The New England Journal of Statistics in Data Science

Cure models are gaining more and more popularity for modeling time-to-event data for different forms of cancer, for which a considerable proportion of patients are considered “cured.” Two types of cure models are widely used, the mixture cure model (MCM) and the promotion time cure model (PTCM). In this article, we propose a unified estimand Δ for comparing treatment and control groups under the survival models with cure fraction, which focuses on whether the treatment extends survival for patients. In addition, we introduce a general framework of Bayesian inference under the cure models. Simulation studies demonstrate that regardless of whether the model is correctly specified, the inference of the unified estimand Δ yields desirable empirical performance. We analyze the ECOG’s melanoma cancer data E1684 via the unified estimand Δ under different models to further demonstrate the proposed methodology.