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Log-Rank Test Simulation for Enrichment Design

Source: R/lrsim.R
lrsimsub.Rd

Performs simulation for two-arm group sequential trials based on weighted log-rank test for a biomarker enrichment design. The looks are either driven by the total number of events in the ITT population or the biomarker positive sub population. Alternatively, the analyses can be planned to occur at specified calendar times.

Usage

lrsimsub(
  kMax = 1,
  kMaxitt = 1,
  hazardRatioH0itt = 1,
  hazardRatioH0pos = 1,
  hazardRatioH0neg = 1,
  allocation1 = 1,
  allocation2 = 1,
  accrualTime = 0,
  accrualIntensity = NA,
  piecewiseSurvivalTime = 0,
  stratumFraction = 1,
  p_pos = NA,
  lambda1itt = NA,
  lambda2itt = NA,
  lambda1pos = NA,
  lambda2pos = NA,
  gamma1itt = 0,
  gamma2itt = 0,
  gamma1pos = 0,
  gamma2pos = 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.

kMaxitt

Number of stages with timing determined by events in the ITT population. Ranges from 0 (none) to kMax.

hazardRatioH0itt

Hazard ratio under the null hypothesis for the ITT population. Defaults to 1 for superiority test.

hazardRatioH0pos

Hazard ratio under the null hypothesis for the biomarker positive sub population. Defaults to 1 for superiority test.

hazardRatioH0neg

Hazard ratio under the null hypothesis for the biomarker negative sub population. 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.

p_pos

The prevalence of the biomarker positive sub population in each stratum.

lambda1itt

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

lambda2itt

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

lambda1pos

A vector of hazard rates for the event in each analysis time interval by stratum for the treatment group in the biomarker positive sub population.

lambda2pos

A vector of hazard rates for the event in each analysis time interval by stratum for the control group in the biomarker positive sub population.

gamma1itt

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 in the ITT population.

gamma2itt

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 in the ITT population.

gamma1pos

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 in the biomarker positive sub population.

gamma2pos

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 in the biomarker positive sub population.

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 events in the ITT population at Look 1 to Look kMaxitt and the planned cumulative total number of events at Look kMaxitt+1 to Look kMax in the biomarker positive sub population.

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.

    • population: The population ("ITT", "Biomarker Positive", "Biomarker Negative") under consideration.

    • 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.

    • logRankStatistic: The log-rank test Z-statistic for the population.

  • 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.

    • biomarker: The biomarker status for the subject (1 for positive, 0 for negative).

    • 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 for the subject.

    • event: Whether the subject experienced an event.

    • dropoutEvent: Whether the subject dropped out.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


sim1 = lrsimsub(
  kMax = 2,
  kMaxitt = 2,
  allocation1 = 1,
  allocation2 = 1,
  accrualTime = seq(0,9),
  accrualIntensity = c(seq(10,70,10),rep(70,3)),
  piecewiseSurvivalTime = c(0,12,24),
  p_pos = 0.6,
  lambda1itt = c(0.00256, 0.00383, 0.00700),
  lambda2itt = c(0.00427, 0.00638, 0.01167),
  lambda1pos = c(0.00299, 0.00430, 0.01064),
  lambda2pos = c(0.00516, 0.00741, 0.01835),
  gamma1itt = -log(1-0.04)/12,
  gamma2itt = -log(1-0.04)/12,
  gamma1pos = -log(1-0.04)/12,
  gamma2pos = -log(1-0.04)/12,
  n = 500,
  plannedEvents = c(108,144),
  maxNumberOfIterations = 1000,
  maxNumberOfRawDatasetsPerStage = 1,
  seed = 314159,
  nthreads = 1)

head(sim1$sumdata)
#>   iterNumber events1NotAchieved events2NotAchieved stageNumber analysisTime
#> 1          1              FALSE              FALSE           1     47.20050
#> 2          1              FALSE              FALSE           1     47.20050
#> 3          1              FALSE              FALSE           1     47.20050
#> 4          1              FALSE              FALSE           2     59.14058
#> 5          1              FALSE              FALSE           2     59.14058
#> 6          1              FALSE              FALSE           2     59.14058
#>   population accruals1 accruals2 totalAccruals events1 events2 totalEvents
#> 1        ITT       250       250           500      38      70         108
#> 2 Biomarker+       143       136           279      32      45          77
#> 3 Biomarker-       107       114           221       6      25          31
#> 4        ITT       250       250           500      56      88         144
#> 5 Biomarker+       143       136           279      49      62         111
#> 6 Biomarker-       107       114           221       7      26          33
#>   dropouts1 dropouts2 totalDropouts     uscore    vscore logRankStatistic
#> 1        29        39            68 -19.822223 26.812336        -3.828115
#> 2        16        23            39 -11.136324 18.868887        -2.563709
#> 3        13        16            29  -9.566429  7.687120        -3.450389
#> 4        36        45            81 -22.525041 35.622174        -3.774030
#> 5        20        28            48 -14.240702 27.082819        -2.736431
#> 6        16        17            33 -10.008313  8.228709        -3.488952
head(sim1$rawdata)
#>   iterationNumber stageNumber analysisTime subjectId arrivalTime stratum
#> 1               1           1      47.2005         1  0.07129358       1
#> 2               1           1      47.2005         2  0.15135848       1
#> 3               1           1      47.2005         3  0.25417963       1
#> 4               1           1      47.2005         4  0.31318945       1
#> 5               1           1      47.2005         5  0.48171673       1
#> 6               1           1      47.2005         6  0.74681987       1
#>   biomarker treatmentGroup survivalTime dropoutTime timeUnderObservation event
#> 1      TRUE              1     14.73791   223.63615             14.73791  TRUE
#> 2     FALSE              2    140.84362   269.95567             47.04914 FALSE
#> 3      TRUE              2    154.76417   802.30215             46.94632 FALSE
#> 4      TRUE              1     32.82033    32.87180             32.82033  TRUE
#> 5     FALSE              2    521.59369   235.55130             46.71878 FALSE
#> 6      TRUE              1     53.80430    31.18759             31.18759 FALSE
#>   dropoutEvent
#> 1        FALSE
#> 2        FALSE
#> 3        FALSE
#> 4        FALSE
#> 5        FALSE
#> 6         TRUE