
followupTime	Follow-up time for the last enrolled subject.
fixedFollowup	Whether a fixed follow-up design is used. Defaults to 0 for variable follow-up.
spendingTime	A vector of length kMax for the error spending time at each analysis. Defaults to missing, in which case, it is the same as informationRates.
studyDuration	Study duration for fixed follow-up design. Defaults to missing, which is to be replaced with the sum of accrualDuration and followupTime. If provided, the value is allowed to be less than the sum of accrualDuration and followupTime.

Value

An S3 class kmpower object with 4 components:

• overallResults: A data frame containing the following variables:

  • overallReject: The overall rejection probability.

  • alpha: The overall significance level.

  • numberOfEvents: The total number of events.

  • numbeOfSubjects: The total number of subjects.

  • studyDuration: The total study duration.

  • information: The maximum information.

  • expectedNumberOfEvents: The expected number of events.

  • expectedNumberOfSubjects: The expected number of subjects.

  • expectedStudyDuration: The expected study duration.

  • expectedInformation: The expected information.

  • accrualDuration: The accrual duration.

  • followupTime: The follow-up duration.

  • fixedFollowup: Whether a fixed follow-up design is used.

  • kMax: The number of stages.

  • milestone: The milestone time relative to randomization.

  • survDiffH0: The difference in milestone survival probabilities under the null hypothesis.

  • surv1: The milestone survival probability for the treatment group.

  • surv2: The milestone survival probability for the control group.

  • survDiff: The difference in milestone survival probabilities, equal to surv1 - surv2.

• byStageResults: A data frame containing the following variables:

  • informationRates: The information rates.

  • efficacyBounds: The efficacy boundaries on the Z-scale.

  • futilityBounds: The futility boundaries on the Z-scale.

  • rejectPerStage: The probability for efficacy stopping.

  • futilityPerStage: The probability for futility stopping.

  • cumulativeRejection: The cumulative probability for efficacy stopping.

  • cumulativeFutility: The cumulative probability for futility stopping.

  • cumulativeAlphaSpent: The cumulative alpha spent.

  • numberOfEvents: The number of events.

  • numberOfDropouts: The number of dropouts.

  • numberOfSubjects: The number of subjects.

  • numberOfMilestone: The number of subjects reaching milestone.

  • analysisTime: The average time since trial start.

  • efficacySurvDiff: The efficacy boundaries on the survival difference scale.

  • futilitySurvDiff: The futility boundaries on the survival difference scale.

  • efficacyP: The efficacy boundaries on the p-value scale.

  • futilityP: The futility boundaries on the p-value scale.

  • information: The cumulative information.

  • efficacyStopping: Whether to allow efficacy stopping.

  • futilityStopping: Whether to allow futility stopping.

• settings: A list containing the following input parameters: typeAlphaSpending, parameterAlphaSpending, userAlphaSpending, typeBetaSpending, parameterBetaSpending, allocationRatioPlanned, accrualTime, accuralIntensity, piecewiseSurvivalTime, stratumFraction, lambda1, lambda2, gamma1, gamma2, and spendingTime.

• byTreatmentCounts: A list containing the following counts by treatment group:

  • numberOfEvents1: The number of events by stage for the treatment group.

  • numberOfDropouts1: The number of dropouts by stage for the treatment group.

  • numberOfSubjects1: The number of subjects by stage for the treatment group.

  • numberOfMilestone1: The number of subjects reaching milestone by stage for the active treatment group.

  • numberOfEvents2: The number of events by stage for the control group.

  • numberOfDropouts2: The number of dropouts by stage for the control group.

  • numberOfSubjects2: The number of subjects by stage for the control group.

  • numberOfMilestone2: The number of subjects reaching milestone by stage for the control group.

  • expectedNumberOfEvents1: The expected number of events for the treatment group.

  • expectedNumberOfDropouts1: The expected number of dropouts for the active treatment group.

  • expectedNumberOfSubjects1: The expected number of subjects for the active treatment group.

  • expectedNumberOfMilestone1: The expected number of subjects reaching milestone for the active treatment group.

  • expectedNumberOfEvents2: The expected number of events for control group.

  • expectedNumberOfDropouts2: The expected number of dropouts for the control group.

  • expectedNumberOfSubjects2: The expected number of subjects for the control group.

  • expectedNumberOfMilestone2: The expected number of subjects reaching milestone for the control group.

Author(s)

Kaifeng Lu, [e-mail]

Examples

# Piecewise accrual, piecewise exponential survival, and 5% dropout by
# the end of 1 year.

kmpower(kMax = 2, informationRates = c(0.8, 1),
        alpha = 0.025, typeAlphaSpending = "sfOF",
        milestone = 18,
        allocationRatioPlanned = 1, accrualTime = seq(0, 8),
        accrualIntensity = 26/9*seq(1, 9),
        piecewiseSurvivalTime = c(0, 6),
        stratumFraction = c(0.2, 0.8),
        lambda1 = c(0.0533, 0.0309, 1.5*0.0533, 1.5*0.0309),
        lambda2 = c(0.0533, 0.0533, 1.5*0.0533, 1.5*0.0533),
        gamma1 = -log(1-0.05)/12,
        gamma2 = -log(1-0.05)/12, accrualDuration = 22,
        followupTime = 18, fixedFollowup = FALSE)

lrstat documentation built on Aug. 8, 2025, 7:36 p.m.