Improved Logrank-Type Tests for Survival Data Using Adaptive Weights

Summary .  For testing for treatment effects with time-to-event data, the logrank test is the most popular choice and has some optimality properties under proportional hazards alternatives. It may also be combined with other tests when a range of nonproportional alternatives are entertained. We introduce some versatile tests that use adaptively weighted logrank statistics. The adaptive weights utilize the hazard ratio obtained by fitting the model of Yang and Prentice (2005,  Biometrika   92 , 1–17). Extensive numerical studies have been performed under proportional and nonproportional alternatives, with a wide range of hazard ratios patterns. These studies show that these new tests typically improve the tests they are designed to modify. In particular, the adaptively weighted logrank test maintains optimality at the proportional alternatives, while improving the power over a wide range of nonproportional alternatives. The new tests are illustrated in several real data examples.