Improved inference for doubly robust estimators of heterogeneous treatment effects

• Published in: Biometrics Vol. 79; no. 4; pp. 3140 - 3152
• Main Authors: Shin, Heejun, Antonelli, Joseph
• Format: Journal Article
• Language: English
• Published: United States Blackwell Publishing Ltd 01.12.2023
• Subjects: Bayesian nonparametrics; causal inference; Causality; Computer Simulation; doubly robust estimation; environmental exposure; Epidemiology; Heterogeneity; high‐dimensional statistics; Inference; Models, Statistical; National Health and Nutrition Examination Survey; Nutrition Surveys; Observational studies; Propensity Score; Regression analysis; Regression models; Robustness; Treatment Effect Heterogeneity; variance; Variance analysis; treatment effect heterogeneity; Bayesian nonparametrics; causal inference; high-dimensional statistics; doubly robust estimation
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.13837

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.