Copula-Based Endogeneity Correction for Doubly Robust Estimation of Treatment Effect

2026-05-04

AI Summary

This study addresses endogeneity arising from unobserved confounding in doubly robust estimation—such as the correlation between proxy variables and error terms in medical research—by proposing a correction method based on Gaussian copulas. The approach innovatively integrates copula modeling into the doubly robust framework, jointly characterizing the dependence structure between endogenous covariates and the error term without requiring instrumental variables, while preserving the key doubly robust property that consistent estimation is achievable if either the treatment or outcome model is correctly specified. Monte Carlo simulations demonstrate the method’s effectiveness in mitigating endogeneity bias. Application to NHANES data reveals that the estimated effect of nutritional counseling on blood pressure shifts from statistically significant to insignificant, aligning more closely with established medical consensus.

Abstract

Doubly Robust (DR) estimation of treatment effect relies on an untestable assumption that is the absence of unobserved confounding. This assumption is par- ticularly problematic in the context of healthcare research, where variables like pre- scription refill rates serve as proxies for unobserved behaviors such as medication adherence. These proxy variables are often endogenous, exhibiting correlation with the regression error term due to unmeasured confounding or measurement error. We propose a copula-corrected doubly robust estimator that addresses endogeneity in both the treatment and outcome models without requiring instrumental variables. Gaussian copulas model the joint distribution of endogenous covariates and the error term, enabling consistent estimation while preserving the doubly robust property that requires correct specification of either the treatment or outcome model, not both. Monte Carlo simulations demonstrate that naive DR estimation exhibits substantial bias under endogeneity, whereas our corrected estimator recovers unbiased treatment effects across different data-generating processes. We apply our method to examine the effect of nutritional counseling on blood pressure using the National Health and Nutrition Examination Survey (NHANES) data. Naive DR estimation suggests counseling is associated with increased blood pressure. After copula correction, this effect becomes statistically insignificant, consistent with literature showing modest effects of nutri- Counseling in reducing blood pressure. Our methodology provides researchers with a practical tool for obtaining treatment effects in the presence of endogeneity.

Problem

• endogeneity
• unobserved confounding
• doubly robust estimation
• treatment effect
• proxy variables

Innovation

• Copula
• Endogeneity Correction
• Doubly Robust Estimation
• Treatment Effect
• Gaussian Copula