# Incorporating External Controls for Estimating the Average Treatment Effect on the Treated with High-Dimensional Data: Retaining Double Robustness and Ensuring Double Safety

arXiv: https://arxiv.org/abs/2509.20586 · HTML: https://mlsanity.com/paper/2509.20586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 17 of 17)

- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data](https://mlsanity.com/paper/1710.08074/) (2017)
- [A unifying approach for doubly-robust ℓ1 regularized estimation of causal contrasts](https://mlsanity.com/paper/1904.03737/) (2019)
- [Uniformly Valid Post-Regularization Confidence Regions for Many Functional Parameters in Z-Estimation Framework](https://mlsanity.com/paper/1512.07619/) (2015)
- [Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score](https://mlsanity.com/paper/1812.08683/) (2018)
- [Improving efficiency of inference in clinical trials with external control data](https://mlsanity.com/paper/2011.07234/) (2020)
- [Prognostic Adjustment with Efficient Estimators to Unbiasedly Leverage Historical Data in Randomized Trials](https://mlsanity.com/paper/2305.19180/) (2023)
- [Model-Assisted Inference for Covariate-Specific Treatment Effects with High-dimensional Data](https://mlsanity.com/paper/2105.11362/) (2021)
- [Dynamic treatment effects: high-dimensional inference under model misspecification](https://mlsanity.com/paper/2111.06818/) (2021)
- [High-dimensional Model-assisted Inference for Local Average Treatment Effects with Instrumental Variables](https://mlsanity.com/paper/2009.09286/) (2020)
- [Doubly Robust Semiparametric Inference Using Regularized Calibrated Estimation with High-dimensional Data](https://mlsanity.com/paper/2009.12033/) (2020)
- [SAM: Self-adapting Mixture Prior to Dynamically Borrow Information from Historical Data in Clinical Trials](https://mlsanity.com/paper/2305.12279/) (2023)
- [Harmonized Estimation of Subgroup-Specific Treatment Effects in Randomized Trials: The Use of External Control Data](https://mlsanity.com/paper/2308.05073/) (2023)
- [Enhancing Statistical Validity and Power in Hybrid Controlled Trials: A Randomization Inference Approach with Conformal Selective Borrowing](https://mlsanity.com/paper/2410.11713/) (2024)
- [A Causal Inference Framework for Leveraging External Controls in Hybrid Trials](https://mlsanity.com/paper/2305.08969/) (2023)
- [Nonparametric Bayesian approach for dynamic borrowing of historical control data](https://mlsanity.com/paper/2411.11675/) (2024)

## Abstract (arXiv)

Randomized controlled trials (RCTs) are widely regarded as the gold standard for causal inference in biomedical research. For instance, when estimating the average treatment effect on the treated (ATT), a doubly robust estimation procedure can be applied, requiring either the propensity score model or the control outcome model to be correctly specified. In this paper, we address scenarios where external control data, often with a much larger sample size, are available. Such data are typically easier to obtain from historical records or third-party sources. However, we find that incorporating external controls into the standard doubly robust estimator for ATT may paradoxically result in reduced efficiency compared to using the estimator without external controls. This counterintuitive outcome suggests that the naive incorporation of external controls could be detrimental to estimation efficiency. To resolve this issue, we propose a novel doubly robust estimator that guarantees higher efficiency than the standard approach without external controls, even under model misspecification. When all models are correctly specified, this estimator aligns with the standard doubly robust estimator that incorporates external controls and achieves semiparametric efficiency. The asymptotic theory developed in this work applies to high-dimensional confounder settings, which are increasingly common with the growing prevalence of electronic health record data. We demonstrate the effectiveness of our methodology through extensive simulation studies and a real-world data application.