Prediction Intervals for Interim Events in Randomized Clinical Trials with Time-to-Event Endpoints

Time-to-event endpoints are central to evaluate treatment efficacy across many disease areas. Many trial protocols include interim analyses within group-sequential designs that control type I error via spending functions or boundary methods. The corresponding operating characteristics depend on the number of looks and the information accrued. Planning interim analyses with time-to-event endpoints is challenging because statistical information depends on the number of observed events. Ensuring adequate follow-up to accrue the required events is therefore critical, making interim prediction of information at scheduled looks and at the final analysis essential. While several methods have been developed to predict the calendar time required to reach a target number of events, to the best of our knowledge there is no established framework that addresses the prediction of the number of events at a future date with corresponding prediction intervals. Starting from an prediction interval approach originally developed in reliability engineering for the number of future component failures, we reformulated and extended it to the context of interim monitoring in clinical trials. This adaptation yields a general framework for event-count prediction intervals in the clinical setting, taking the patient as the unit of analysis and accommodating a range of parametric survival models, patient-level covariates, stagged entry and possible dependence between entry dates and lost to follow-up. Prediction intervals are obtained in a frequentist framework from a bootstrap estimator of the conditional distribution of future events. The performance of the proposed approach is investigated via simulation studies and illustrated by analyzing a real-world phase III trial in childhood acute lymphoblastic leukaemia.