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.

翻译：双稳健（DR）治疗效应估计依赖于一个不可检验的假设，即不存在未观测到的混淆因素。在医疗健康研究背景下，该假设尤其存在问题，因为诸如处方续药率等变量常作为未观测行为（如用药依从性）的代理变量，而这些代理变量往往具有内生性，即由于未测量的混淆因素或测量误差而与回归误差项相关。我们提出了一种Copula校正的双稳健估计量，无需工具变量即可解决治疗模型和结果模型中的内生性问题。高斯Copula对内生协变量与误差项的联合分布进行建模，从而在保持双稳健性质（即只需正确指定治疗模型或结果模型之一，而非两者均需正确指定）的同时实现一致估计。蒙特卡洛模拟表明：在存在内生性的情况下，朴素DR估计表现出显著偏差，而我们的校正估计量在不同数据生成过程中均能恢复无偏的治疗效应。我们应用该方法，使用美国国家健康与营养调查（NHANES）数据，检验营养咨询对血压的影响。朴素DR估计显示咨询与血压升高相关，但经Copula校正后，该效应在统计上不显著，这与文献中关于营养咨询降低血压效果适中的结论一致。本方法为研究者提供了存在内生性时获取治疗效应的实用工具。