Stratified Difference in Restricted Mean Survival Times

Obtains the stratified restricted mean survival times and difference in restricted mean survival times at given calendar times.

Usage

rmstat(
  time = NA_real_,
  milestone = NA_real_,
  allocationRatioPlanned = 1,
  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 = FALSE
)

Arguments

time: A vector of calendar times for data cut.
milestone: The milestone time at which to calculate the restricted mean survival time.
allocationRatioPlanned: Allocation ratio for the active treatment versus control. 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.
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 FALSE for variable follow-up.

Value

A data frame containing the following variables:

time: The calendar time since trial start.
subjects: The number of enrolled subjects.
nevents: The total number of events.
nevents1: The number of events in the active treatment group.
nevents2: The number of events in the control group.
ndropouts: The total number of dropouts.
ndropouts1: The number of dropouts in the active treatment group.
ndropouts2: The number of dropouts in the control group.
milestone: The milestone time relative to randomization.
nmilestone: The total number of subjects reaching milestone.
nmilestone1: The number of subjects reaching milestone in the active treatment group.
nmiletone2: The number of subjects reaching milestone in the control group.
rmst1: The restricted mean survival time for the treatment group.
rmst2: The restricted mean survival time for the control group.
rmstDiff: The difference in restricted mean survival times, i.e., rmst1 - rmst2.
vrmst1: The variance for rmst1.
vrmst2: The variance for rmst2.
vrmstDiff: The variance for rmstDiff.
information: The information for rmstDiff, equal to 1/vrmstDiff.
rmstDiffZ: The Z-statistic value, i.e., rmstDiff/sqrt(vrmstDiff).

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

# Piecewise accrual, piecewise exponential survivals, and 5% dropout by
# the end of 1 year.

rmstat(time = c(22, 40),
       milestone = 18,
       allocationRatioPlanned = 1,
       accrualTime = seq(0, 8),
       accrualIntensity = 26/9*seq(1, 9),
       piecewiseSurvivalTime = c(0, 6),
       stratumFraction = c(0.2, 0.8),
       lambda1 = c(0.0533, 0.0309, 1.5*0.0533, 1.5*0.0309),
       lambda2 = c(0.0533, 0.0533, 1.5*0.0533, 1.5*0.0533),
       gamma1 = -log(1-0.05)/12,
       gamma2 = -log(1-0.05)/12,
       accrualDuration = 22,
       followupTime = 18, fixedFollowup = FALSE)
#>   time subjects  nevents  nevents1 nevents2 ndropouts ndropouts1 ndropouts2
#> 1   22      468 195.2491  91.89764 103.3514  12.16925   6.202213   5.967036
#> 2   40      468 356.3965 164.83437 191.5622  24.15559  13.010003  11.145587
#>   milestone nmilestone nmilestone1 nmilestone2    rmst1    rmst2  rmstDiff
#> 1        18   8.700526    5.138325    3.562201 10.85387 9.948097 0.9057767
#> 2        18 140.948521   83.240865   57.707656 10.85387 9.948097 0.9057767
#>      vrmst1    vrmst2 vrmstDiff information rmstDiffZ
#> 1 0.2848075 0.2641123 0.5489198    1.821760  1.222550
#> 2 0.2029210 0.1785637 0.3814847    2.621337  1.466502