lrsamplesize: Log-Rank Test Sample Size

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Log-Rank Test Sample Size

Description

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

Usage

lrsamplesize(
  beta = 0.2,
  kMax = 1L,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  futilityStopping = NA_integer_,
  criticalValues = NULL,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NULL,
  futilityCP = NULL,
  futilityHR = NULL,
  typeBetaSpending = "none",
  parameterBetaSpending = NA_real_,
  userBetaSpending = 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 = FALSE,
  rho1 = 0,
  rho2 = 0,
  typeOfComputation = "",
  spendingTime = NA_real_,
  rounding = TRUE
)

Arguments

beta	Type II error. Defaults to 0.2.
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(-8, kMax-1) if left unspecified. The futility bounds are non-binding for the calculation of critical values.
futilityCP	A vector of length kMax - 1 for the futility bounds on the conditional power scale.
futilityHR	A vector of length kMax - 1 for the futility bounds on the hazard ratio scale.
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.
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, \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.
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.
typeOfComputation	The type of computation, either "direct" for the direct approximation method, or "schoenfeld" for the Schoenfeld method. Defaults to empty, which selects the Schoenfeld method under proportional hazards and ordinary log-rank test and the direct method otherwise.
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 and events. Defaults to 1 for sample size rounding.

Value

A list of two components:

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

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

Author(s)

Kaifeng Lu, [e-mail]

See Also

lrpower

Examples

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

# Example 1: Obtains accrual duration given power and follow-up time

lrsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.8, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualTime = seq(0, 8),
             accrualIntensity = 26/9*seq(1, 9),
             piecewiseSurvivalTime = c(0, 6),
             lambda1 = c(0.0533, 0.0309),
             lambda2 = c(0.0533, 0.0533),
             gamma1 = -log(1-0.05)/12,
             gamma2 = -log(1-0.05)/12,
             accrualDuration = NA,
             followupTime = 18, fixedFollowup = FALSE)


# Example 2: Obtains follow-up time given power and accrual duration

lrsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.8, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualTime = seq(0, 8),
             accrualIntensity = 26/9*seq(1, 9),
             piecewiseSurvivalTime = c(0, 6),
             lambda1 = c(0.0533, 0.0309),
             lambda2 = c(0.0533, 0.0533),
             gamma1 = -log(1-0.05)/12,
             gamma2 = -log(1-0.05)/12,
             accrualDuration = 22,
             followupTime = NA, fixedFollowup = FALSE)


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

lrsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.8, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualTime = seq(0, 8),
             accrualIntensity = 26/9*seq(1, 9),
             piecewiseSurvivalTime = c(0, 6),
             lambda1 = c(0.0533, 0.0309),
             lambda2 = c(0.0533, 0.0533),
             gamma1 = -log(1-0.05)/12,
             gamma2 = -log(1-0.05)/12,
             accrualDuration = 22,
             followupTime = 18, fixedFollowup = FALSE)

lrstat documentation built on May 13, 2026, 9:06 a.m.