A Bayesian Approach to Causal Cure Models
Time-to-event data often include individuals who will never experience the failure event, and are therefore considered cured. In such settings, frequently encountered in clinical research, a substantial proportion of patients may remain event-free throughout the observation period, leading to the appearance of a survival plateau that is commonly interpreted as evidence of a cured fraction. Analysing such data requires inference on the cure fraction and on the survival function for the uncured subpopulation, tasks which are traditionally achieved with mixture cure models. However, assessing the causal effect of a treatment on these quantities is non-trivial. We consider principal stratification causal estimands, which have been proposed to evaluate effects on the cure fraction and on the survival for an always-uncured stratum. We additionally introduce a novel estimand, which considers the causal effect on the survival for a non-always-cured union of strata. We frame the problem from a Bayesian model-based perspective, which provides a flexible and unified estimation strategy while maintaining a direct link with classical mixture cure model quantities. The reliability of the proposed approach is validated through simulations, demonstrating competitive and robust performance relative to existing methods. Finally, we illustrate its practical usefulness through an application to a randomized trial comparing non-invasive ventilation with standard oxygen therapy in patients with hypoxemic respiratory failure following abdominal surgery.