Improving testing and description of treatment effect in clinical trials with survival outcomes

Cox model inference and the log-rank test have been the cornerstones for design and analysis of clinical trials with survival outcomes. In this article, we summarize some recently developed methods for analyzing survival data when the hazards may possibly be nonproportional and also propose some new estimators for summary measures of the treatment effect. These methods utilize the short-term and long-term hazard ratio model proposed in Yang and Prentice (2005), which contains the Cox model and also accommodates various nonproportional hazards scenarios. Without the proportional hazards assumption, these methods often improve the log-rank test and inference procedures based on the Cox model, as well as nonparametric procedures currently available in the literature. The proposed methods have sound theoretical justifications and can be computed quickly. R codes for implementing them are available. Detailed illustrations with 3 clinical trials are provided.