Robust Gamma regression models for the analysis of health care cost data

Abstract: The population-mean cost of patients with certain pathologies is the parameter of interest for allocating health resources. It generally depends upon a number of covariates and the presence of outliers yields difficulties in the estimation procedure. Recent research in parametric robust techniques proposed the use of robust estimating equations via M-estimation for the Gamma model [2] and a class of high efficiency and high breakdown point estimators [14] extended to the case of generalized log-gamma regression [12]. In the present work, we compared results obtained by the two parametric robust procedures with the standard GLM (Generalized Linear Model) Gamma with log link, both in a simulation study and in a cardiovascular trial. The robust procedures outperformed the GLM Gamma in the contaminated simulation scenario and in the real dataset the significance of some covariates changed between the three estimators, with a better ability of the Log Gamma Robust in isolating the outliers driving these changes.