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Log-Rank Test Simulation for Phase 2/3 Seamless Design

Source: R/lrsim_seamless.R
lrsim_seamless.Rd

Simulate phase 2/3 seamless 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_seamless(
  M = 2,
  K = 1,
  criticalValues = NA,
  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 in Phase 2.

K

Number of sequential looks in Phase 3.

criticalValues

Numeric vector of length \(K + 1\) giving the critical value for the Wald statistic at each look (Look 1 through Look \(K + 1\)). 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.

  • If the Look 1 stopping rule is not met, select the active arm with the largest Wald statistic as the "best" arm and continue with that arm only versus control at subsequent looks.

  • For each look \(j = 2,\ldots,K+1\), compare the selected arm to control; if its Wald statistic exceeds the Look \(j\) critical value, stop for efficacy; otherwise continue.

  • If no critical value is exceeded by Look \(K + 1\), the procedure ends without rejection.

futilityBounds

Numeric vector of length \(K\) giving the futility boundaries for Phase 2 and the first \(K-1\) looks in Phase 3. The study stops for futility:

  • in Phase 2 if all active treatment arms cross the phase-2 futility boundary;

  • in Phase 3 if the selected arm crosses the futility boundary at an interim look; 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:

    • selectAsBest: Probability of selecting each active arm as the best arm at the end of phase 2.

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

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

    • cumulativeRejection: Cumulative probability of rejection by stage.

    • cumulativeFutility: Cumulative futility stopping probabilities by stage.

    • numberOfEvents: Cumulative event counts by stage, including events from all arms in stage 1 and events from the selected arm and control in later stages.

    • numberOfDropouts: Cumulative dropouts by stage.

    • numberOfSubjects: Cumulative enrollments by stage.

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

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

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

    • 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 critical values for each stage.

    • futilityBounds: The input futility boundaries for each stage.

    • 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, bestArm, 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

Kaifeng Lu, kaifenglu@gmail.com

Examples

(sim1 <- lrsim_seamless(
  M = 2,
  K = 2,
  criticalValues = c(3.882, 2.733, 2.222),
  futilityBounds = c(0.259, 1.201),
  accrualTime = c(0, 8),
  accrualIntensity = c(10, 28),
  piecewiseSurvivalTime = 0,
  lambdas = list(log(2)/12*0.5, log(2)/12*0.7, log(2)/12),
  n = 700,
  plannedEvents = c(42, 84, 126),
  maxNumberOfIterations = 10000,
  maxNumberOfRawDatasetsPerStage = 1,
  seed = 314159,
  nthreads = 0))
#>                                                              
#> Phase 2/3 seamless group-sequential design for log-rank test 
#> Empirical power: 0.8969                                      
#> Number of active arms in phase 2: 2                          
#> Number of looks in phase 3: 2                                
#> Expected # events: 117.2                                     
#> Expected # dropouts: 0                                       
#> Expected # subjects: 417                                     
#> Expected study duration: 22.2                                
#> n: 700, fixed follow-up: FALSE                               
#> Number of simulations: 10000                                 
#>                                                              
#>                           Stage 1 Stage 2 Stage 3
#> Efficacy bounds (z-scale) 3.882   2.733   2.222  
#> Futility bounds (z-scale) 0.259   1.201   2.222  
#> 
#>                              Arm 1  Arm 2
#> Selected as best in phase 2 0.8277 0.1723
#> 
#>         Reject Active 1 Reject Active 2 Overall Rejection Futility Continue
#> Stage 1          0.0391          0.0025            0.0406   0.0120   0.9474
#> Stage 2          0.5396          0.0495            0.5891   0.0297   0.3286
#> Stage 3          0.2092          0.0580            0.2672   0.0614   0.0000
#> Total            0.7879          0.1100            0.8969   0.1031       NA
#> 
#>  activeArm stage cumReject cumFutility nEvents nDropouts nSubjects analysisTime
#>          1     1    0.0391      0.0120    63.3       0.0     298.5         15.8
#>          1     2    0.5787      0.0220   105.3       0.0     398.3         21.2
#>          1     3    0.7879      0.0448   147.8       0.0     477.6         25.4
#>          2     1    0.0025      0.0120    56.6       0.0     278.9         15.1
#>          2     2    0.0520      0.0317   104.4       0.0     383.3         20.7
#>          2     3    0.1100      0.0703   152.7       0.0     467.2         25.2
#>    Overall     1    0.0406      0.0120    62.1       0.0     295.1         15.7
#>    Overall     2    0.6297      0.0417   105.1       0.0     395.7         21.1
#>    Overall     3    0.8969      0.1031   149.2       0.0     474.5         25.3