On the versatility of the combination of the weighted log-rank statistics

In many applied situations, it is difficult to specify in advance the types of survival differences that may exist between two groups. Therefore, it is tempting to use some tests that emphasize these differences, but are sensitive to a wide range of the survival differences. In this paper such versatile tests are considered, whose procedures are based on the simultaneous use of the weighted log-rank statistics that are asymptotically normal under the null hypothesis of no difference between two groups. Simulations are performed to examine power of the tests in small and moderate sample sizes when the data are uncensored to heavily censored. Implementation of the procedures are discussed in a real data example for illustration.