A competing risks framework refers to multiple risks acting simultaneously on a subject or on a system. A cure rate, or a limited-failure model, postulates a fraction of the subjects/systems to be cured or failure-free, and can be formulated as a mixture model, or alternatively by a bounded cumulative hazard model. We develop models that unify the competing risks and limited-failure approaches. We describe Bayesian analysis of these models, and discuss conceptual, methodological and computational issues related to model fitting and model selection. We describe detailed applications in survival data from breast cancer patients in the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute (NCI) of the United States.
Groupe d’études et de recherche en analyse des décisions