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

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.

A Two-Stage Interpretable Matching Framework for Causal Inference

Matching in causal inference from observational data aims to construct treatment and control groups with similar distributions of covariates, thereby reducing confounding and ensuring an unbiased estimation of treatment effects. This matched sample closely mimics a randomized controlled trial (RCT), thus improving the quality of causal estimates. We introduce a novel Two-stage Interpretable Matching (TIM) framework for transparent and interpretable covariate matching. In the first stage, we perform exact matching across all available covariates. For treatment and control units without an exact match in the first stage, we proceed to the second stage. Here, we iteratively refine the matching process by removing the least significant confounder in each iteration and attempting exact matching on the remaining covariates. We learn a distance metric for the dropped covariates to quantify closeness to the treatment unit(s) within the corresponding strata. We used these high- quality matches to estimate the conditional average treatment effects (CATEs). To validate TIM, we conducted experiments on synthetic datasets with varying association structures and correlations. We assessed its performance by measuring bias in CATE estimation and evaluating multivariate overlap between treatment and control groups before and after matching. Additionally, we apply TIM to a real-world healthcare dataset from the Centers for Disease Control and Prevention (CDC) to estimate the causal effect of high cholesterol on diabetes. Our results demonstrate that TIM improves CATE estimates, increases multivariate overlap, and scales effectively to high-dimensional data, making it a robust tool for causal inference in observational data.