A class of semiparametric joint frailty-copula models for recurrent events subjected to a terminal event

Abstract

Survival analysis is one of the most important areas of statistics. One of its objectives is to assess potential risk factors in the occurrence of events. Proportional hazard (PH) regression models are the most commonly used tools for this purpose, but they have some limitations. Their strong assumption that the hazard rate ratio is constant can prevent the use of PH models in some cases. Alternatives to the PH model, such as proportional odds (PO) and Yang and Prentice (YP) models, are discussed in the literature. However, these models are not capable of accommodating the correlation between events. Some studies discuss the introduction of a random effect (or frailty) into the regression structure of the PH and PO models or the use of copulas to accommodate dependencies. Survival data can exhibit dependence in various ways. This work addresses cases where an individual may experience successive events, called recurrent events. Furthermore, these individuals are subject to experiencing a terminal event, that is, an event that prevents the continuation of the individual's follow-up, thus preventing new recurrent events. Therefore, the processes of recurrent and terminal events show some dependence. Our goal is to develop, under the Bayesian approach, a class of joint frailty-copula models to fit recurrent events subject to a terminal event. Due to its attractive mathematical form, we use the Archimedean Clayton copula. We couple Bernstein polynomials (BP) and the piecewise exponential model (PEM) as baseline hazard functions. Additionally, we present a class of Yang and Prentice regression models to fit only terminal or recurrent events using the same baseline functions. We present a simulation study and exemplify our models using a real case.