A Class of Permutation Tests for Stratified Survival Data

Summary. We propose a class of permutation tests for stratified survival data. The tests are derived using the framework of Fay and Shih (1998, Journal of the American Statistical Association93, 387–396), which creates tests by permuting scores based on a functional of estimated distribution functions. Here the estimated distribution function for each possibly right-, left-, or interval-censored observation is based on a shrinkage estimator similar to the nonparametric empirical estimator of Ghosh, Lahiri, and Tiwari (1989, Communications in Statistics—Theory and Methods18, 121–146), and permutation is carried out within strata. The proposed test with a weighted Mann-Whitney functional is similar to the permutation form of the stratified log-rank test when there is a large strata effect or the sample size in each stratum is large and is similar to the permutation form of the ordinary log-rank test when there is little strata effect. Thus, the proposed test unifies the advantages of both the stratified and ordinary log-rank tests. By changing the functional, we may obtain a stratified Prentice–Wilcoxon test or a difference in means test with similar unifying properties. We show through simulations the advantage of the proposed test over existing tests for uncensored and right-censored data.