R: Log-rank test simulation for two endpoints and three arms

lrsim2e3a {lrstat}

R Documentation

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. Defaults to 1.
`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, kaifenglu@gmail.com

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 = 1000,
  maxNumberOfRawDatasetsPerStage = 1,
  seed = 314159)

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

[Package lrstat version 0.2.6 Index]