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In this paper robust statistical procedures are presented for the analysis of skewed and heavy-tailed outcomes as they typically occur in health care data. The new estimators and test statistics are extensions of classical maximum likelihood techniques for generalized linear models. In contrast to their classical counterparts, the new robust techniques show lower variability and excellent efficiency properties in the presence of small deviations from the assumed model, i.e. when the underlying distribution of the data lies in a neighborhood of the model. A simulation study, an analysis on real data, and a sensitivity analysis confirm the good theoretical statistical properties of the new techniques.