# Estimation of Causal Effects of Multiple Treatments in Observational Studies with a Binary Outcome

arXiv: https://arxiv.org/abs/2001.06483 · HTML: https://mlsanity.com/paper/2001.06483/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 13 of 13)

- [Causal Effect Estimation: Recent Advances, Challenges, and Opportunities](https://mlsanity.com/paper/2302.00848/) (2023)
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- [Generalized Causal Tree for Uplift Modeling](https://mlsanity.com/paper/2202.02416/) (2022)
- [Heterogeneous Treatment Effect Estimation for Observational Data using Model-based Forests](https://mlsanity.com/paper/2210.02836/) (2022)
- [Bayesian Causal Forests for Multivariate Outcomes: Application to Irish Data From an International Large Scale Education Assessment](https://mlsanity.com/paper/2303.04874/) (2023)
- [A flexible Bayesian g-formula for causal survival analyses with time-dependent confounding](https://mlsanity.com/paper/2402.02306/) (2024)
- [Variable selection with missing data in both covariates and outcomes: Imputation and machine learning](https://mlsanity.com/paper/2104.02769/) (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)
- [CIMLA: Interpretable AI for inference of differential causal networks](https://mlsanity.com/paper/2304.12523/) (2023)
- [Educational Effects in Mathematics: Conditional Average Treatment Effect depending on the Number of Treatments](https://mlsanity.com/paper/2411.01498/) (2024)
- [Causal rule ensemble approach for multi-arm data](https://mlsanity.com/paper/2504.17166/) (2025)
- [Estimating Treatment Effects with Independent Component Analysis](https://mlsanity.com/paper/2507.16467/) (2025)

## Abstract (arXiv)

There is a dearth of robust methods to estimate the causal effects of multiple treatments when the outcome is binary. This paper uses two unique sets of simulations to propose and evaluate the use of Bayesian Additive Regression Trees (BART) in such settings. First, we compare BART to several approaches that have been proposed for continuous outcomes, including inverse probability of treatment weighting (IPTW), targeted maximum likelihood estimator (TMLE), vector matching and regression adjustment. Results suggest that under conditions of non-linearity and non-additivity of both the treatment assignment and outcome generating mechanisms, BART, TMLE and IPTW using generalized boosted models (GBM) provide better bias reduction and smaller root mean squared error. BART and TMLE provide more consistent 95 per cent CI coverage and better large-sample convergence property. Second, we supply BART with a strategy to identify a common support region for retaining inferential units and for avoiding extrapolating over areas of the covariate space where common support does not exist. BART retains more inferential units than the generalized propensity score based strategy, and shows lower bias, compared to TMLE or GBM, in a variety of scenarios differing by the degree of covariate overlap. A case study examining the effects of three surgical approaches for non-small cell lung cancer demonstrates the methods.