Marked point process models for the admissions of heart failure patients

The aim of this paper is to model the stochastic process of hospitalizations with marked point processes (MPPs). We examine the longitudinal data set including the admissions of heart failure patients to Lombardia hospitals on a follow-up period of 6 years since January 1, 2006. We analyze four separate groups of patients, which we call heart failure groups, according to their diagnoses-codes contained in the SDO (hospital discharge form) of their first hospitalizations. The statistical model links the temporal trend of hospitalization (the ground process) with the length of stay (the mark) at each event. Instead of framing our application in the more theoretical context of the counting measures and processes, we make use of the conditional intensity function, a parametric approach which leads us to deal with Hawkes processes. Hypotheses are made on the mark concerning its distribution as well as its independence or dependence with the ground process. Independence is better to model and give us significant results while dependence is harder to be dealt with due to computational and modeling issues. Finally, we provide a general framework for modeling longitudinal data with a MPP as a method for statistical inference and suggest a specific model for our topic, validating it through a goodness of fit technique