R: Power for difference in milestone survival probabilities

kmpower {lrstat}

R Documentation

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 3 components:

overallResults: A data frame containing the following variables:
- overallReject: The overall rejection probability.
- alpha: The overall significance level.
- drift: The drift parameter, equal to (survDiff - survDiffH0)*sqrt(information).
- inflationFactor: The inflation factor (relative to the fixed design).
- numbeOfSubjects: The total number of subjects.
- studyDuration: The total study duration.
- information: The maximum information.
- 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.
- numberOfSubjects: The number of subjects.
- 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.

Author(s)

Kaifeng Lu, kaifenglu@gmail.com

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)

[Package lrstat version 0.2.9 Index]