  In the context of clinical and biomedical studies, joint frailty models have
been developed to study the joint temporal evolution of recurrent and terminal
events, capturing both the heterogeneous susceptibility to experiencing a new
episode and the dependence between the two processes. While
discretely-distributed frailty is usually more exploitable by clinicians and
healthcare providers, existing 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, with an unknown finite number
of mass points. This approach facilitates the identification of latent
structures among subjects, grouping them into sub-populations defined by a
shared frailty value. We propose an estimation routine via
Expectation-Maximization algorithm, which not only estimates the number of
subgroups but also serves as an unsupervised classification tool. This work is
motivated by a study of patients with Heart Failure (HF) receiving ACE
inhibitors treatment in the Lombardia region of Italy. Recurrent events of
interest are hospitalizations due to HF and terminal event is death for any
cause.
