Modeling the Effect of Recurrent Events on Time-to-event Processes by Means of Functional Data

In this paper we propose a methodological framework for modeling information carried out by a longitudinal process by means of functional data, within a survival framework targeting the time-to-event process of interest. In particular, the longitudinal process is represented by the compensator of a marked point process the recurrent events are supposed to derive from. By means of Functional Principal Component Analysis (FPCA), a suitable dimensional reduction of these objects is carried out in order to plug them into a survival Cox regression model. In doing so, we enrich the information available for modeling survival with relevant dynamic features, whose time-varying nature is properly taken into account. Such methodology is applied to data provided by the healthcare division of Lombardia regional district in Italy, related to patients hospitalized for Heart Failure (HF) between 2000 and 2012, who assume multiple drugs over time. The model enables personalized predictions, quantifying the effect of personal behaviors and therapeutic patterns on long-term survival.