lrsim2e3a: Log-Rank Test Simulation for Two Endpoints and Three Arms

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

Log-Rank Test Simulation for Two Endpoints and Three Arms

Description

Performs simulation for two-endpoint three-arm group sequential trials based on weighted log-rank test. The first kMaxe1 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 = NA_integer_,
  kMaxe1 = NA_integer_,
  hazardRatioH013e1 = 1,
  hazardRatioH023e1 = 1,
  hazardRatioH012e1 = 1,
  hazardRatioH013e2 = 1,
  hazardRatioH023e2 = 1,
  hazardRatioH012e2 = 1,
  allocation1 = 1L,
  allocation2 = 1L,
  allocation3 = 1L,
  accrualTime = 0L,
  accrualIntensity = NA_real_,
  piecewiseSurvivalTime = 0L,
  stratumFraction = 1L,
  rho = 0,
  lambda1e1 = NA_real_,
  lambda2e1 = NA_real_,
  lambda3e1 = NA_real_,
  lambda1e2 = NA_real_,
  lambda2e2 = NA_real_,
  lambda3e2 = NA_real_,
  gamma1e1 = 0L,
  gamma2e1 = 0L,
  gamma3e1 = 0L,
  gamma1e2 = 0L,
  gamma2e2 = 0L,
  gamma3e2 = 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.
kMaxe1	Number of stages with timing determined by PFS events. Ranges from 0 (none) to kMax.
hazardRatioH013e1	Hazard ratio under the null hypothesis for arm 1 vs arm 3 for endpoint 1 (PFS). Defaults to 1 for superiority test.
hazardRatioH023e1	Hazard ratio under the null hypothesis for arm 2 vs arm 3 for endpoint 1 (PFS). Defaults to 1 for superiority test.
hazardRatioH012e1	Hazard ratio under the null hypothesis for arm 1 vs arm 2 for endpoint 1 (PFS). Defaults to 1 for superiority test.
hazardRatioH013e2	Hazard ratio under the null hypothesis for arm 1 vs arm 3 for endpoint 2 (OS). Defaults to 1 for superiority test.
hazardRatioH023e2	Hazard ratio under the null hypothesis for arm 2 vs arm 3 for endpoint 2 (OS). Defaults to 1 for superiority test.
hazardRatioH012e2	Hazard ratio under the null hypothesis for arm 1 vs arm 2 for endpoint 2 (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, 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.
rho	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.
lambda1e1	A vector of hazard rates for the event in each analysis time interval by stratum for arm 1 and endpoint 1 (PFS).
lambda2e1	A vector of hazard rates for the event in each analysis time interval by stratum for arm 2 and endpoint 1 (PFS).
lambda3e1	A vector of hazard rates for the event in each analysis time interval by stratum for arm 3 and endpoint 1 (PFS).
lambda1e2	A vector of hazard rates for the event in each analysis time interval by stratum for arm 1 and endpoint 2 (OS).
lambda2e2	A vector of hazard rates for the event in each analysis time interval by stratum for arm 2 and endpoint 2 (OS).
lambda3e2	A vector of hazard rates for the event in each analysis time interval by stratum for arm 3 and endpoint 2 (OS).
gamma1e1	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 endpoint 1 (PFS).
gamma2e1	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 endpoint 1 (PFS).
gamma3e1	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 endpoint 1 (PFS).
gamma1e2	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 endpoint 2 (OS).
gamma2e2	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 endpoint 2 (OS).
gamma3e2	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 endpoint 2 (OS).
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 PFS events at Look 1 to Look kMaxe1 for Arms A and C combined and the planned cumulative total number of OS events at Look kMaxe1+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. The seed from the environment will be used if left unspecified.

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 or 2) 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.

  • survivalTime1: The underlying survival time for event endpoint 1 for the subject.

  • dropoutTime1: The underlying dropout time for event endpoint 1 for the subject.

  • timeUnderObservation1: The time under observation since randomization for event endpoint 1 for the subject.

  • event1: Whether the subject experienced event endpoint 1.

  • dropoutEvent1: Whether the subject dropped out for endpoint 1.

  • survivalTime2: The underlying survival time for event endpoint 2 for the subject.

  • dropoutTime2: The underlying dropout time for event endpoint 2 for the subject.

  • timeUnderObservation2: The time under observation since randomization for event endpoint 2 for the subject.

  • event2: Whether the subject experienced event endpoint 2.

  • dropoutEvent2: Whether the subject dropped out for endpoint 2.

Author(s)

Kaifeng Lu, [e-mail]

Examples

sim1 = lrsim2e3a(
  kMax = 3,
  kMaxe1 = 2,
  allocation1 = 2,
  allocation2 = 2,
  allocation3 = 1,
  accrualTime = c(0, 8),
  accrualIntensity = c(10, 28),
  piecewiseSurvivalTime = 0,
  rho = 0,
  lambda1e1 = log(2)/12*0.60,
  lambda2e1 = log(2)/12*0.70,
  lambda3e1 = log(2)/12,
  lambda1e2 = log(2)/30*0.65,
  lambda2e2 = log(2)/30*0.75,
  lambda3e2 = log(2)/30,
  accrualDuration = 30.143,
  plannedEvents = c(186, 259, 183),
  maxNumberOfIterations = 500,
  maxNumberOfRawDatasetsPerStage = 1,
  seed = 314159)

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

lrstat documentation built on Oct. 18, 2024, 9:06 a.m.