lrsim: Log-Rank Test Simulation

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

Log-Rank Test Simulation

Description

Performs simulation for two-arm group sequential trials based on weighted log-rank test.

Usage

lrsim(
  kMax = 1L,
  informationRates = NA_real_,
  criticalValues = NA_real_,
  futilityBounds = NA_real_,
  hazardRatioH0 = 1,
  allocation1 = 1L,
  allocation2 = 1L,
  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,
  plannedEvents = NA_integer_,
  plannedTime = NA_real_,
  maxNumberOfIterations = 1000L,
  maxNumberOfRawDatasetsPerStage = 0L,
  seed = NA_integer_
)

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. Fixed prior to the trial. If left unspecified, it defaults to plannedEvents / plannedEvents[kMax] when plannedEvents is provided and to plannedTime / plannedTime[kMax] otherwise.
criticalValues	Upper boundaries on the z-test statistic scale for stopping for efficacy.
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.
hazardRatioH0	Hazard ratio under the null hypothesis for the active treatment versus control. Defaults to 1 for superiority test.
allocation1	Number of subjects in the active treatment group in a randomization block. Defaults to 1 for equal randomization.
allocation2	Number of subjects in the control group in a randomization block. 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.
plannedEvents	The planned cumulative total number of events at each stage.
plannedTime	The calendar times for the analyses. To use calendar time to plan the analyses, plannedEvents should be missing.
maxNumberOfIterations	The number of simulation iterations. Defaults to 1000.
maxNumberOfRawDatasetsPerStage	The number of raw datasets per stage to extract.
seed	The seed to reproduce the simulation results. The seed from the environment will be used if left unspecified.

Value

An S3 class lrsim object with 3 components:

• overview: A list containing the following information:

  • rejectPerStage: The efficacy stopping probability by stage.

  • futilityPerStage: The futility stopping probability by stage.

  • cumulativeRejection: Cumulative efficacy stopping probability by stage.

  • cumulativeFutility: The cumulative futility stopping probability by stage.

  • numberOfEvents: The average number of events by stage.

  • numberOfDropouts: The average number of dropouts by stage.

  • numberOfSubjects: The average number of subjects by stage.

  • analysisTime: The average analysis time by stage.

  • overallReject: The overall rejection probability.

  • expectedNumberOfEvents: The expected number of events for the overall study.

  • expectedNumberOfDropouts: The expected number of dropouts for the overall study.

  • expectedNumberOfSubjects: The expected number of subjects for the overall study.

  • expectedStudyDuration: The expected study duration.

  • hazardRatioH0: Hazard ratio under the null hypothesis for the active treatment versus control.

  • useEvents: whether the analyses are planned based on the number of events or calendar time.

  • accrualDuration: Duration of the enrollment period.

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

  • 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.

  • kMax: The maximum number of stages.

• sumdata: A data frame of summary data by iteration and stage:

  • iterationNumber: The iteration number.

  • stopStage: The stage at which the trial stops.

  • eventsNotAchieved: Whether the target number of events is not achieved for the iteration.

  • stageNumber: The stage number, covering all stages even if the trial stops at an interim look.

  • analysisTime: The time for the stage since trial start.

  • accruals1: The number of subjects enrolled at the stage for the treatment group.

  • accruals2: The number of subjects enrolled at the stage for the control group.

  • totalAccruals: The total number of subjects enrolled at the stage.

  • events1: The number of events at the stage for the treatment group.

  • events2: The number of events at the stage for the control group.

  • totalEvents: The total number of events at the stage.

  • dropouts1: The number of dropouts at the stage for the treatment group.

  • dropouts2: The number of dropouts at the stage for the control group.

  • totalDropouts: The total number of dropouts at the stage.

  • uscore: The numerator of the log-rank test statistic.

  • vscore: The variance of the log-rank test statistic.

  • logRankStatistic: The log-rank test Z-statistic.

  • rejectPerStage: Whether to reject the null hypothesis at the stage.

  • futilityPerStage: Whether to stop the trial for futility at the stage.

• rawdata (exists if maxNumberOfRawDatasetsPerStage is a positive integer): A data frame for subject-level data for selected replications, containing the following variables:

  • iterationNumber: The iteration number.

  • stopStage: The stage at which the trial stops.

  • analysisTime: The time for the stage since trial start.

  • subjectId: The subject ID.

  • arrivalTime: The enrollment time for the subject.

  • stratum: The stratum for the subject.

  • treatmentGroup: The treatment group (1 or 2) for the subject.

  • survivalTime: The underlying survival time for the subject.

  • dropoutTime: The underlying dropout time for the subject.

  • timeUnderObservation: The time under observation since randomization.

  • event: Whether the subject experienced the event.

  • dropoutEvent: Whether the subject dropped out.

Author(s)

Kaifeng Lu, [e-mail]

Examples

# Example 1: analyses based on number of events

sim1 = lrsim(kMax = 2, informationRates = c(0.5, 1),
             criticalValues = c(2.797, 1.977),
             accrualIntensity = 11,
             lambda1 = 0.018, lambda2 = 0.030,
             accrualDuration = 12,
             plannedEvents = c(60, 120),
             maxNumberOfIterations = 1000,
             maxNumberOfRawDatasetsPerStage = 1,
             seed = 314159)

# summary statistics
sim1

# summary for each simulated data set
head(sim1$sumdata)

# raw data for selected replication
head(sim1$rawdata)


# Example 2: analyses based on calendar time have similar power

sim2 = lrsim(kMax = 2, informationRates = c(0.5, 1),
             criticalValues = c(2.797, 1.977),
             accrualIntensity = 11,
             lambda1 = 0.018, lambda2 = 0.030,
             accrualDuration = 12,
             plannedTime = c(31.9, 113.2),
             maxNumberOfIterations = 1000,
             maxNumberOfRawDatasetsPerStage = 1,
             seed = 314159)

# summary statistics
sim2

# summary for each simulated data set
head(sim2$sumdata)

lrstat documentation built on Aug. 8, 2025, 7:36 p.m.