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.

翻译：在临床与生物医学研究背景下，联合脆弱性模型被用于研究复发事件与终末事件的联合时间演化过程，既能捕捉个体间对新事件发生的异质性易感性，也能刻画两个过程之间的依赖关系。尽管离散型脆弱性通常更便于临床医师和医疗保健提供者利用，但现有关于联合脆弱性模型的文献主要假设随机效应服从连续分布。本文提出一种新型联合脆弱性模型，该模型假设双变量离散型非参数脆弱性，其质量点数量未知且有限。这种方法有助于识别受试者间的潜在结构，将其划分为由共享脆弱性值定义的子群体。我们提出基于期望最大化算法的估计流程，该算法不仅能估计子群体数量，还能作为无监督分类工具。本研究受一项伦巴第大区接受ACE抑制剂治疗的心力衰竭患者研究的启发。其中关注的复发事件为因心力衰竭导致的再住院，终端事件为任何原因的死亡。