Robust tests for treatment effect in survival analysis under covariate‐adaptive randomization

Covariate‐adaptive randomization is popular in clinical trials with sequentially arrived patients for balancing treatment assignments across prognostic factors that may have influence on the response. However, existing theory on tests for the treatment effect under covariate‐adaptive randomization is limited to tests under linear or generalized linear models, although the covariate‐adaptive randomization method has been used in survival analysis for a long time. Often, practitioners will simply adopt a conventional test to compare two treatments, which is controversial since tests derived under simple randomization may not be valid in terms of type I error under other randomization schemes. We derive the asymptotic distribution of the partial likelihood score function under covariate‐adaptive randomization and a working model that is subject to possible model misspecification. Using this general result, we prove that the partial likelihood score test that is robust against model misspecification under simple randomization is no longer robust but conservative under covariate‐adaptive randomization. We also show that the unstratified log‐rank test is conservative and the stratified log‐rank test remains valid under covariate‐adaptive randomization. We propose a modification to variance estimation in the partial likelihood score test, which leads to a score test that is valid and robust against arbitrary model misspecification under a large family of covariate‐adaptive randomization schemes including simple randomization. Furthermore, we show that the modified partial likelihood score test derived under a correctly specified model is more powerful than log‐rank‐type tests in terms of Pitman's asymptotic relative efficiency. Simulation studies about the type I error and power of various tests are presented under several popular randomization schemes.