SCI: A Bayesian adaptive phase I/II dose‐finding design accounting for semi‐competing risks outcomes for immunotherapy trials

An immunotherapy trial often uses the phase I/II design to identify the optimal biological dose, which monitors the efficacy and toxicity outcomes simultaneously in a single trial. The progression‐free survival rate is often used as the efficacy outcome in phase I/II immunotherapy trials. As a result, patients developing disease progression in phase I/II immunotherapy trials are generally seriously ill and are often treated off the trial for ethical consideration. Consequently, the happening of disease progression will terminate the toxicity event but not vice versa, so the issue of the semi‐competing risks arises. Moreover, this issue can become more intractable with the late‐onset outcomes, which happens when a relatively long follow‐up time is required to ascertain progression‐free survival. This paper proposes a novel Bayesian adaptive phase I/II design accounting for semi‐competing risks outcomes for immunotherapy trials, referred to as the dose‐finding design accounting for semi‐competing risks outcomes for immunotherapy trials (SCI) design. To tackle the issue of the semi‐competing risks in the presence of late‐onset outcomes, we re‐construct the likelihood function based on each patient's actual follow‐up time and develop a data augmentation method to efficiently draw posterior samples from a series of Beta‐binomial distributions. We propose a concise curve‐free dose‐finding algorithm to adaptively identify the optimal biological dose using accumulated data without making any parametric dose–response assumptions. Numerical studies show that the proposed SCI design yields good operating characteristics in dose selection, patient allocation, and trial duration.