Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects (1706.09523v4)

Abstract: This paper presents a novel nonlinear regression model for estimating heterogeneous treatment effects from observational data, geared specifically towards situations with small effect sizes, heterogeneous effects, and strong confounding. Standard nonlinear regression models, which may work quite well for prediction, have two notable weaknesses when used to estimate heterogeneous treatment effects. First, they can yield badly biased estimates of treatment effects when fit to data with strong confounding. The Bayesian causal forest model presented in this paper avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. Second, standard approaches to response surface modeling do not provide adequate control over the strength of regularization over effect heterogeneity. The Bayesian causal forest model permits treatment effect heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively "shrink to homogeneity". We illustrate these benefits via the reanalysis of an observational study assessing the causal effects of smoking on medical expenditures as well as extensive simulation studies.

• The paper presents a Bayesian causal forest model that isolates treatment effects and reduces bias from confounding.
• It employs a modular structure to separate prognostic effects from treatment effects through distinct regularization.
• Empirical evaluations demonstrate improved precision in estimating heterogeneous effects in challenging observational scenarios.

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects

The paper "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" presents a novel approach to estimating heterogeneous treatment effects from observational data using Bayesian causal forests. This work engages with the weaknesses of traditional nonlinear regression models in the context of small effect sizes, strong confounding, and treatment effect heterogeneity, proposing methodological enhancements through the Bayesian causal forest model.

Key Contributions

The Bayesian causal forest model is positioned as a robust alternative to standard regression models, most notably addressing the following weaknesses:

1. Bias Due to Confounding: Traditional models often yield biased treatment effect estimates when confounding is pronounced. The Bayesian causal forest model integrates an estimate of the propensity function into the response model specification, which implicitly induces a covariate-dependent prior on the regression function, thus mitigating this bias.
2. Regularization of Treatment Effect Heterogeneity: Standard response surface modeling approaches lack robust control over regularization of treatment effect heterogeneity. The new model allows for distinct regularization of treatment effect heterogeneity and prognostic effects through a sum-of-regression-trees representation. This separation enables informative shrinkage towards homogeneity where appropriate.

Methodology

The proposed methodology builds upon previous work in Bayesian hierarchical modeling and regression trees. The paper's model is implemented through a Bayesian additive regression tree (BART) prior on the regression function. The primary innovation lies in the parameterization that isolates the treatment effect within the model:

• Modular Regression Structure: The model introduces a modular structure for the regression function, expressed as the sum of two components — a prognostic function and a treatment effect function. Each component is represented as a 'forest', adhering to BART's framework.
• Covariate-Dependent Priors: By including the propensity score as a covariate, the model leverages response surface estimation to handle confounding. This strategy grounds the model's flexibility while maintaining control over confounding-induced bias.

Empirical Evaluation

The research underpins these theoretical advances with empirical assessments using simulation studies and a reanalysis of the impact of smoking on medical expenditures. These simulations reveal significant improvements in the precision of treatment effect estimates, particularly under conditions of strong confounding and targeted selection. Moreover, the application to observational data reinforces the model's adaptability and practical utility in deriving meaningful causal inferences from complex datasets.

Implications and Future Directions

This paper lays important groundwork for integrating machine learning approaches with causal inference. The Bayesian causal forest model offers substantial improvements over existing methodologies in addressing confounding bias and effect heterogeneity. The separation of prognostic and treatment effect modeling allows for more transparent and interpretable analysis of treatment impacts.

The implications of this work are primarily in fields where observational studies dominate and randomized experiments are unfeasible. Future research may extend these models to dynamic treatment regimes or explore the interaction of different forms of heterogeneity in complex systems. As computational power increases, the analytical depth brought by Bayesian methods like these will become even more pivotal in applied statistical inference.

In conclusion, the development of Bayesian causal forests marks an advancement in the toolkit available for causal inference, offering a nuanced approach to regularization and confounding in treatment effect estimation. This paper contributes not just a methodological innovation, but also a paradigm for integrating statistical rigor with flexible modeling frameworks in causal analysis.