kmsamplesize {lrstat}

Sample size for difference in milestone survival probabilities

Description

Obtains the needed accrual duration given power, accrual intensity, and follow-up time, the needed follow-up time given power, accrual intensity, and accrual duration, or the needed absolute accrual intensity given power, relative accrual intensity, accrual duration, and follow-up time in a two-group survival design.

Usage

kmsamplesize(
  beta = 0.2,
  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_,
  userBetaSpending = 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,
  interval = as.numeric(c(0.001, 240)),
  spendingTime = NA_real_,
  rounding = 1L
)

Arguments

beta

Type II error. Defaults to 0.2.

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, "user" for user defined spending, 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".

userBetaSpending

The user defined beta spending. Cumulative beta spent up to each stage.

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.

interval

The interval to search for the solution of accrualDuration, followupTime, or the proportionality constant of accrualIntensity. Defaults to c(0.001, 240).

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.

rounding

Whether to round up sample size. Defaults to 1 for sample size rounding.

Value

A list of two components:

• resultsUnderH1: An S3 class kmpower object under the alternative hypothesis.

• resultsUnderH0: An S3 class kmpower object under the null hypothesis.

Author(s)

Kaifeng Lu, [e-mail]

See Also

kmpower

Examples

# Example 1: Obtains follow-up time given power, accrual intensity,
# and accrual duration for variable follow-up. Of note, the power
# reaches the maximum when the follow-up time equals milestone.

kmsamplesize(beta = 0.25, 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 = NA, fixedFollowup = FALSE)

# Example 2: Obtains accrual intensity given power, accrual duration, and
# follow-up time for variable follow-up

kmsamplesize(beta = 0.2, 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)


# Example 3: Obtains accrual duration given power, accrual intensity, and
# follow-up time for fixed follow-up

kmsamplesize(beta = 0.2, 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 = NA,
             followupTime = 18, fixedFollowup = TRUE)