Some versatile tests based on the simultaneous use of weighted logrank and weighted Kaplan-Meier statistics

It is well known that the logrank test is locally most powerful under proportional hazards model for right censored data when two groups have same censoring distributions. For a given data set, however, one seldom knows what the exact alternative is. Therefore, Lee (1) constructed versatile tests by combining four weighted logrank (WLR) tests with various weight functions detecting proportional, early, late and middle hazards differences, respectively. However, Pepe and Fleming (2) had pointed out that WLR tests are based on ranks, and these tests might not be sensitive to the magnitude of the difference in survival times against a specific alternative. Hence, they constructed weighted Kaplan-Meier (WKM) tests that are more sensitive than the logrank test under various alternatives. Therefore, another type of versatile tests based on the simultaneous use of WLR and WKM tests is developed in this paper and the performances of the proposed tests and Lee's tests are compared by simulation. None of the tests investigated in this paper is uniformly better than the others. Lee's maximum test is more robust for detecting various alternatives; however, for computation simplicity, the linear combination of WLR and WKM tests is recommended to apply in practice and its overall performance is better than Lee's linear combination test.