# Multi-Study R-Learner for Estimating Heterogeneous Treatment Effects Across Studies Using Statistical Machine Learning

arXiv: https://arxiv.org/abs/2306.01086 · HTML: https://mlsanity.com/paper/2306.01086/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 59 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 15 of 15)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [Causal inference methods for combining randomized trials and observational studies: a review](https://mlsanity.com/paper/2011.08047/) (2020)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [A Review of Generalizability and Transportability](https://mlsanity.com/paper/2102.11904/) (2021)
- [Adaptive Combination of Randomized and Observational Data](https://mlsanity.com/paper/2111.15012/) (2021)
- [An Adaptive Kernel Approach to Federated Learning of Heterogeneous Causal Effects](https://mlsanity.com/paper/2301.00346/) (2023)
- [A Tree-based Model Averaging Approach for Personalized Treatment Effect Estimation from Heterogeneous Data Sources](https://mlsanity.com/paper/2103.06261/) (2021)
- [Efficient and robust methods for causally interpretable meta-analysis: transporting inferences from multiple randomized trials to a target population](https://mlsanity.com/paper/1908.09230/) (2019)
- [Comparison of meta-learners for estimating multi-valued treatment heterogeneous effects](https://mlsanity.com/paper/2205.14714/) (2022)
- [Methods for Integrating Trials and Non-Experimental Data to Examine Treatment Effect Heterogeneity](https://mlsanity.com/paper/2302.13428/) (2023)
- [Causal effect on a target population: a sensitivity analysis to handle missing covariates](https://mlsanity.com/paper/2105.06435/) (2021)
- [Multi-Study Boosting: Theoretical Considerations for Merging vs. Ensembling](https://mlsanity.com/paper/2207.04588/) (2022)

## Built on by (most cited first, 4 of 4)

- [Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data](https://mlsanity.com/paper/2412.11136/) (2024)
- [Robust estimation of heterogeneous treatment effects in randomized trials leveraging external data](https://mlsanity.com/paper/2507.03681/) (2025)
- [Debiased Machine Learning for Conformal Prediction of Counterfactual Outcomes Under Runtime Confounding](https://mlsanity.com/paper/2604.03772/) (2026)
- [Bayesian fusion forests for heterogeneous treatment effects on survival from randomised and real-world data](https://mlsanity.com/paper/2607.29295/) (2026)

## Abstract (arXiv)

Estimating heterogeneous treatment effects (HTEs) is crucial for precision medicine. While multiple studies can improve the generalizability of results, leveraging them for estimation is statistically challenging. Existing approaches often assume identical HTEs across studies, but this may be violated due to various sources of between-study heterogeneity, including differences in study design, study populations, and data collection protocols, among others. To this end, we propose a framework for multi-study HTE estimation that accounts for between-study heterogeneity in the nuisance functions and treatment effects. Our approach, the multi-study R-learner, extends the R-learner to obtain principled statistical estimation with machine learning (ML) in the multi-study setting. It involves a data-adaptive objective function that links study-specific treatment effects with nuisance functions through membership probabilities, which enable information to be borrowed across potentially heterogeneous studies. The multi-study R-learner framework can combine data from randomized controlled trials, observational studies, or a combination of both. It's easy to implement and flexible in its ability to incorporate ML for estimating HTEs, nuisance functions, and membership probabilities. In the series estimation framework, we show that the multi-study R-learner is asymptotically normal and more efficient than the R-learner when there is between-study heterogeneity in the propensity score model under homoscedasticity. We illustrate using cancer data that the proposed method performs favorably compared to existing approaches in the presence of between-study heterogeneity.