Hazard reconstruction and clustering for better prognosis of disease progression in heart failure

Nowadays Heart Failure (HF) is considered the leading cause of repeated hospitalisations in patients aged over 65. The resulting longitudinal dataset and its analyses are consequently becoming of a great interest for clinicians and statisticians worldwide. We analysed HF data collected from the administrative databank of an Italian regional district (Lombardia), concentrating our study on the days elapsed from one admission to the next for each patient in our dataset. The aim behind this project is to identify groups of patients, conjecturing that the variables in our study, the time segments between two consecutive hospitalisations, are Weibull distributed in each hidden cluster. Therefore, the comprehensive distribution for each variable results in a Weibull Mixture Model. From this assumption we developed a survival analysis in order to estimate, through a proportional hazards model, the corresponding hazard function for the proposed model and to obtain the desired clusters. We find that the selected dataset, a good representative of the complete population, can be categorized into three clusters, corresponding to "healthy", "sick" and "terminally ill" patients. Furthermore, we attempted a reconstruction of the patient-specific hazard function, adding a frailty parameter to the considered model.