lrsim_mams: Log-Rank Test Simulation for Multi-Arm Multi-Stage Design

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

Log-Rank Test Simulation for Multi-Arm Multi-Stage Design

Description

Simulate a multi-arm multi-stage design using a weighted log-rank test. Analyses can be triggered either by the cumulative number of events (combined for an active arm and the common control) or by pre-specified calendar times.

Usage

lrsim_mams(
  M = 2,
  kMax = 1,
  criticalValues = NULL,
  futilityBounds = NULL,
  hazardRatioH0s = 1,
  allocations = 1,
  accrualTime = 0,
  accrualIntensity = NA,
  piecewiseSurvivalTime = 0,
  stratumFraction = 1,
  lambdas = NULL,
  gammas = NULL,
  n = NA,
  followupTime = NA,
  fixedFollowup = FALSE,
  rho1 = 0,
  rho2 = 0,
  plannedEvents = NA,
  plannedTime = NA,
  maxNumberOfIterations = 1000,
  maxNumberOfRawDatasetsPerStage = 0,
  seed = 0,
  nthreads = 0
)

Arguments

M	Number of active treatment arms.
kMax	Number of sequential looks.
criticalValues	The matrix of by-level upper boundaries on the max z-test statistic scale for efficacy stopping. The first column is for level M, the second column is for level M - 1, and so on, with the last column for level 1. Decision rule: At Look 1, compute the Wald statistic for each active arm versus the common control. If the maximum of these statistics exceeds the Look 1 critical value, stop for efficacy and check whether there is any other active arm which can be rejected using a relaxed boundary under the closed testing principle. If the Look 1 stopping rule is not met, continue to the next look; if the maximum of Wald statistics at this look exceeds the corresponding level M critical value, stop for efficacy; otherwise continue. If no critical value is exceeded by Look kMax, the procedure ends without rejection.
futilityBounds	Numeric vector of length kMax - 1 giving the futility boundaries on the max-Z scale for the first kMax - 1 analyses. At an interim look, the study stops for futility if all active treatment arms cross the futility boundary. At the final look, the study is counted as stopping for futility if none of the active treatment arms can be rejected. If omitted, no interim futility stopping is applied.
hazardRatioH0s	Numeric vector of length M. Hazard ratios under H_0 for each active arm versus the common control. Defaults to 1 for superiority tests.
allocations	Integer or integer vector of length M + 1. Number of subjects per arm within a randomization block. A single value implies equal allocation; defaults to 1.
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.
lambdas	List of length M (one element per arm). Each element is a scalar or a numeric vector of event hazard rates for the corresponding arm, given by analysis interval and stratum as required by the simulation.
gammas	List of length M (one element per arm). Each element is a scalar or a numeric vector of dropout hazard rates for the corresponding arm, by analysis interval and stratum.
n	Planned total sample size across all active arms and control.
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.
plannedEvents	Numeric vector of length K + 1 giving the planned cumulative number of events to trigger Look 1 through Look K + 1. Each entry refers to the combined events for the first active arm and the common control. Use plannedEvents to schedule event-driven looks.
plannedTime	Numeric vector of calendar times for the analyses. If plannedTime is supplied, analyses are scheduled by calendar time and plannedEvents should be left missing.
maxNumberOfIterations	Number of Monte Carlo replications. Defaults to 1000.
maxNumberOfRawDatasetsPerStage	Number of subject-level raw datasets to retain per stage (for selected replications).
seed	Random seed for reproducibility.
nthreads	Number of threads for parallel simulation. Use 0 to accept the default RcppParallel behavior.

Value

An S3 object of class "lrsim_seamless" with these components:

• overview: A list summarizing trial-level results and settings:

  • overallReject: Overall probability of rejecting the null by trial end.

  • overallFutility: Overall probability of stopping for futility by trial end.

  • rejectPerStage: Probability of rejecting the null for each active arm at each stage.

  • futilityPerStage: Probability of futility stopping for each arm at each stage.

  • cumulativeRejection: Cumulative probability of rejection for each active arm by stage.

  • cumulativeFutility: Cumulative probability of futility stopping for each active arm by stage.

  • numberOfEvents: Cumulative event counts by stage and arm.

  • numberOfDropouts: Cumulative dropouts by stage and arm.

  • numberOfSubjects: Cumulative enrollments by stage and arm.

  • analysisTime: Average calendar time for each stage by arm among replications that reached that stage.

  • expectedNumberOfEvents: Expected cumulative events at trial end.

  • expectedNumberOfDropouts: Expected cumulative dropouts at trial end.

  • expectedNumberOfSubjects: Expected cumulative enrollments at trial end.

  • expectedStudyDuration: Expected study duration.

  • criticalValues: The input matrix of by-level critical boundaries.

  • futilityBounds: The input vector of futility boundaries.

  • hazardRatioH0s: The input hazard ratios under H_0.

  • useEvents: Logical indicating whether analyses were event-driven.

  • numberOfIterations: Number of simulation iterations performed.

  • n: Planned total sample size.

  • fixedFollowup: Logical indicating whether fixed follow-up was used.

  • rho1, rho2: Fleming–Harrington weighting parameters used.

  • M: Number of active arms in Phase 2.

  • K: Number of sequential looks in Phase 3.

• sumdata1: Data frame summarizing each iteration, stage, and treatment group:

  • iterationNumber, eventsNotAchieved, stopStage, stageNumber, analysisTime, treatmentGroup, accruals, events, dropouts.

  • For each stage the final row summarizes the overall study (all arms combined).

• summdata2: Data frame summarizing log-rank statistics by iteration, stage, and active arm:

  • iterationNumber, stopStage, stageNumber, analysisTime, activeArm, totalAccruals, totalEvents, totalDropouts, uscore, vscore, logRankStatistic, reject, futility.

  • For each active arm, total accruals, events, and dropouts refer to the combined counts for that arm and the common control at that stage.

• rawdata (present when maxNumberOfRawDatasetsPerStage > 0): Subject-level data for selected replications with variables:

  • iterationNumber, stopStage, stageNumber, analysisTime, subjectId, arrivalTime, stratum, treatmentGroup, survivalTime, dropoutTime, timeUnderObservation, event, dropoutEvent.

Author(s)

Kaifeng Lu, [e-mail]

Examples

(sim1 <- lrsim_mams(
  M = 2,
  kMax = 3,
  criticalValues = matrix(c(3.880, 2.747, 2.275,
                            3.710, 2.511, 1.993), 3, 2),
  futilityBounds = c(0.074, 1.207),
  accrualTime = c(0, 8),
  accrualIntensity = c(10, 28),
  piecewiseSurvivalTime = 0,
  lambdas = list(log(2)/12*0.5, log(2)/12*0.75, log(2)/12),
  n = 700,
  plannedEvents = c(36, 72, 108),
  maxNumberOfIterations = 10000,
  maxNumberOfRawDatasetsPerStage = 1,
  seed = 314159,
  nthreads = 0))

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