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Title: Modelling the extremes of flu cases Authors:  Setareh Ranjbar - University of Geneva (Switzerland)
Eva Cantoni - University of Geneva (Switzerland) [presenting]
Valerie Chavez-Demoulin - University of Lausanne (Switzerland)
Giampiero Marra - University College London (United Kingdom)
Rosalba Radice - Cass Business School (United Kingdom)
Abstract: From a health care managerial point of view, the number of tested patients showing flu-like symptoms and the number of positive (or negative) cases of the flu are important indicators of the epidemic of flu and of congestion in a hospital, respectively. We model the extremes of positive cases of flu, of suspicious cases to be tested as well as the ratio of the two. We analyse three years (2016 - 2019) of daily data from the University hospital (CHUV) in Lausanne (Switzerland) with the peak over threshold method. We fit a Discrete Generalized Pareto Distribution (DGPD) to the number of tested patients and number of positive cases, and a Generalized Pareto Distribution (GPD) to the ratio of positive to tested in the framework of Generalized Additive Model for Location, Shape and Scale, which allows full flexibility on the functional form between the covariates and the parameters of the distributions. Since the data show the potential presence of outlying observations, possibly related to the simultaneous outbreak of other diseases sharing the same symptoms with the flu, we develop robust methods to fit the DGPD and GPD. The robust method is crucial for providing a reliable prediction of the flu episodes. The robust data analysis show that the seasonality in the flu data is better explained by meteorological data rather than calendar dates. The reliability of the proposal is supported by an extensive simulation study.