A Maximum Weighted Logrank Test in Detecting Crossing Hazards.

In practice, the logrank test is the most widely used method for testing the equality of survival distributions. It is the optimal method under the proportional hazard assumption. However, since non-proportional hazards are often encountered in oncology trials, alternative tests have been proposed. The maximum weighted logrank test was shown to be robust in general situations. In this manuscript, we propose a new maximum test that incorporates the weight for detecting crossing hazards. The new weight is a function of the crossing time-point. Extensive simulation studies are conducted to compare our methods with other methods proposed in the literature under scenarios with various hazard ratio patterns, sample sizes, censoring rates, and censoring patterns. For crossing hazards, the proposed test is shown to be the most powerful one with a known crossing time-point. It has a similar performance as the Maxcombo test in the misspecified crossing time-point scenario. Under other alternative situations, the new test remains comparatively powerful as the Maxcombo test. Finally, we illustrate the test in a real data example and discuss the procedures to extend the test to detect crossing hazards specifically.