Doubly robust weighted log-rank tests and Renyi-type tests under non-random treatment assignment and dependent censoring.

The log-rank test is widely used to test difference in event time distribution between treatment groups. However, if subjects are not randomly assigned to treatment groups, which is often the case in observation studies, the log-rank test is not asymptotically correct for detecting group survival difference due to the imbalance of confounding variables between groups. We develop a class of modified weighted log-rank tests and Renyi-type tests for two-sample survival comparison under non-random treatment assignment. The new tests can also account for non-random censoring that depends on baseline covariates. The proposed methods involve building working models for treatment assignment, cause-specific hazard of dependent censoring, and the time to event. We prove that, when either the models for treatment assignment and dependent censoring or the model for the event time is true, the new tests are asymptotically correct, i.e. being doubly robust. Numerical experiments demonstrate the tests' double-robustness property in finite samples of realistic sizes, and also show that the doubly robust log-rank test is at least as powerful as the regular log-rank test when the treatment assignment is random and there is no dependent censoring. An application to a kidney transplant data set illustrates the utility of the proposed methods.