  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.
