# Robust estimation of heterogeneous treatment effects in randomized trials leveraging external data

arXiv: https://arxiv.org/abs/2507.03681 · HTML: https://mlsanity.com/paper/2507.03681/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 52 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 25 of 25)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2202.12891/) (2022)
- [Applied Causal Inference Powered by ML and AI](https://mlsanity.com/paper/2403.02467/) (2024)
- [Elastic Integrative Analysis of Randomized Trial and Real-World Data for Treatment Heterogeneity Estimation](https://mlsanity.com/paper/2005.10579/) (2020)
- [Increasing the efficiency of randomized trial estimates via linear adjustment for a prognostic score](https://mlsanity.com/paper/2012.09935/) (2020)
- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Falsification of Internal and External Validity in Observational Studies via Conditional Moment Restrictions](https://mlsanity.com/paper/2301.13133/) (2023)
- [On Weighted Orthogonal Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2303.12687/) (2023)
- [Efficient Randomized Experiments Using Foundation Models](https://mlsanity.com/paper/2502.04262/) (2025)
- [Detecting critical treatment effect bias in small subgroups](https://mlsanity.com/paper/2404.18905/) (2024)
- [Prognostic Adjustment with Efficient Estimators to Unbiasedly Leverage Historical Data in Randomized Trials](https://mlsanity.com/paper/2305.19180/) (2023)
- [Transfer learning of individualized treatment rules from experimental to real-world data](https://mlsanity.com/paper/2108.08415/) (2021)
- [Multi-Study R-Learner for Estimating Heterogeneous Treatment Effects Across Studies Using Statistical Machine Learning](https://mlsanity.com/paper/2306.01086/) (2023)
- [Improving Precision of RCT-Based CATE Estimation using Data Borrowing with Double Calibration](https://mlsanity.com/paper/2306.17478/) (2023)
- [The Hardness of Validating Observational Studies with Experimental Data](https://mlsanity.com/paper/2503.14795/) (2025)
- [Study designs for extending causal inferences from a randomized trial to a target population](https://mlsanity.com/paper/1905.07764/) (2019)
- [Robust integration of external control data in randomized trials](https://mlsanity.com/paper/2406.17971/) (2024)
- [Identification strategies for combining an experimental study with external data](https://mlsanity.com/paper/2406.03302/) (2024)

## Built on by (most cited first, 1 of 1)

- [Improving RCT-Based Treatment Effect Estimation Under Covariate Mismatch via Calibrated Alignment](https://mlsanity.com/paper/2603.19186/) (2026)

## Abstract (arXiv)

Randomized trials are typically designed to detect average treatment effects but often lack the statistical power to uncover individual-level treatment effect heterogeneity, limiting their value for personalized decision-making. To address this, we propose the QR-learner, a model-agnostic learner that estimates conditional average treatment effects (CATE) within the trial population by leveraging external data from other trials or observational studies. The proposed method is robust: it can reduce the mean squared error relative to a trial-only CATE learner, and is guaranteed to recover the true CATE even when the external data are not aligned with the trial. Moreover, we introduce a procedure that combines the QR-learner with a trial-only CATE learner and show that it asymptotically matches or exceeds both component learners in terms of mean squared error. We examine the performance of our approach in simulation studies and apply the methods to a real-world dataset, demonstrating improvements in both CATE estimation and statistical power for detecting heterogeneous effects.