permGS: permGS
In permGS: Permutational Group Sequential Test for Time-to-Event Data

Description Author(s) References Examples

This package implements permutational group-sequential tests for time-to-event data based on (weighted) log-rank test statistics. It supports exact permutation test when the censoring distributions are equal in the treatment and the control group and the approximate imputation-permutation methods of Heinze et al. (2003) and Wang et al. (2010) and when the censoring distributions are different. Permutations can be stratified, i.e. only patients within the same stratum are treated as exchangeable. Rejection boundaries are monotone and finite even when only a random subset of all permutations is used. One- and Two-sided testing possible.

Matthias Brueckner m.bruckner@lancaster.ac.uk, Franz Koenig Franz.Koenig@meduniwien.ac.at, Martin Posch martin.posch@meduniwien.ac.at

Brueckner, M., Koenig, F. and Posch, M. Group-sequential permutation tests for time-to-event data.

Heinze, G., Gnant, M. and Schemper, M. Exact Log-Rank Tests for Unequal Follow-Up. Biometrics, 59(4), December 2003.

Wang, R., Lagakos, S.~W. and Gray, R.~J. Testing and interval estimation for two-sample survival comparisons with small sample sizes and unequal censoring. Biostatistics, 11(4), 676–692, January 2010.

Kelly, P., Zhou, Y., Whitehead, N. J., Stallard, N. and Bowman, C. Sequentially testing for a gene<e2><80><93>drug interaction in a genomewide analysis. Statistics in Medicine, 27(11), 2022–2034, May 2008.

## IPZ method based on logrank test with 1000 restricted random permutations
x <- createPermGS(1000, TRUE, "IPZ", type="logrank")

T <- rexp(100) ## event times
R <- runif(100, 0, 12)  ## recruitment times
Z <- rbinom(100, 1, 0.5)  ## treatment assignment
C <- rexp(100) ## drop-out times

## two-stage design
t1 <- 9  ## calendar time of interim analysis
t2 <- 18  ## calendar time of final analysis

## Stage 1
data.t1 <- data.frame(time=pmin(T, C, max(0, (t1-R))), status=(T<=pmin(C, t1-R)), trt=Z)
data.t1 <- data.t1[R <= t1,] 
x <- nextStage(x, 0.00153, Surv(time, status) ~ trt, data.t1)
summary(x)

if(!x$results$reject[1]) { ## Stage 2
   data.t2 <- data.frame(time=pmin(T, C, max(0, (t2-R))), status=(T<=pmin(C, t2-R)), trt=Z)
   data.t2 <- data.t2[R <= t2,]
   data.t2$strata <- rep.int(c(1,2), c(nrow(data.t1), nrow(data.t2)-nrow(data.t1)))
   x <- nextStage(x, alpha=0.025, Surv(time, status) ~ trt + strata(strata), data.t2)           
   summary(x)
}