R: Log-rank test simulation

lrsim {lrstat}

R Documentation

Log-rank test simulation

Description

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

Usage

lrsim(
  kMax = NA_integer_,
  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. Defaults to 1.
`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, kaifenglu@gmail.com

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)

[Package lrstat version 0.2.6 Index]