# Estimation of causal effects with multiple treatments: a review and new ideas

arXiv: https://arxiv.org/abs/1701.05132 · HTML: https://mlsanity.com/paper/1701.05132/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2017.

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

- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Causal Balancing for Domain Generalization](https://mlsanity.com/paper/2206.05263/) (2022)
- [NCoRE: Neural Counterfactual Representation Learning for Combinations of Treatments](https://mlsanity.com/paper/2103.11175/) (2021)
- [Causal Effect Estimation: Recent Advances, Challenges, and Opportunities](https://mlsanity.com/paper/2302.00848/) (2023)
- [Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2210.05446/) (2022)
- [Causal Contrastive Learning for Counterfactual Regression Over Time](https://mlsanity.com/paper/2406.00535/) (2024)
- [Preference Learning for AI Alignment: a Causal Perspective](https://mlsanity.com/paper/2506.05967/) (2025)
- [RMT-Net: Reject-aware Multi-Task Network for Modeling Missing-not-at-random Data in Financial Credit Scoring](https://mlsanity.com/paper/2206.00568/) (2022)
- [Matching for causal effects via multimarginal unbalanced optimal transport](https://mlsanity.com/paper/2112.04398/) (2021)
- [Estimating Causal Effects of Multi-Aspect Online Reviews with Multi-Modal Proxies](https://mlsanity.com/paper/2112.10274/) (2021)
- [Effects of Multi-Aspect Online Reviews with Unobserved Confounders: Estimation and Implication](https://mlsanity.com/paper/2110.01746/) (2021)
- [Deep Stable Representation Learning on Electronic Health Records](https://mlsanity.com/paper/2209.01321/) (2022)
- [Calibrated and Conformal Propensity Scores for Causal Effect Estimation](https://mlsanity.com/paper/2306.00382/) (2023)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [Interpretable Multiple Treatment Revenue Uplift Modeling](https://mlsanity.com/paper/2101.03336/) (2021)
- [RealPatch: A Statistical Matching Framework for Model Patching with Real Samples](https://mlsanity.com/paper/2208.02192/) (2022)
- [Causal Dynamic Variational Autoencoder for Counterfactual Regression in Longitudinal Data](https://mlsanity.com/paper/2310.10559/) (2023)
- [The Importance of Causality in Decision Making: A Perspective on Recommender Systems](https://mlsanity.com/paper/2410.01822/) (2024)
- [Multiple Treatments Causal Effects Estimation with Task Embeddings and Balanced Representation Learning](https://mlsanity.com/paper/2511.09814/) (2025)
- [Multi-treatment Effect Estimation from Biomedical Data](https://mlsanity.com/paper/2112.07574/) (2021)
- [Fair Effect Attribution in Parallel Online Experiments](https://mlsanity.com/paper/2210.08338/) (2022)
- [TCFimt: Temporal Counterfactual Forecasting from Individual Multiple Treatment Perspective](https://mlsanity.com/paper/2212.08890/) (2022)
- [Conditional Front-door Adjustment for Heterogeneous Treatment Assignment Effect Estimation Under Non-adherence](https://mlsanity.com/paper/2505.05677/) (2025)
- [Which Company Adjustment Matter? Insights from Uplift Modeling on Financial Health](https://mlsanity.com/paper/2506.19049/) (2025)
- [Causal Representation Learning with Optimal Compression under Complex Treatments](https://mlsanity.com/paper/2603.11907/) (2026)
- [Supervised Learning Objectives for High-Dimensional Treatment Effects](https://mlsanity.com/paper/2605.27281/) (2026)
- [Shrinkage priors for Bayesian Substitute Confounders](https://mlsanity.com/paper/2606.18535/) (2026)
- [Ensuring Trustworthy Online A/B Testing: Addressing Five Key Questions on CUPED](https://mlsanity.com/paper/2606.18750/) (2026)
- [Estimating Treatment Effects for Depression in Longitudinal Therapy Switching Settings](https://mlsanity.com/paper/2607.27214/) (2026)

## Abstract (arXiv)

The propensity score is a common tool for estimating the causal effect of a binary treatment in observational data. In this setting, matching, subclassification, imputation, or inverse probability weighting on the propensity score can reduce the initial covariate bias between the treatment and control groups. With more than two treatment options, however, estimation of causal effects requires additional assumptions and techniques, the implementations of which have varied across disciplines. This paper reviews current methods, and it identifies and contrasts the treatment effects that each one estimates. Additionally, we propose possible matching techniques for use with multiple, nominal categorical treatments, and use simulations to show how such algorithms can yield improved covariate similarity between those in the matched sets, relative the pre-matched cohort. To sum, this manuscript provides a synopsis of how to notate and use causal methods for categorical treatments.