A class of permutation tests for stratified survival data

We propose a class of permutation tests for stratified survival data. The t ests are derived using the framework of Fay and Shih (1998, Journal of the American Statistical Association. 93, 387-396), which creates tests by perm uting scores based on a functional of estimated distribution functions. Her e the estimated distribution function for each possibly right-, left-, or i nterval-censored observation is based on a shrinkage estimator similar to t he nonparametric empirical estimator of Ghosh, Lahiri, and Tiwari (1989, Co mmunications in. Statistics-Theory and Methods 18, 121-146), and permutatio n is carried out within strata. The proposed test with a weighted Mann-Whit ney functional is similar to the permutation form of the stratified log-ran k test when there is a large strata effect or the sample size in each strat um 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 t he advantages of both the stratified and ordinary log-rank tests. By changi ng the functional, we may obtain a stratified Prentice-Wilcoxon test or a d ifference in means test with similar unifying properties. We show through s imulations the advantage of the proposed test over existing tests for uncen sored and right-censored data.