Number of Subjects Having an Event and Log-Rank Statistics

Obtains the number of subjects accrued, number of events, number of dropouts, and number of subjects reaching the maximum follow-up in each group, mean and variance of weighted log-rank score statistic, estimated hazard ratio from weighted Cox regression and variance of log hazard ratio estimate at given calendar times.

Usage

lrstat(
  time = NA_real_,
  hazardRatioH0 = 1,
  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,
  rho1 = 0,
  rho2 = 0,
  predictTarget = 2L
)

Arguments

time: A vector of calendar times at which to calculate the number of events and the mean and variance of log-rank test score statistic.
hazardRatioH0: Hazard ratio under the null hypothesis for the active treatment versus control. Defaults to 1 for superiority test.
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.
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.
predictTarget: The target of prediction. Set predictTarget = 1 to predict the number of events only. Set predictTarget = 2 (default) to predict the number of events and log-rank score statistic mean and variance. Set predictTarget = 3 to predict the number of events, log-rank score statistic mean and variance, and hazard ratio and variance of log hazard ratio.

Value

A data frame containing the following variables if predictTarget = 1:

time: The analysis 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.
nfmax: The total number of subjects reaching maximum follow-up.
nfmax1: The number of subjects reaching maximum follow-up in the active treatment group.
nfmax2: The number of subjects reaching maximum follow-up in the control group.

If predictTarget = 2, the following variables will also be included:

uscore: The numerator of the log-rank test statistic.
vscore: The variance of the log-rank score test statistic.
logRankZ: The log-rank test statistic on the Z-scale.
hazardRatioH0: The hazard ratio under the null hypothesis.

Furthermore, if predictTarget = 3, the following additional variables will also be included:

HR: The average hazard ratio from weighted Cox regression.
vlogHR: The variance of log hazard ratio.
zlogHR: The Z-statistic for log hazard ratio.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

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

lrstat(time = c(22, 40), allocationRatioPlanned = 1,
       accrualTime = seq(0, 8),
       accrualIntensity = 26/9*seq(1, 9),
       piecewiseSurvivalTime = c(0, 6),
       lambda1 = c(0.0533, 0.0309),
       lambda2 = c(0.0533, 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      468 154.4040  71.83183  82.57218  13.45783   6.835885    6.62195
#> 2   40      468 307.5078 138.43661 169.07120  29.03037  15.471551   13.55882
#>   nfmax nfmax1 nfmax2     uscore   vscore  logRankZ hazardRatioH0
#> 1     0      0      0  -6.404097 38.56497 -1.031244             1
#> 2     0      0      0 -24.351805 76.18939 -2.789870             1