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Abstract:
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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. Since non-proportional hazards are often encountered in oncology trials, alternative tests have been proposed. The maximum weighted logrank test is shown to be robust in general situations. In this manuscript, we propose a new maximum test that incorporates the weight for detecting crossing hazard alternatives. The new weight is a function of the crossing timepoint. Extensive simulation studies are conducted to compare our methods with other methods proposed in the literature under scenarios with varied hazard ratios, sample sizes, censoring rates, and censoring patterns. For crossing hazards, the proposed test is shown to be the most powerful one with known crossing timepoint and has similar performance as the maxcombo test in the mis-specified crossing timepoint scenario. Under other alternatives, 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 specifically detect crossing hazards.
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