# Enhancing Treatment Effect Estimation: A Model Robust Approach Integrating Randomized Experiments and External Controls using the Double Penalty Integration Estimator

arXiv: https://arxiv.org/abs/2307.04304 · HTML: https://mlsanity.com/paper/2307.04304/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2023.

## Built on by (most cited first, 6 of 6)

- [Combining Experimental and Historical Data for Policy Evaluation](https://mlsanity.com/paper/2406.00317/) (2024)
- [Towards Generalizing Inferences from Trials to Target Populations](https://mlsanity.com/paper/2402.17042/) (2024)
- [Generalizing Multi-Step Inverse Models for Representation Learning to Finite-Memory POMDPs](https://mlsanity.com/paper/2404.14552/) (2024)
- [Meta-Router: Bridging Gold-standard and Preference-based Evaluations in Large Language Model Routing](https://mlsanity.com/paper/2509.25535/) (2025)
- [Transportability without Graphs: A Bayesian Approach to Identifying s-Admissible Backdoor Sets](https://mlsanity.com/paper/2505.12801/) (2025)
- [Integrating RCTs, RWD, AI/ML and Statistics: Next-Generation Evidence Synthesis](https://mlsanity.com/paper/2511.19735/) (2025)

## Abstract (arXiv)

Randomized experiments (REs) are the cornerstone for treatment effect evaluation. However, due to practical considerations, REs may encounter difficulty recruiting sufficient patients. External controls (ECs) can supplement REs to boost estimation efficiency. Yet, there may be incomparability between ECs and concurrent controls (CCs), resulting in misleading treatment effect evaluation. We introduce a novel bias function to measure the difference in the outcome mean functions between ECs and CCs. We show that the ANCOVA model augmented by the bias function for ECs renders a consistent estimator of the average treatment effect, regardless of whether or not the ANCOVA model is correct. To accommodate possibly different structures of the ANCOVA model and the bias function, we propose a double penalty integration estimator (DPIE) with different penalization terms for the two functions. With an appropriate choice of penalty parameters, our DPIE ensures consistency, oracle property, and asymptotic normality even in the presence of model misspecification. DPIE is more efficient than the estimator derived from REs alone, validated through theoretical and experimental results.