Two-sample tests for survival data from observational studies

When observational data are used to compare treatment-specific survivals, regular two-sample tests, such as the log-rank test, need to be adjusted for the imbalance between treatments with respect to baseline covariate distributions. Besides, the standard assumption that survival time and censoring time are conditionally independent given the treatment, required for the regular two-sample tests, may not be realistic in observational studies. Moreover, treatment-specific hazards are often non-proportional, resulting in small power for the log-rank test. In this paper, we propose a set of adjusted weighted log-rank tests and their supremum versions by inverse probability of treatment and censoring weighting to compare treatment-specific survivals based on data from observational studies. These tests are proven to be asymptotically correct. Simulation studies show that with realistic sample sizes and censoring rates, the proposed tests have the desired Type I error probabilities and are more powerful than the adjusted log-rank test when the treatment-specific hazards differ in non-proportional ways. A real data example illustrates the practical utility of the new methods.