Um novo modelo de sobrevivência com fração de cura: inferência, diagnóstico e aplicações

Abstract

Survival models with a cure rate are essential when a portion of individuals does not experience the event of interest during follow-up. In many settings, it is assumed that unobservable latent causes exist which, upon activation, may trigger the event; this activation mechanism can link the outcome to the first cause, the last cause, or one selected at random. In this work, we study cure rate models that combine Weibull failure times with the discrete Bilal distribution for the number of latent causes. Parameter estimation is conducted under both classical and Bayesian approaches, and performance is assessed through simulation studies and an application to real data. The analysis also employs Cox--Snell residuals as a diagnostic tool, underscoring the role of residual assessment in this context. Within the Bayesian framework, we use model comparison criteria and case-deletion influence analysis. Taken together, the results highlight the usefulness of the proposed family in capturing latent heterogeneity and distinct activation mechanisms, offering a flexible and interpretable alternative for biomedical and/or industrial applications.