# Calibrated Optimal Decision Making with Multiple Data Sources and Limited Outcome

arXiv: https://arxiv.org/abs/2104.10554 · HTML: https://mlsanity.com/paper/2104.10554/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 21 Apr 2021.

## Builds on (most cited first, 11 of 11)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Learning When-to-Treat Policies](https://mlsanity.com/paper/1905.09751/) (2019)
- [Residual Weighted Learning for Estimating Individualized Treatment Rules](https://mlsanity.com/paper/1508.03179/) (2015)
- [On the role of surrogates in the efficient estimation of treatment effects with limited outcome data](https://mlsanity.com/paper/2003.12408/) (2020)
- [Combining multiple observational data sources to estimate causal effects](https://mlsanity.com/paper/1801.00802/) (2018)
- [Using Experiments to Correct for Selection in Observational Studies](https://mlsanity.com/paper/2006.09676/) (2020)
- [Learning Optimal Distributionally Robust Individualized Treatment Rules](https://mlsanity.com/paper/2006.15121/) (2020)
- [More Efficient Policy Learning via Optimal Retargeting](https://mlsanity.com/paper/1906.08611/) (2019)
- [Policy Learning with Observational Data](https://mlsanity.com/paper/1702.02896/) (2017)
- [Prediction of ICD Codes with Clinical BERT Embeddings and Text Augmentation with Label Balancing using MIMIC-III](https://mlsanity.com/paper/2008.10492/) (2020)

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

- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)

## Abstract (arXiv)

We consider the optimal decision-making problem in a primary sample of interest with multiple auxiliary sources available. The outcome of interest is limited in the sense that it is only observed in the primary sample. In reality, such multiple data sources may belong to heterogeneous studies and thus cannot be combined directly. This paper proposes a new framework to handle heterogeneous samples and address the limited outcome simultaneously through a novel calibrated optimal decision-making method, by leveraging the common intermediate outcomes in multiple data sources. Specifically, our method allows the baseline covariates across different samples to have either homogeneous or heterogeneous distributions. Under the equal conditional means of intermediate outcomes in different samples given baseline covariates and the treatment information, we show that the proposed estimator of the conditional mean outcome is asymptotically normal and more efficient than using the primary sample solely. Extensive experiments on simulated datasets demonstrate empirical validity and improved efficiency using our approach, followed by a real application to electronic health records.