Predicting events in clinical trials using two time-to-event outcomes

In clinical trials with time-to-event outcomes, it is of interest to predict when a prespecified number of events can be reached. Interim analysis is conducted to estimate the underlying survival function. When another correlated time-to-event endpoint is available, both outcome variables can be used to improve estimation efficiency. In this paper, we propose to use the convolution of two time-to-event variables to estimate the survival function of interest. Propositions and examples are provided based on exponential models that accommodate possible change points. We further propose a new estimation equation about the expected time that exploits the relationship of two endpoints. Simulations and the analysis of real data show that the proposed methods with bivariate information yield significant improvement in prediction over that of the univariate method.