A testing strategy for two crossing survival curves

In biomedical studies, the testing problem of two sample survival curves is commonly seen. The most popular approach is the log-rank test. However, the log-rank test may lead to misleading results when two survival curves cross each other. From Li et al., it is difficult to find a good method to test two sample survival curves for all situations. Here, we propose a strategy procedure to combine some existing approaches for the testing problem. Then, we conduct simulations to examine the power and Type I error rate, and compare the proposed methods with five competitive approaches from Li et al. under various crossing situations of two survival curves. From the results, we suggest the Strategy 2 for the two survival curves testing problem, which has higher power and appropriate Type I error for each situation. Finally, we analyze two real data examples with the proposed methods for illustrations.