Testing treatment effect by combining weighted log-rank tests and using empirical likelihood

For testing treatment effect with time to event data, combinations of several tests are often desired when the hazard functions of the two groups are nonproportional. Yang and Prentice [2005. Semiparametric analysis of short term and long term hazard ratios with two sample survival data. Biometrika 92, 1-17.] defined a new two-sample semiparametric model that accommodates nonproportional hazard functions and contains the Cox model and the proportional odds model as two submodels. They also obtained a [chi]2 test on the parameter that reduces to the [chi]2 test based on weighted log-rank tests for testing the null hypothesis of no treatment effect. In this paper, we consider a new [chi]2 test using the empirical likelihood method. Extensive simulation studies were conducted to compare the performance of the test with other related ones, for a variety of combinations of the short-term and long-term treatment effects.