Weighted reverse counting process (WRCP): A novel approach to quantify the overall treatment effect with multiple time-to-event outcomes by adaptive weighting

In a longitudinal randomized study where multiple time-to-event outcomes are collected, the overall treatment effect may be quantified by a composite endpoint defined as the time to the first occurrence of any of the selected events including death. The reverse counting process (RCP) was recently proposed to extend the restricted mean survival time (RMST) approach with an advantage of utilizing observations of events beyond the "first-occurrence" endpoint. However, the interpretation may be questionable because RCP treats all events equally without considering their different associations with the overall survival. In this work, we propose a novel approach, the weighted reverse counting process (WRCP), to construct a weighted composite endpoint to evaluate the overall treatment effect. A multi-state transition model is used to model the association between events, and an adaptive weighting algorithm is developed to determine the weight for individual endpoints based on the association between the nonfatal endpoints and death using the trial data. Simulation studies are presented to compare the performance of WRCP with RCP, log-rank test and RMST approach. The results show that WRCP is a powerful and robust method to detect the overall treatment effect while controlling the clinically false positive rate well across different simulation scenarios.