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Title: Non parametric frailty Cox model for clustering time-to-event data Authors:  Anna Maria Paganoni - MOX-Politecnico di Milano (Italy) [presenting]
Francesca Gasperoni - MRC Biostatistics Unit, University of Cambridge (United Kingdom)
Francesca Ieva - Politecnico di Milano (Italy)
Chris Jackson - MRC Biostatistics Unit -Cambridge (United Kingdom)
Linda Sharples - Department of Medical Statistics - London School of Hygiene and Tropical Medicine - London (United Kingdom)
Abstract: An innovative model for hierarchical time-to-event data (i.e., healthcare data in which patients are grouped by healthcare providers) is described. The most popular model for this kind of data is the Cox proportional hazard model, with parametric frailties shared among patients belonging to the same group. We relax the parametric assumption on the frailty term by using a nonparametric discrete distribution with an unknown finite number of points in its support. Our aim is two-fold: on one hand, we want to propose a more flexible model for grouped survival data; on the other hand, we want to detect clusters of providers and characterize them through an a posteriori analysis supported by group specific covariates. A tailored expectation-maximization algorithm is introduced to estimate the number of clusters, the frailty discrete distribution, the proportion associated to each cluster and the classical parameters of a Cox model. To conclude, we show an application to a clinical administrative database, in which some information of patients suffering from heart failure is collected. We are able to detect a latent clustering structure among hospitals and this result has a clear impact both on patients' side and on hospital managements' side.