A hybrid approach to predicting events in clinical trials with time-to-event outcomes

In many clinical trials with time-to-event outcomes there are interim analyses planned at pre-specified event counts. It is of great value to predict when the pre-specified event milestones can be reached based on the available data as the timeline for a study is essential to the study sponsors and data monitoring committees for logistic planning purposes. Both parametric and non-parametric approaches exist in the literature for estimating the underlining survival function, based on which the predictions of future event times can be determined. The parametric approaches assume that the survival function is smooth, which is often not the case as the survival function usually has one or multiple change points and the hazard functions can differ significantly before and after a change point. The existing non-parametric method bases predictions on the Kaplan–Meier survival curve appended with a parametric tail to the largest observation, and all of the available data is used to estimate the parametric tail. This approach also requires a smooth survival function in order to achieve an accurate estimate of the tail distribution. In this article, we propose a hybrid parametric, non-parametric approach to predicting events in clinical trials with time-to-event outcomes. The change points in the survival function are first detected, and the survival function before the last change point is estimated non-parametrically and the tail distribution beyond the last change point is estimated parametrically. Numerical results show that the proposed approach provides accurate predictions for future event times and outperforms the existing approaches.