Improved inference for doubly robust estimators of heterogeneous treatment effects

TL;DR

This paper introduces a new doubly robust inference method for estimating heterogeneous treatment effects in observational studies, effectively handling high-dimensional and nonparametric models with valid, conservative inference.

Contribution

It develops a frequentist inferential procedure using posterior distributions for propensity scores and outcome models, ensuring valid inference even under model misspecification.

Findings

Provides conservative inference in finite samples and under misspecification

Offers a consistent variance estimator when models are correctly specified

Demonstrates utility in high-dimensional and flexible modeling settings

Abstract

We propose a doubly robust approach to characterizing treatment effect heterogeneity in observational studies. We develop a frequentist inferential procedure that utilizes posterior distributions for both the propensity score and outcome regression models to provide valid inference on the conditional average treatment effect even when high-dimensional or nonparametric models are used. We show that our approach leads to conservative inference in finite samples or under model misspecification, and provides a consistent variance estimator when both models are correctly specified. In simulations, we illustrate the utility of these results in difficult settings such as high-dimensional covariate spaces or highly flexible models for the propensity score and outcome regression. Lastly, we analyze environmental exposure data from NHANES to identify how the effects of these exposures vary by subject-level characteristics.