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

TL;DR

This paper develops a new statistical framework for predicting the number of future events in clinical trials with time-to-event endpoints, incorporating covariates and patient entry patterns, to improve interim analysis planning.

Contribution

It extends reliability engineering prediction intervals to clinical trial event prediction, accommodating complex models and patient data for more accurate interim monitoring.

Findings

The proposed method provides valid prediction intervals in simulations.

Application to a real trial demonstrates practical utility.

Framework accommodates covariates and staggered patient entry.

Abstract

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, with operating characteristics determined by 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, so adequate follow-up to accrue the required events is critical and interim prediction of information at scheduled looks and at the final analysis becomes 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 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 loss 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.