Sahil Shikalgar

Sahil Shikalgar, Md. Noor-E-Alam

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.

Sahil Shikalgar, Md. Noor-E-Alam

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.

Md Saiful Islam, Sahil Shikalgar, Md. Noor-E-Alam

A Randomized Control Trial (RCT) is considered as the gold standard for evaluating the effect of any intervention or treatment. However, its feasibility is often hindered by ethical, economical, and legal considerations, making observational data a valuable alternative for drawing causal conclusions. Nevertheless, healthcare observational data presents a difficult challenge due to its high dimensionality, requiring careful consideration to ensure unbiased, reliable, and robust causal inferences. To overcome this challenge, in this study, we propose a novel two-stage feature selection technique called, Outcome Adaptive Elastic Net (OAENet), explicitly designed for making robust causal inference decisions using matching techniques. OAENet offers several key advantages over existing methods: superior performance on correlated and high-dimensional data compared to the existing methods and the ability to select specific sets of variables (including confounders and variables associated only with the outcome). This ensures robustness and facilitates an unbiased estimate of the causal effect. Numerical experiments on simulated data demonstrate that OAENet significantly outperforms state-of-the-art methods by either producing a higher-quality estimate or a comparable estimate in significantly less time. To illustrate the applicability of OAENet, we employ large-scale US healthcare data to estimate the effect of Opioid Use Disorder (OUD) on suicidal behavior. When compared to competing methods, OAENet closely aligns with existing literature on the relationship between OUD and suicidal behavior. Performance on both simulated and real-world data highlights that OAENet notably enhances the accuracy of estimating treatment effects or evaluating policy decision-making with causal inference.