lrpower {lrstat}

Log-rank test power

Description

Estimates the power, stopping probabilities, and expected sample size in a two-group survival design.

Usage

lrpower(
  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_,
  hazardRatioH0 = 1,
  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,
  rho1 = 0,
  rho2 = 0,
  numSubintervals = 300L,
  estimateHazardRatio = 1L,
  typeOfComputation = "direct",
  spendingTime = NA_real_,
  studyDuration = NA_real_
)

Arguments

kMax

The maximum number of stages.

informationRates

The information rates in terms of number of events for the conventional log-rank test and in terms of the actual information for weighted log-rank tests. 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".

hazardRatioH0

Hazard ratio under the null hypothesis for the active treatment versus control. Defaults to 1 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.

rho1

The first parameter of the Fleming-Harrington family of weighted log-rank test. Defaults to 0 for conventional log-rank test.

rho2

The second parameter of the Fleming-Harrington family of weighted log-rank test. Defaults to 0 for conventional log-rank test.

numSubintervals

Number of sub-intervals to approximate the mean and variance of the weighted log-rank test score statistic. Defaults to 300. Specify a larger number for better approximation.

estimateHazardRatio

Whether to estimate the hazard ratio from weighted Cox regression model and report the stopping boundaries on the hazard ratio scale.

typeOfComputation

The type of computation, either "direct" for the direct approximation method, or "schoenfeld" for the Schoenfeld method. Defaults to "direct". Can use "Schoenfeld" under proportional hazards and conventional log-rank test.

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 lrpower 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.

  • numberOfDropouts: The total number of dropouts.

  • numbeOfSubjects: The total number of subjects.

  • studyDuration: The total study duration.

  • information: The maximum information.

  • expectedNumberOfEvents: The expected number of events.

  • expectedNumberOfDropouts: The expected number of dropouts.

  • expectedNumberOfSubjects: The expected number of subjects.

  • expectedStudyDuration: The expected study duration.

  • expectedInformation: The expected information.

  • accrualDuration: The accrual duration.

  • followupTime: The follow-up time.

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

  • rho1: The first parameter of the Fleming-Harrington family of weighted log-rank test.

  • rho2: The second parameter of the Fleming-Harrington family of weighted log-rank test.

  • kMax: The number of stages.

  • hazardRatioH0: The hazard ratio under the null hypothesis.

  • typeOfComputation: The type of computation, either "direct" for the direct approximation method, or "schoenfeld" for the Schoenfeld method.

• 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.

  • analysisTime: The average time since trial start.

  • efficacyHR: The efficacy boundaries on the hazard ratio scale if estimateHazardRatio.

  • futilityHR: The futility boundaries on the hazard ratio scale if estimateHazardRatio.

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

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

  • information: The cumulative information.

  • HR: The average hazard ratio.

  • 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, estimateHazardRatio, 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.

  • 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.

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

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

  • expectedNumberOfSubjects1: The expected number of subjects for the 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.

Author(s)

Kaifeng Lu, [e-mail]

Examples

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

lrpower(kMax = 2, informationRates = c(0.8, 1),
        alpha = 0.025, typeAlphaSpending = "sfOF",
        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)