Adjusted Log-rank Test with Double Inverse Weighting under Dependent Censoring

It is a common issue to compare treatment-specific survival and the weighted log-rank test is the most popular method for group comparison. However, in observational studies, treatments and censoring times are usually not independent, which invalidates the weighted log-rank tests. In this paper, we propose adjusted weighted log-rank tests in the presence of non-random treatment assignment and dependent censoring. A double-inverse weighted technique is developed to adjust the weighted log-rank tests. Specifically, inverse probabilities of treatment and censoring weighting are involved to balance the baseline treatment assignment and to overcome dependent censoring, respectively. We derive the asymptotic distribution of the proposed adjusted tests under the null hypothesis, and propose a method to obtain the critical values. Simulation studies show that the adjusted log-rank tests have correct sizes whereas the traditional weighted log-rank tests may fail in the presence of non-random treatment assignment and dependent censoring. An application to oropharyngeal carcinoma data from the Radiation Therapy Oncology Group is provided for illustration.