Multiply robust estimation of causal quantile treatment effects

Abstract

In causal inference, often the interest lies in the estimation of the average causal effect. Other quantities such as the quantile treatment effect may be of interest as well. In this article, we propose a multiply robust method for estimating the marginal quantiles of potential outcomes by achieving mean balance in (a) the propensity score, and (b) the conditional distributions of potential outcomes. An empirical likelihood or entropy measure approach can be utilized for estimation instead of inverse probability weighting, which is known to be sensitive to the misspecification of the propensity score model. Simulation studies are conducted across different scenarios of correctness in both the propensity score models and the outcome models. Both simulation results and theoretical development indicate that our proposed estimator is consistent if any of the models are correctly specified. In the data analysis, we investigate the quantile treatment effect of mothers' smoking status on infants' birthweight.

A Data Fusion Method for Quantile Treatment Effects

“…In this section, we apply our data fusion method to evaluate the causal effect of smoking during pregnancy on birth weight (Abrevaya, 2001;Almond et al, 2005;Xie et al, 2020). Based on the Natality Data Set published by National Center for Health Statistics, Almond et al (2005) showed that births of low-birthweight babies result in both economic costs for society and the children themselves.…”

“…To illustrate the validity of our data fusion method, we construct the main dataset by including only the basic confounders: mother's marital status, mother's race (either black or white), gender the infant, mother's age, mother's education and the number of prenatal visits. These five confounders are used as full confounders to evaluate the 0.5th QTE inXie et al (2020). However, there are additional key confounders not included in their analyses: alcohol use during pregnancy, the average number of drinks per week, and adequacy of care.…”