Comparison of Methods to Analyze Time-to-Event Endpoints When Treatment Effect is Delayed

The statistical evaluation of time-to-event endpoints like overall survival demands careful consideration as commonly used methods rely on the assumption of proportional hazards. This assumption is, however, violated if the treatment effect is delayed and even though usual methods may control the specified type I error rate they will have reduced power to detect a difference. To provide a basis for selecting appropriate methods we investigated the performance of various alternatives to the standard logrank test in terms of type I error and power in this setting. A broad variety of methods, including weighted logrank tests, combinations thereof or regression-based methods, were identified within a literature search and then compared in an extensive simulation study. We found that most of the methods controlled type I error. With respect to power, the methods that come close to the data-generating process performed best in the simulation study and were not sensitive to parameter misspecification. The interpretation of the results of these methods is, however, often complicated due to the absence of interpretable summary measures. Overall, the results of our simulation study together with the proposed ranking system can help to make a substantiated choice of an appropriate statistical method to analyze future studies.