title: Dynamic clustering of hazard functions: an application to disease progression in chronic heart failure.
abstract: We analyse data collected from the administrative datawarehouse of an Italian regional district (Lombardia) concerning patients affected by Chronic Heart Failure. The longitudinal data gathering for each patient hospital readmissions in time, as well as patient-specific covariates, is studied as a realization of non homogeneous Poisson process. Since the aim behind this study is to identify groups of patients behaving similarly in terms of disease progression and then healthcare consumption, we conjectured the time segments between two consecutive hospitalizations to be Weibull distributed in each hidden cluster. Adding a frailty term to take into account the within subjects unknown variability, the corresponding patient-specific hazard functions are reconstructed. Therefore, the comprehensive distribution for each time to event variable is modelled as a Weibull Mixture. We are then able to easily interpret the related hidden groups as healthy, sick, and terminally ill subjects.
authors: ADAMSS Center & Department of Mathematics "F. Enriques", Università degli Studi di Milano, via Saldini 50, 20133, Milan, Italy.
authors: Francesca
authors: F
authors: Ieva
authors: MOX - Department of Mathematics, Politecnico di Milano, via Bonardi 9, 20133, Milan, Italy. anna.paganoni@polimi.it.
authors: Anna Maria
authors: AM
authors: Paganoni
authors: MOX - Department of Mathematics, Politecnico di Milano, via Bonardi 9, 20133, Milan, Italy.
authors: Teresa
authors: T
authors: Pietrabissa
keywords: Frailty models; Heart failure; Proportional hazards model; Survival analysis