|Abstract:|| The aim of this paper is to model the stochastic process of hospitalizations with Marked Point Processes. We examine the longitudinal dataset including the admissions of heart failured patients to Lombardia hospitals on a follow-up period of six years since January 1st, 2006. We analyse four separate groups of patients, which we call HF groups, according to their diagnoses-codes contained in the SDO (dimission 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 of methods for statistical inference and suggest a specific model
for our topic, validating it through a goodness of fit technique.|