Disease progression models are a powerful tool for understanding the development of a disease, given some clinical measurements obtained from longitudinal events related to a sample of patients. These models are able to give some insights about the disease progression through the analysis of patients histories and can be also used to predict the future course of the disease for an individual. In particular, Hidden Markov Models are suitable for disease progression since they model the latent unobservable states of the disease. In this work, we propose a HMM where the outcome is multivariate and its components are not independent; to accomplish our aim, since we do not make any usual normality assumptions, we model the outcome using copulas. We first test the performance of our model in a simulation setting and show the validity of the method. Then, we study the course of Heart Failure, applying our model to an administrative dataset from Lombardia Region in Italy, showing how episodes of hospitalization can give information about the disease status of a patient.

中文翻译：

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疾病进展的多元隐马尔可夫模型

鉴于从与患者样本有关的纵向事件获得的一些临床测量结果，疾病进展模型是了解疾病发展的强大工具。这些模型能够通过分析患者的病史来提供有关疾病进展的一些见解，还可以用于预测个人的未来病程。隐马尔可夫模型特别适合疾病发展，因为它们可以对疾病的潜在不可观察状态进行建模。在这项工作中，我们提出了一种HMM，其结果是多元的并且其组成部分不是独立的。为了实现我们的目标，由于我们没有做出任何通常的正态性假设，因此我们使用copulas对结果进行建模。我们首先在仿真设置中测试模型的性能，并证明该方法的有效性。然后，