Nonparametric tests for stratum effects in the Cox model

This paper considers the stratified proportional hazards model with a focus on the assessment of stratum effects. The assessment of such effects is often of interest, for example, in clinical trials. In this case, two relevant tests are the test of stratum interaction with covariates and the test of stratum interaction with baseline hazard functions. For the test of stratum interaction with covariates, one can use the partial likelihood method (Kalbfleisch and Prentice, 1980; Lin, 1994). For the test of stratum interaction with baseline hazard functions, however, there seems to be no formal test available. We consider this problem and propose a class of nonparametric tests. The asymptotic distributions of the tests are derived using the martingale theory. The proposed tests can also be used for survival comparisons which need to be adjusted for covariate effects. The method is illustrated with data from a lung cancer clinical trial.