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We propose a new general approach for estimating the effect of a binarytreatment on a continuous and potentially highly skewed response variable, thegeneralized quantile treatment effect (GQTE). The GQTE is defined as thedifference between a function of the quantiles under the two treatmentconditions. As such, it represents a generalization over the standardapproaches typically used for estimating a treatment effect (i.e., the averagetreatment effect and the quantile treatment effect) because it allows thecomparison of any arbitrary characteristic of the outcome's distribution underthe two treatments. Following Dominici et al. (2005), we assume that apre-specified transformation of the two quantiles is modeled as a smoothfunction of the percentiles. This assumption allows us to link the two quantilefunctions and thus to borrow information from one distribution to the other.The main theoretical contribution we provide is the analytical derivation of aclosed form expression for the likelihood of the model. Exploiting this resultwe propose a novel Bayesian inferential methodology for the GQTE. We show somefinite sample properties of our approach through a simulation study whichconfirms that in some cases it performs better than other nonparametricmethods. As an illustration we finally apply our methodology to the 1987National Medicare Expenditure Survey data to estimate the difference in thesingle hospitalization medical cost distributions between cases (i.e., subjectsaffected by smoking attributable diseases) and controls.

Generalized Quantile Treatment Effect: A Flexible Bayesian Approach Using Quantile Ratio Smoothing