# Collaborative Heterogeneous Causal Inference Beyond Meta-analysis

arXiv: https://arxiv.org/abs/2404.15746 · HTML: https://mlsanity.com/paper/2404.15746/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 24 Apr 2024.

## Builds on (most cited first, 19 of 19)

- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Model Evaluation, Model Selection, and Algorithm Selection in Machine Learning](https://mlsanity.com/paper/1811.12808/) (2018)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Causal inference methods for combining randomized trials and observational studies: a review](https://mlsanity.com/paper/2011.08047/) (2020)
- [Combining multiple observational data sources to estimate causal effects](https://mlsanity.com/paper/1801.00802/) (2018)
- [Federated Causal Inference in Heterogeneous Observational Data](https://mlsanity.com/paper/2107.11732/) (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)
- [Federated Adaptive Causal Estimation (FACE) of Target Treatment Effects](https://mlsanity.com/paper/2112.09313/) (2021)
- [Entropy balancing is doubly robust](https://mlsanity.com/paper/1501.03571/) (2015)
- [Multiply Robust Federated Estimation of Targeted Average Treatment Effects](https://mlsanity.com/paper/2309.12600/) (2023)
- [Robust Inference for Federated Meta-Learning](https://mlsanity.com/paper/2301.00718/) (2023)
- [Diagnosing the role of observable distribution shift in scientific replications](https://mlsanity.com/paper/2309.01056/) (2023)
- [Federated Causal Inference from Observational Data](https://mlsanity.com/paper/2308.13047/) (2023)
- [Privacy-Preserving, Communication-Efficient, and Target-Flexible Hospital Quality Measurement](https://mlsanity.com/paper/2203.00768/) (2022)
- [Collaborative causal inference with a distributed data-sharing management](https://mlsanity.com/paper/2204.00857/) (2022)
- [Debiased Inverse-Variance Weighted Estimator in Two-Sample Summary-Data Mendelian Randomization](https://mlsanity.com/paper/1911.09802/) (2019)

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

- [Federated Causal Inference: Multi-Study ATE Estimation beyond Meta-Analysis](https://mlsanity.com/paper/2410.16870/) (2024)
- [FedDAG: Federated Domain Adversarial Generation Towards Generalizable Medical Image Analysis](https://mlsanity.com/paper/2501.13967/) (2025)
- [Federated Causal Inference from Multi-Site Observational Data via Propensity Score Aggregation](https://mlsanity.com/paper/2505.17961/) (2025)
- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)

## Abstract (arXiv)

Collaboration between different data centers is often challenged by heterogeneity across sites. To account for the heterogeneity, the state-of-the-art method is to re-weight the covariate distributions in each site to match the distribution of the target population. Nevertheless, this method could easily fail when a certain site couldn't cover the entire population. Moreover, it still relies on the concept of traditional meta-analysis after adjusting for the distribution shift. In this work, we propose a collaborative inverse propensity score weighting estimator for causal inference with heterogeneous data. Instead of adjusting the distribution shift separately, we use weighted propensity score models to collaboratively adjust for the distribution shift. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases. To account for the vulnerable density estimation, we further discuss the double machine method and show the possibility of using nonparametric density estimation with d<8 and a flexible machine learning method to guarantee asymptotic normality. We propose a federated learning algorithm to collaboratively train the outcome model while preserving privacy. Using synthetic and real datasets, we demonstrate the advantages of our method.