  Covariate-adaptive randomization is popular in clinical trials with
sequentially arrived patients for balancing treatment assignments across
prognostic factors which may have influence on the response. However, existing
theory on tests for treatment effect under covariate-adaptive randomization is
limited to tests under linear or generalized linear models, although
covariate-adaptive randomization has been used in survival analysis for a long
time and its main application is in survival analysis. Often times,
practitioners would simply adopt a conventional test such as the log-rank test
or score test to compare two treatments, which is controversial since tests
derived under simple randomization may not be valid under other randomization
schemes. In this article, we prove that the log-rank test valid under simple
randomization is conservative in terms of type I error under covariate-adaptive
randomization, and the robust score test developed under simple randomization
is no longer robust under covariate-adaptive randomization. We then propose a
calibration type log-rank or score test that is valid and robust under both
simple randomization and a large family of covariate-adaptive randomization
schemes. Furthermore, we obtain Pitman's efficacy of log-rank and score tests
to compare their asymptotic relative efficiency. Simulation studies about the
type I error and power of various tests are presented under several popular
randomization schemes.
