# The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimation

arXiv: https://arxiv.org/abs/2309.17283 · HTML: https://mlsanity.com/paper/2309.17283/

## Key facts

- Cited by 1 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 29 Sep 2023.

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

- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [On Multi-Cause Causal Inference with Unobserved Confounding: Counterexamples, Impossibility, and Alternatives](https://mlsanity.com/paper/1902.10286/) (2019)
- [Identifying effects of multiple treatments in the presence of unmeasured confounding](https://mlsanity.com/paper/2011.04504/) (2020)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Document Context Language Models](https://mlsanity.com/paper/1511.03962/) (2015)
- [Causal Discovery from Subsampled Time Series with Proxy Variables](https://mlsanity.com/paper/2305.05276/) (2023)
- [Estimating scaled treatment effects with multiple outcomes](https://mlsanity.com/paper/1608.02273/) (2016)
- [Wasserstein Conditional Independence Testing](https://mlsanity.com/paper/2107.14184/) (2021)
- [Comment: Reflections on the Deconfounder](https://mlsanity.com/paper/1910.08042/) (2019)
- [Efficient Heterogeneous Treatment Effect Estimation With Multiple Experiments and Multiple Outcomes](https://mlsanity.com/paper/2206.04907/) (2022)
- [Doubly Robust Proximal Causal Learning for Continuous Treatments](https://mlsanity.com/paper/2309.12819/) (2023)
- [The Promises of Parallel Outcomes](https://mlsanity.com/paper/2012.05849/) (2020)
- [Causal Discovery via Conditional Independence Testing with Proxy Variables](https://mlsanity.com/paper/2305.05281/) (2023)
- [Distributionally-Robust Optimization with Noisy Data for Discrete Uncertainties Using Total Variation Distance](https://mlsanity.com/paper/2302.07454/) (2023)

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

- [A Diffusion-Based Method for Learning the Multi-Outcome Distribution of Medical Treatments](https://mlsanity.com/paper/2506.01533/) (2025)

## Abstract (arXiv)

Assessing causal effects in the presence of unobserved confounding is a challenging problem. Existing studies leveraged proxy variables or multiple treatments to adjust for the confounding bias. In particular, the latter approach attributes the impact on a single outcome to multiple treatments, allowing estimating latent variables for confounding control. Nevertheless, these methods primarily focus on a single outcome, whereas in many real-world scenarios, there is greater interest in studying the effects on multiple outcomes. Besides, these outcomes are often coupled with multiple treatments. Examples include the intensive care unit (ICU), where health providers evaluate the effectiveness of therapies on multiple health indicators. To accommodate these scenarios, we consider a new setting dubbed as multiple treatments and multiple outcomes. We then show that parallel studies of multiple outcomes involved in this setting can assist each other in causal identification, in the sense that we can exploit other treatments and outcomes as proxies for each treatment effect under study. We proceed with a causal discovery method that can effectively identify such proxies for causal estimation. The utility of our method is demonstrated in synthetic data and sepsis disease.