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Log-Rank Test Simulation for PFS and OS Endpoints

Source: R/lrsim.R
lrsim2e.Rd

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

Usage

lrsim2e(
  kMax = 1,
  kMaxpfs = 1,
  hazardRatioH0pfs = 1,
  hazardRatioH0os = 1,
  allocation1 = 1,
  allocation2 = 1,
  accrualTime = 0,
  accrualIntensity = NA,
  piecewiseSurvivalTime = 0,
  stratumFraction = 1,
  rho_pd_os = 0,
  lambda1pfs = NA,
  lambda2pfs = NA,
  lambda1os = NA,
  lambda2os = NA,
  gamma1pfs = 0,
  gamma2pfs = 0,
  gamma1os = 0,
  gamma2os = 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.

hazardRatioH0pfs

Hazard ratio under the null hypothesis for the active treatment vs control for PFS. Defaults to 1 for superiority test.

hazardRatioH0os

Hazard ratio under the null hypothesis for the active treatment vs control for OS. Defaults to 1 for superiority test.

allocation1

Number of subjects in the 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 \([3, \infty)\).

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 (PD) 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 the treatment group and PFS.

lambda2pfs

A vector of hazard rates for the event in each analysis time interval by stratum for the control group and PFS.

lambda1os

A vector of hazard rates for the event in each analysis time interval by stratum for the treatment group and OS.

lambda2os

A vector of hazard rates for the event in each analysis time interval by stratum for the control group 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 the treatment group 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 the control group 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 the treatment group 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 the control group 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 and the planned cumulative total number of OS events at Look kMaxpfs+1 to Look kMax.

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 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.

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

    • 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 for the endpoint.

    • vscore: The variance of the log-rank test statistic for the endpoint.

    • logRankStatistic: The log-rank test Z-statistic 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 or 2) for the subject.

    • endpoint: The endpoint (1 for PFS or 2 for OS) under consideration for the row. Each subject will have two rows, one for each endpoint.

    • 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

Kaifeng Lu, kaifenglu@gmail.com

Examples


sim1 = lrsim2e(
  kMax = 3,
  kMaxpfs = 2,
  allocation1 = 2,
  allocation2 = 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,
  lambda1os = log(2)/30*0.65,
  lambda2os = log(2)/30,
  n = 420,
  plannedEvents = c(186, 259, 183),
  maxNumberOfIterations = 1000,
  maxNumberOfRawDatasetsPerStage = 1,
  seed = 314159,
  nthreads = 1)

head(sim1$sumdata)
#>   iterationNumber events1NotAchieved events2NotAchieved stageNumber
#> 1               1              FALSE              FALSE           1
#> 2               1              FALSE              FALSE           1
#> 3               1              FALSE              FALSE           2
#> 4               1              FALSE              FALSE           2
#> 5               1              FALSE              FALSE           3
#> 6               1              FALSE              FALSE           3
#>   analysisTime accruals1 accruals2 totalAccruals endpoint events1 events2
#> 1     27.70630       280       140           420      PFS     103      83
#> 2     27.70630       280       140           420       OS      51      49
#> 3     37.52269       280       140           420      PFS     151     108
#> 4     37.52269       280       140           420       OS      79      65
#> 5     47.22055       280       140           420      PFS     186     120
#> 6     47.22055       280       140           420       OS     106      77
#>   totalEvents dropouts1 dropouts2 totalDropouts    uscore   vscore
#> 1         186         0         0             0 -28.79721 38.19448
#> 2         100         0         0             0 -17.97413 21.35703
#> 3         259         0         0             0 -37.96130 50.38427
#> 4         144         0         0             0 -22.15222 29.94302
#> 5         306         0         0             0 -41.09552 57.62563
#> 6         183         0         0             0 -23.62725 37.66037
#>   logRankStatistic
#> 1        -4.659615
#> 2        -3.889354
#> 3        -5.348027
#> 4        -4.048271
#> 5        -5.413606
#> 6        -3.850090
head(sim1$rawdata)
#>   iterationNumber stageNumber analysisTime subjectId arrivalTime stratum
#> 1               1           1      27.7063         1  0.07129358       1
#> 2               1           1      27.7063         1  0.07129358       1
#> 3               1           1      27.7063         2  0.08504918       1
#> 4               1           1      27.7063         2  0.08504918       1
#> 5               1           1      27.7063         3  0.11887660       1
#> 6               1           1      27.7063         3  0.11887660       1
#>   treatmentGroup endpoint survivalTime dropoutTime timeUnderObservation event
#> 1              1      PFS    51.581804         Inf            27.635011 FALSE
#> 2              1       OS    52.812341         Inf            27.635011 FALSE
#> 3              1      PFS    81.221695         Inf            27.621255 FALSE
#> 4              1       OS   136.515641         Inf            27.621255 FALSE
#> 5              2      PFS     3.331084         Inf             3.331084  TRUE
#> 6              2       OS    18.301343         Inf            18.301343  TRUE
#>   dropoutEvent
#> 1        FALSE
#> 2        FALSE
#> 3        FALSE
#> 4        FALSE
#> 5        FALSE
#> 6        FALSE