Estimates the power for testing the difference in milestone survival probabilities in a two-sample survival design.
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_
)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.
The maximum number of stages.
The information rates.
Defaults to (1:kMax) / kMax if left unspecified.
Indicators of whether efficacy stopping is allowed at each stage. Defaults to true if left unspecified.
Indicators of whether futility stopping is allowed at each stage. Defaults to true if left unspecified.
Upper boundaries on the z-test statistic scale for stopping for efficacy.
The significance level. Defaults to 0.025.
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".
The parameter value for the alpha spending. Corresponds to Delta for "WT", rho for "sfKD", and gamma for "sfHSD".
The user defined alpha spending. Cumulative alpha spent up to each stage.
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.
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".
The parameter value for the beta spending. Corresponds to rho for "sfKD", and gamma for "sfHSD".
The milestone time at which to calculate the survival probability.
The difference in milestone survival probabilities under the null hypothesis. Defaults to 0 for superiority test.
Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization.
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).
A vector of accrual intensities. One for each accrual time interval.
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.
A vector of stratum fractions that sum to 1. Defaults to 1 for no stratification.
A vector of hazard rates for the event in each analysis time interval by stratum for the active treatment group.
A vector of hazard rates for the event in each analysis time interval by stratum for the control group.
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.
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.
Duration of the enrollment period.
Follow-up time for the last enrolled subject.
Whether a fixed follow-up design is used. Defaults to 0 for variable follow-up.
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.
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.
Kaifeng Lu, kaifenglu@gmail.com
# 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)
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