A Bayesian Additive Regression Trees Framework for Individualized Causal Effect Estimation

Lulu He, Lixia Cao, Tonghui Wang (), Zhenqi Cao and Xin Shi
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Lulu He: School of Science, Xi’an Technological University, Xi’an 710064, China
Lixia Cao: School of Science, Xi’an Technological University, Xi’an 710064, China
Tonghui Wang: Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA
Zhenqi Cao: School of Science, Xi’an Technological University, Xi’an 710064, China
Xin Shi: School of Science, Xi’an Technological University, Xi’an 710064, China

Mathematics, 2025, vol. 13, issue 13, 1-30

Abstract: In causal inference research, accurate estimation of individualized treatment effects (ITEs) is at the core of effective intervention. This paper proposes a dual-structure ITE-estimation model based on Bayesian Additive Regression Trees (BART), which constructs independent BART sub-models for the treatment and control groups, estimates ITEs using the potential outcome framework and enhances posterior stability and estimation reliability through Markov Chain Monte Carlo (MCMC) sampling. Based on psychological stress questionnaire data from graduate students, the study first integrates BART with the Shapley value method to identify employment pressure as a key driving factor and reveals substantial heterogeneity in ITEs across subgroups. Furthermore, the study constructs an ITE model using a dual-structured BART framework (BART-ITE), where employment pressure is defined as the treatment variable. Experimental results show that the model performs well in terms of credible interval width and ranking ability, demonstrating superior heterogeneity detection and individual-level sorting. External validation using both the Bootstrap method and matching-based pseudo-ITE estimation confirms the robustness of the proposed model. Compared with mainstream meta-learning methods such as S-Learner, X-Learner and Bayesian Causal Forest, the dual-structure BART-ITE model achieves a favorable balance between root mean square error and bias. In summary, it offers clear advantages in capturing ITE heterogeneity and enhancing estimation reliability and individualized decision-making.

Keywords: individual-treatment effect; Bayesian additive regression trees; Shapley values; heterogeneous treatment effects (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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