Accounting for long-term survival: a smoothed piecewise model for event time projection in cellular immunotherapy trials

In clinical trials with time-to-event outcomes, one of the main tasks is predicting the number of events over time and the time to reach a specific number of events. This is particularly challenging in cellular immunotherapy trials due to the unique, time-dependent nature of the hazard rate. The typical survival pattern shows a high early event rate followed by a long-term survival plateau. While piecewise parametric survival models are commonly used to address this hazard heterogeneity, they often introduce abrupt changes in hazard rates between intervals. In this work, we extend it to a smoothed piecewise model for event-time prediction, aiming to reduce abrupt changes in hazard rates between adjacent intervals. Simulation studies and real trial examples demonstrate the enhanced utility and improved accuracy of our proposed methods for event-time prediction in cellular immunotherapy trials.