lrsim2e3a: Log-Rank Test Simulation for Two Endpoints (PFS and OS) and...

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

Log-Rank Test Simulation for Two Endpoints (PFS and OS) and Three Arms

Description

Performs simulation for two-endpoint (PFS and OS) three-arm group sequential trials based on weighted log-rank test. The first kMaxpfs looks are driven by the total number of PFS events in Arm A and Arm C combined, and the subsequent looks are driven by the total number of OS events in Arm A and Arm C combined. Alternatively, the analyses can be planned to occur at specified calendar times.

Usage

lrsim2e3a(
  kMax = 1,
  kMaxpfs = 1,
  hazardRatioH013pfs = 1,
  hazardRatioH023pfs = 1,
  hazardRatioH012pfs = 1,
  hazardRatioH013os = 1,
  hazardRatioH023os = 1,
  hazardRatioH012os = 1,
  allocation1 = 1,
  allocation2 = 1,
  allocation3 = 1,
  accrualTime = 0,
  accrualIntensity = NA,
  piecewiseSurvivalTime = 0,
  stratumFraction = 1,
  rho_pd_os = 0,
  lambda1pfs = NA,
  lambda2pfs = NA,
  lambda3pfs = NA,
  lambda1os = NA,
  lambda2os = NA,
  lambda3os = NA,
  gamma1pfs = 0,
  gamma2pfs = 0,
  gamma3pfs = 0,
  gamma1os = 0,
  gamma2os = 0,
  gamma3os = 0,
  n = NA,
  followupTime = NA,
  fixedFollowup = FALSE,
  rho1 = 0,
  rho2 = 0,
  plannedEvents = NA,
  plannedTime = NA,
  maxNumberOfIterations = 1000,
  maxNumberOfRawDatasetsPerStage = 0,
  seed = 0,
  nthreads = 0
)

Arguments

kMax	The maximum number of stages.
kMaxpfs	Number of stages with timing determined by PFS events. Ranges from 0 (none) to kMax.
hazardRatioH013pfs	Hazard ratio under the null hypothesis for arm 1 vs arm 3 for PFS. Defaults to 1 for superiority test.
hazardRatioH023pfs	Hazard ratio under the null hypothesis for arm 2 vs arm 3 for PFS. Defaults to 1 for superiority test.
hazardRatioH012pfs	Hazard ratio under the null hypothesis for arm 1 vs arm 2 for PFS. Defaults to 1 for superiority test.
hazardRatioH013os	Hazard ratio under the null hypothesis for arm 1 vs arm 3 for OS. Defaults to 1 for superiority test.
hazardRatioH023os	Hazard ratio under the null hypothesis for arm 2 vs arm 3 for OS. Defaults to 1 for superiority test.
hazardRatioH012os	Hazard ratio under the null hypothesis for arm 1 vs arm 2 for OS. Defaults to 1 for superiority test.
allocation1	Number of subjects in Arm A in a randomization block. Defaults to 1 for equal randomization.
allocation2	Number of subjects in Arm B in a randomization block. Defaults to 1 for equal randomization.
allocation3	Number of subjects in Arm C 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, \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.
rho_pd_os	The correlation coefficient for the standard bivariate normal random variables used to generate time to disease progression and time to death using the inverse CDF method.
lambda1pfs	A vector of hazard rates for the event in each analysis time interval by stratum for arm 1 and PFS.
lambda2pfs	A vector of hazard rates for the event in each analysis time interval by stratum for arm 2 and PFS.
lambda3pfs	A vector of hazard rates for the event in each analysis time interval by stratum for arm 3 and PFS.
lambda1os	A vector of hazard rates for the event in each analysis time interval by stratum for arm 1 and OS.
lambda2os	A vector of hazard rates for the event in each analysis time interval by stratum for arm 2 and OS.
lambda3os	A vector of hazard rates for the event in each analysis time interval by stratum for arm 3 and OS.
gamma1pfs	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 arm 1 and PFS.
gamma2pfs	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 arm 2 and PFS.
gamma3pfs	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 arm 3 and PFS.
gamma1os	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 arm 1 and OS.
gamma2os	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 arm 2 and OS.
gamma3os	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 arm 3 and OS.
n	Sample size.
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	The planned cumulative total number of PFS events at Look 1 to Look kMaxpfs for Arms A and C combined and the planned cumulative total number of OS events at Look kMaxpfs+1 to Look kMax for Arms A and C combined.
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.
nthreads	The number of threads to use in simulations (0 means the default RcppParallel behavior).

Value

A list with 2 components:

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

  • iterationNumber: The iteration number.

  • 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 active treatment 1 group.

  • accruals2: The number of subjects enrolled at the stage for the active treatment 2 group.

  • accruals3: The number of subjects enrolled at the stage for the control group.

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

  • endpoint: The endpoint (1 for PFS or 2 for OS) under consideration.

  • events1: The number of events at the stage for the active treatment 1 group.

  • events2: The number of events at the stage for the active treatment 2 group.

  • events3: 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 active treatment 1 group.

  • dropouts2: The number of dropouts at the stage for the active treatment 2 group.

  • dropouts3: The number of dropouts at the stage for the control group.

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

  • logRankStatistic13: The log-rank test Z-statistic comparing the active treatment 1 to the control for the endpoint.

  • logRankStatistic23: The log-rank test Z-statistic comparing the active treatment 2 to the control for the endpoint.

  • logRankStatistic12: The log-rank test Z-statistic comparing the active treatment 1 to the active treatment 2 for the endpoint.

• 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.

  • stageNumber: The stage under consideration.

  • 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, 2, or 3) for the subject.

  • endpoint: The endpoint (1 for PFS or 2 for OS) under consideration.

  • survivalTime: The underlying survival time for the event endpoint for the subject.

  • dropoutTime: The underlying dropout time for the event endpoint for the subject.

  • timeUnderObservation: The time under observation since randomization for the event endpoint for the subject.

  • event: Whether the subject experienced the event endpoint.

  • dropoutEvent: Whether the subject dropped out for the endpoint.

Author(s)

Kaifeng Lu, [e-mail]

Examples

sim1 <- lrsim2e3a(
  kMax = 3,
  kMaxpfs = 2,
  allocation1 = 2,
  allocation2 = 2,
  allocation3 = 1,
  accrualTime = c(0, 8),
  accrualIntensity = c(10, 28),
  piecewiseSurvivalTime = 0,
  rho_pd_os = 0,
  lambda1pfs = log(2)/12*0.60,
  lambda2pfs = log(2)/12*0.70,
  lambda3pfs = log(2)/12,
  lambda1os = log(2)/30*0.65,
  lambda2os = log(2)/30*0.75,
  lambda3os = log(2)/30,
  n = 700,
  plannedEvents = c(186, 259, 183),
  maxNumberOfIterations = 1000,
  maxNumberOfRawDatasetsPerStage = 1,
  seed = 314159,
  nthreads = 1)

head(sim1$sumdata)
head(sim1$rawdata)

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