Simulating Joint Models for Recurrent and Terminal Events with Discrete Frailty

In the context of biomedical studies, joint frailty models have been developed to study the joint temporal evolution of recurrent and terminal events, capturing the dependence between the two processes.The literature on joint frailty models predominantly assumes continuous distributions for the random effects. In this article, we present a novel Joint frailty Model that assumes bivariate Discretely-distributed non-parametric Frailties (JMDF), with an unknown finite number of mass points. This approach facilitates the identification of latent structures among subjects, grouping them into subpopulations defined by a shared frailty value. We propose an estimation routine through Expectation-Maximization algorithm, which not only estimates the number of sub-groups, but also serves as an unsupervised classification tool. This works motivated by a study of patients with Heart Failure (HF) in Lombardia region, Italy. A simulation study to evaluate JMDF performance under different scenarios of random-effects distribution is performed, and represents the core of the present contribution.