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

TL;DR

This paper introduces a flexible Bayesian method for estimating the generalized quantile treatment effect, allowing comparison of arbitrary distribution features under different treatments, especially for skewed responses.

Contribution

It derives a closed-form likelihood for the GQTE and develops a novel Bayesian inference approach, extending treatment effect estimation beyond traditional mean or quantile differences.

Findings

Method performs well in simulations, often outperforming nonparametric alternatives.

Application to Medicare data reveals distributional differences in medical costs between smoking-related and non-smoking subjects.

Bayesian approach effectively captures complex distributional effects in treatment analysis.

Abstract

We propose a new general approach for estimating the effect of a binary treatment on a continuous and potentially highly skewed response variable, the generalized quantile treatment effect (GQTE). The GQTE is defined as the difference between a function of the quantiles under the two treatment conditions. As such, it represents a generalization over the standard approaches typically used for estimating a treatment effect (i.e., the average treatment effect and the quantile treatment effect) because it allows the comparison of any arbitrary characteristic of the outcome's distribution under the two treatments. Following Dominici et al. (2005), we assume that a pre-specified transformation of the two quantiles is modeled as a smooth function of the percentiles. This assumption allows us to link the two quantile functions and thus to borrow information from one distribution to the other. The main theoretical contribution we provide is the analytical derivation of a closed form expression for the likelihood of the model. Exploiting this result we propose a novel Bayesian inferential methodology for the GQTE. We show some finite sample properties of our approach through a simulation study which confirms that in some cases it performs better than other nonparametric methods. As an illustration we finally apply our methodology to the 1987 National Medicare Expenditure Survey data to estimate the difference in the single hospitalization medical cost distributions between cases (i.e., subjects affected by smoking attributable diseases) and controls.