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Title: Using Coxian phase-type distributions and survival trees to model length of stay of elderly patients in Italy hospitals Authors:  Adele Marshall - Queens University Belfast (United Kingdom) [presenting]
Mariangela Zenga - University of Milano-Bicocca (Italy)
Abstract: Coxian phase-type distributions are a special type of Markov chain which describe the time which elapses until a certain event occurs as a series of sequential phases. The Coxian phase-type distribution will be used for modelling the length of stay in hospital of elderly patients. The data consists of records for four years (2012-2015 inclusive) for both private and public hospitals in all 21 regions of Italy for all patients aged 65 and over. The optimum number of phases for modelling the elderly patient data was determined to be three. It was found that the optimal three phase Coxian distribution was a better fit to the data than normal, Weibull and log-normal distributions. Survival methods have previously been used to investigate the length of time elderly patients in Italy spend in hospital and had shown that depending on the hospital, the patient length of stay may differ. This is further investigated by producing survival trees for the current, more recent data, where the covariates are analysed to evaluate which variables significantly influence patient survival.