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Log-Rank Test Simulation for Two Endpoints (PFS and OS) and Three Arms

Source: R/lrsim.R
lrsim2e3a.Rd

Performs simulation for two-endpoint (PFS and OS) three-arm group sequential trials based on weighted log-rank test. The first kMaxpfs 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 = 1,
  kMaxpfs = 1,
  hazardRatioH013pfs = 1,
  hazardRatioH023pfs = 1,
  hazardRatioH012pfs = 1,
  hazardRatioH013os = 1,
  hazardRatioH023os = 1,
  hazardRatioH012os = 1,
  allocation1 = 1,
  allocation2 = 1,
  allocation3 = 1,
  accrualTime = 0,
  accrualIntensity = NA,
  piecewiseSurvivalTime = 0,
  stratumFraction = 1,
  rho_pd_os = 0,
  lambda1pfs = NA,
  lambda2pfs = NA,
  lambda3pfs = NA,
  lambda1os = NA,
  lambda2os = NA,
  lambda3os = NA,
  gamma1pfs = 0,
  gamma2pfs = 0,
  gamma3pfs = 0,
  gamma1os = 0,
  gamma2os = 0,
  gamma3os = 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.

hazardRatioH013pfs

Hazard ratio under the null hypothesis for arm 1 vs arm 3 for PFS. Defaults to 1 for superiority test.

hazardRatioH023pfs

Hazard ratio under the null hypothesis for arm 2 vs arm 3 for PFS. Defaults to 1 for superiority test.

hazardRatioH012pfs

Hazard ratio under the null hypothesis for arm 1 vs arm 2 for PFS. Defaults to 1 for superiority test.

hazardRatioH013os

Hazard ratio under the null hypothesis for arm 1 vs arm 3 for OS. Defaults to 1 for superiority test.

hazardRatioH023os

Hazard ratio under the null hypothesis for arm 2 vs arm 3 for OS. Defaults to 1 for superiority test.

hazardRatioH012os

Hazard ratio under the null hypothesis for arm 1 vs arm 2 for 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 \([3, \infty)\).

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 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 arm 1 and PFS.

lambda2pfs

A vector of hazard rates for the event in each analysis time interval by stratum for arm 2 and PFS.

lambda3pfs

A vector of hazard rates for the event in each analysis time interval by stratum for arm 3 and PFS.

lambda1os

A vector of hazard rates for the event in each analysis time interval by stratum for arm 1 and OS.

lambda2os

A vector of hazard rates for the event in each analysis time interval by stratum for arm 2 and OS.

lambda3os

A vector of hazard rates for the event in each analysis time interval by stratum for arm 3 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 arm 1 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 arm 2 and PFS.

gamma3pfs

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 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 arm 1 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 arm 2 and OS.

gamma3os

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 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 for Arms A and C combined and the planned cumulative total number of OS events at Look kMaxpfs+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.

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 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 for PFS or 2 for OS) 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.

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

    • 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 = lrsim2e3a(
  kMax = 3,
  kMaxpfs = 2,
  allocation1 = 2,
  allocation2 = 2,
  allocation3 = 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*0.70,
  lambda3pfs = log(2)/12,
  lambda1os = log(2)/30*0.65,
  lambda2os = log(2)/30*0.75,
  lambda3os = log(2)/30,
  n = 700,
  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 accruals3 totalAccruals endpoint events1
#> 1     32.85250       280       280       140           700      PFS     111
#> 2     32.85250       280       280       140           700       OS      65
#> 3     42.89920       280       280       140           700      PFS     159
#> 4     42.89920       280       280       140           700       OS      96
#> 5     49.48199       280       280       140           700      PFS     177
#> 6     49.48199       280       280       140           700       OS     110
#>   events2 events3 totalEvents dropouts1 dropouts2 dropouts3 totalDropouts
#> 1     125      75         311         0         0         0             0
#> 2      69      40         174         0         0         0             0
#> 3     187     100         446         0         0         0             0
#> 4     111      63         270         0         0         0             0
#> 5     209     118         504         0         0         0             0
#> 6     132      73         315         0         0         0             0
#>     uscore13 vscore13 logRankStatistic13   uscore23 vscore23 logRankStatistic23
#> 1 -19.813095 38.66058          -3.186531 -12.844410 42.65135          -1.966744
#> 2  -6.266267 22.87605          -1.310142  -5.015437 23.66224          -1.031053
#> 3 -25.924031 52.54320          -3.576385 -12.152275 60.83790          -1.558011
#> 4 -12.775991 34.30227          -2.181389  -7.099940 37.91929          -1.152987
#> 5 -35.700291 58.91287          -4.651218 -18.753487 68.82455          -2.260530
#> 6 -15.938713 39.18408          -2.546235  -7.314897 44.61121          -1.095182
#>     uscore12 vscore12 logRankStatistic12
#> 1 -11.937995 58.62876          -1.559107
#> 2  -2.625340 33.49406          -0.453630
#> 3 -24.461124 85.58818          -2.644049
#> 4  -9.406536 51.68518          -1.308419
#> 5 -28.803833 95.43596          -2.948453
#> 6 -13.890340 60.39008          -1.787434
head(sim1$rawdata)
#>   iterationNumber stageNumber analysisTime subjectId arrivalTime stratum
#> 1               1           1      32.8525         1  0.07129358       1
#> 2               1           1      32.8525         1  0.07129358       1
#> 3               1           1      32.8525         2  0.08504918       1
#> 4               1           1      32.8525         2  0.08504918       1
#> 5               1           1      32.8525         3  0.11887660       1
#> 6               1           1      32.8525         3  0.11887660       1
#>   treatmentGroup endpoint survivalTime dropoutTime timeUnderObservation event
#> 1              1      PFS    51.581804         Inf            32.781207 FALSE
#> 2              1       OS    52.812341         Inf            32.781207 FALSE
#> 3              1      PFS    81.221695         Inf            32.767452 FALSE
#> 4              1       OS   136.515641         Inf            32.767452 FALSE
#> 5              3      PFS     3.331084         Inf             3.331084  TRUE
#> 6              3       OS    18.301343         Inf            18.301343  TRUE
#>   dropoutEvent
#> 1        FALSE
#> 2        FALSE
#> 3        FALSE
#> 4        FALSE
#> 5        FALSE
#> 6        FALSE