# Combining multiple observational data sources to estimate causal effects

arXiv: https://arxiv.org/abs/1801.00802 · HTML: https://mlsanity.com/paper/1801.00802/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2018.

## Built on by (most cited first, 29 of 29)

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- [Multi-Source Causal Inference Using Control Variates](https://mlsanity.com/paper/2103.16689/) (2021)
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- [Generating Synthetic Text Data to Evaluate Causal Inference Methods](https://mlsanity.com/paper/2102.05638/) (2021)
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- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [Representation Retrieval Learning for Heterogeneous Data Integration](https://mlsanity.com/paper/2503.09494/) (2025)
- [Collaborative Heterogeneous Causal Inference Beyond Meta-analysis](https://mlsanity.com/paper/2404.15746/) (2024)
- [Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing data](https://mlsanity.com/paper/2107.07371/) (2021)
- [Causal Inference from Small High-dimensional Datasets](https://mlsanity.com/paper/2205.09281/) (2022)
- [Causal Effect Estimation from Observational and Interventional Data Through Matrix Weighted Linear Estimators](https://mlsanity.com/paper/2306.06002/) (2023)
- [Federated Learning for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2402.17705/) (2024)
- [Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data](https://mlsanity.com/paper/2406.06452/) (2024)
- [Calibrated Optimal Decision Making with Multiple Data Sources and Limited Outcome](https://mlsanity.com/paper/2104.10554/) (2021)
- [Assessing Electricity Service Unfairness with Transfer Counterfactual Learning](https://mlsanity.com/paper/2310.03258/) (2023)
- [Causal inference with Machine Learning-Based Covariate Representation](https://mlsanity.com/paper/2311.01709/) (2023)
- [Statistical inference for case-control logistic regression via integrating external summary data](https://mlsanity.com/paper/2405.20655/) (2024)
- [Combining Incomplete Observational and Randomized Data for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2410.21343/) (2024)
- [A Cautionary Tale on Integrating Studies with Disparate Outcome Measures for Causal Inference](https://mlsanity.com/paper/2505.11014/) (2025)
- [Deconfounded Warm-Start Thompson Sampling with Applications to Precision Medicine](https://mlsanity.com/paper/2505.17283/) (2025)
- [Data Fusion for High-Resolution Estimation](https://mlsanity.com/paper/2508.14858/) (2025)
- [Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects](https://mlsanity.com/paper/2604.00915/) (2026)
- [Generation-Powered Inference for Distribution-Valued Outcomes](https://mlsanity.com/paper/2608.14542/) (2026)

## Abstract (arXiv)

The era of big data has witnessed an increasing availability of multiple data sources for statistical analyses. We consider estimation of causal effects combining big main data with unmeasured confounders and smaller validation data with supplementary information on these confounders. Under the unconfoundedness assumption with completely observed confounders, the smaller validation data allow for constructing consistent estimators for causal effects, but the big main data can only give error-prone estimators in general. However, by leveraging the information in the big main data in a principled way, we can improve the estimation efficiencies yet preserve the consistencies of the initial estimators based solely on the validation data. Our framework applies to asymptotically normal estimators, including the commonly-used regression imputation, weighting, and matching estimators, and does not require a correct specification of the model relating the unmeasured confounders to the observed variables. We also propose appropriate bootstrap procedures, which makes our method straightforward to implement using software routines for existing estimators.