Extreme regression models for characterizing high-cost patients.

Healthcare cost distribution generally presents a high level of skewness, with a relatively small number of subjects accounting for a large portion of healthcare expenditures. Information on factors that predict high expenditures is of interest in healthcare planning. The aim of this paper was to inspect the behaviour of extreme regression (ER) models.We performed a simple simulation study, based on the LogNormal distribution, to assess the performance of ER in the special cases of heterogeneity and strong asymmetry of the cost variable. We then discussed the application of ER models to the analysis of three data sets of diabetes, lung cancer and myocardial infarction patients.The ER showed to be able to cope fairly well with skewed distribution but under the condition that all observations have strictly positive costs.The main advantage of the ER model is to unify these approaches in a unique framework, where the estimation of the cut-offs and the production of the prediction rules are performed simultaneously for a continuous response variable. The final model can thus be analysed at any desiderate quantile of the cost distribution, avoiding the need of pre-specifying any cut-off