# Federated Causal Inference in Heterogeneous Observational Data

arXiv: https://arxiv.org/abs/2107.11732 · HTML: https://mlsanity.com/paper/2107.11732/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 88 references that are in the map.
- First posted on arXiv 25 Jul 2021.

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

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Efficient Distributed Learning with Sparsity](https://mlsanity.com/paper/1605.07991/) (2016)
- [Combining Observational and Experimental Datasets Using Shrinkage Estimators](https://mlsanity.com/paper/2002.06708/) (2020)
- [Using Experiments to Correct for Selection in Observational Studies](https://mlsanity.com/paper/2006.09676/) (2020)
- [Heterogeneity-aware and communication-efficient distributed statistical inference](https://mlsanity.com/paper/1912.09623/) (2019)
- [Propensity Score Methods for Merging Observational and Experimental Datasets](https://mlsanity.com/paper/1804.07863/) (2018)
- [Federated Estimation of Causal Effects from Observational Data](https://mlsanity.com/paper/2106.00456/) (2021)
- [Providing Accurate Models across Private Partitioned Data: Secure Maximum Likelihood Estimation](https://mlsanity.com/paper/1710.06933/) (2017)

## Built on by (most cited first, 24 of 24)

- [An Adaptive Kernel Approach to Federated Learning of Heterogeneous Causal Effects](https://mlsanity.com/paper/2301.00346/) (2023)
- [Vertical Federated Learning: A Structured Literature Review](https://mlsanity.com/paper/2212.00622/) (2022)
- [Multiply Robust Federated Estimation of Targeted Average Treatment Effects](https://mlsanity.com/paper/2309.12600/) (2023)
- [Towards Privacy-Aware Causal Structure Learning in Federated Setting](https://mlsanity.com/paper/2211.06919/) (2022)
- [Federated Causality Learning with Explainable Adaptive Optimization](https://mlsanity.com/paper/2312.05540/) (2023)
- [Multi-Source Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2405.09331/) (2024)
- [Collaborative causal inference on distributed data](https://mlsanity.com/paper/2208.07898/) (2022)
- [Collaborative Heterogeneous Causal Inference Beyond Meta-analysis](https://mlsanity.com/paper/2404.15746/) (2024)
- [Federated Causal Inference from Observational Data](https://mlsanity.com/paper/2308.13047/) (2023)
- [Federated Causal Inference: Multi-Study ATE Estimation beyond Meta-Analysis](https://mlsanity.com/paper/2410.16870/) (2024)
- [FedECA: Federated External Control Arms for Causal Inference with Time-To-Event Data in Distributed Settings](https://mlsanity.com/paper/2311.16984/) (2023)
- [Federated Learning for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2402.17705/) (2024)
- [Federated Causal Inference from Multi-Site Observational Data via Propensity Score Aggregation](https://mlsanity.com/paper/2505.17961/) (2025)
- [Estimation of conditional average treatment effects on distributed confidential data](https://mlsanity.com/paper/2402.02672/) (2024)
- [Federated Instrumental Variable Analysis via Federated Generalized Method of Moments](https://mlsanity.com/paper/2505.21012/) (2025)
- [Federated Offline Policy Learning](https://mlsanity.com/paper/2305.12407/) (2023)
- [Data-light Uncertainty Set Merging with Admissibility](https://mlsanity.com/paper/2410.12201/) (2024)
- [Causal Policy Learning in Reinforcement Learning: Backdoor-Adjusted Soft Actor-Critic](https://mlsanity.com/paper/2506.05445/) (2025)
- [From Privacy to Trust in the Agentic Era: A Taxonomy of Challenges in Trustworthy Federated Learning Through the Lens of Trust Report 2.0](https://mlsanity.com/paper/2507.15796/) (2025)
- [Latent Factor Point Processes for Patient Representation in Electronic Health Records](https://mlsanity.com/paper/2508.20327/) (2025)
- [Fed-CausalDiff: Decoupled Synchronization for Federated Do-Simulation and Policy Evaluation](https://mlsanity.com/paper/2606.22510/) (2026)
- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)
- [Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcome](https://mlsanity.com/paper/2608.10664/) (2026)
- [An Accurate and Single-Communication Federated Inference Algorithm](https://mlsanity.com/paper/2608.27063/) (2026)

## Abstract (arXiv)

We are interested in estimating the effect of a treatment applied to individuals at multiple sites, where data is stored locally for each site. Due to privacy constraints, individual-level data cannot be shared across sites; the sites may also have heterogeneous populations and treatment assignment mechanisms. Motivated by these considerations, we develop federated methods to draw inference on the average treatment effects of combined data across sites. Our methods first compute summary statistics locally using propensity scores and then aggregate these statistics across sites to obtain point and variance estimators of average treatment effects. We show that these estimators are consistent and asymptotically normal. To achieve these asymptotic properties, we find that the aggregation schemes need to account for the heterogeneity in treatment assignments and in outcomes across sites. We demonstrate the validity of our federated methods through a comparative study of two large medical claims databases.