Stratified Difference in Milestone Survival Probabilities

Obtains the stratified milestone survival probabilities and difference in milestone survival probabilities at given calendar times.

Usage

kmstat(
  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 survival probability.
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.
surv1: The milestone survival probability for the treatment group.
surv2: The milestone survival probability for the control group.
survDiff: The difference in milestone survival probabilities, i.e., surv1 - surv2.
vsurv1: The variance for surv1.
vsurv2: The variance for surv2.
vsurvDiff: The variance for survDiff.
information: The information for survDiff, equal to 1/vsurvDiff.
survDiffZ: The Z-statistic value, i.e., survDiff/sqrt(vsurvDiff).

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

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

kmstat(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     surv1     surv2  survDiff
#> 1        18   8.700526    5.138325    3.562201 0.3841805 0.2663374 0.1178431
#> 2        18 140.948521   83.240865   57.707656 0.3841805 0.2663374 0.1178431
#>        vsurv1       vsurv2   vsurvDiff information survDiffZ
#> 1 0.003856622 0.0038944814 0.007751103    129.0139  1.338512
#> 2 0.001037023 0.0008598885 0.001896912    527.1726  2.705706