Interim monitoring using the adaptively weighted log‐rank test in clinical trials for survival outcomes

Abstract

For testing treatment effect with survival data, the log‐rank test has been the method of choice and enjoys an optimality property under proportional hazards alternatives. However, there can be significant loss of power in a variety of nonproportional situations. Yang and Prentice proposed an adaptively weighted log‐rank test that improves the power of the log‐rank test over a wide range of hazard ratio scenarios. In clinical trials, the data and safety monitoring board typically monitors the trial results periodically. Here, we develop interim testing procedures for the adaptively weighted log‐rank test. We establish the asymptotic distribution of the test statistics at the interim looks and use a resampling method to obtain the stopping boundaries. Through examination of the test behavior under local alternatives, we show that the adaptively weighted log‐rank test is fully efficient when the limiting censoring distributions in the two groups are equal. Unlike the case for the usual application of the log‐rank test, critical values obtained from the resampling method are asymptotically valid without the assumption of equal censoring distributions in the two groups. Extensive simulation studies show that the new method improves the log‐rank test for a wide range of treatment effect patterns, and that the resampling approach yields better control of the type 1 error rate than the originally proposed approach in the work of Yang and Prentice. The new procedures are illustrated in several clinical trial examples.