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Power for Difference in Milestone Survival Probabilities

Source: R/RcppExports.R
kmpower.Rd

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 = FALSE,
  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 \([3, \infty)\).

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 \([6, \infty)\). 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 FALSE 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.

    • numberOfDropouts: The total number of dropouts.

    • numbeOfSubjects: The total number of subjects.

    • numberOfMilestone: The total number of subjects reaching milestone.

    • 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.

    • expectedNumberOfMilestone: The expected number of subjects reaching milestone.

    • 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

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)
#>                                                                            
#> Group-sequential design with 2 stages for difference in milestone survival 
#> Milestone: 18, survival difference under H0: 0                             
#> Milestone survival on treatment: 0.384, on control: 0.266                  
#> Overall power: 0.7634, overall significance level (1-sided): 0.025         
#> Maximum # events: 356.4, expected # events: 325.3                          
#> Maximum # subjects: 468, expected # subjects: 468                          
#> Maximum information: 527.17, expected information: 467.35                  
#> Total study duration: 40, expected study duration: 34.9                    
#> Accrual duration: 22, follow-up duration: 18, fixed follow-up: FALSE       
#> Allocation ratio: 1                                                        
#> Alpha spending: Lan-DeMets O'Brien-Fleming, beta spending: None            
#>                                                                            
#>                               Stage 1 Stage 2
#> Information rate              0.800   1.000  
#> Efficacy boundary (Z)         2.250   2.025  
#> Cumulative rejection          0.5674  0.7634 
#> Cumulative alpha spent        0.0122  0.0250 
#> Number of events              301.5   356.4  
#> Number of dropouts            19.8    24.2   
#> Number of subjects            468.0   468.0  
#> Number of milestone subjects  71.1    140.9  
#> Analysis time                 31.1    40.0   
#> Efficacy boundary (surv diff) 0.110   0.088  
#> Efficacy boundary (p)         0.0122  0.0214 
#> Information                   421.74  527.17