Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation

This article develops a sparsity-inducing version of Bayesian Causal Forests, a recently proposed nonparametric causal regression model that employs Bayesian Additive Regression Trees and is specifically designed to estimate heterogeneous treatment effects using observational data. The sparsity-inducing component we introduce is motivated by empirical studies where not all the available covariates are relevant, leading to different degrees of sparsity underlying the surfaces of interest in the estimation of individual treatment effects. The extended version presented in this work, which we name Shrinkage Bayesian Causal Forest, is equipped with an additional pair of priors allowing the model to adjust the weight of each covariate through the corresponding number of splits in the tree ensemble. These priors improve the model’s adaptability to sparse data generating processes and allow to perform fully Bayesian feature shrinkage in a framework for treatment effects estimation, and thus to uncover the moderating factors driving heterogeneity. In addition, the method allows prior knowledge about the relevant confounding covariates and the relative magnitude of their impact on the outcome to be incorporated in the model. We illustrate the performance of our method in simulated studies, in comparison to Bayesian Causal Forest and other state-of-the-art models, to demonstrate how it scales up with an increasing number of covariates and how it handles strongly confounded scenarios. Finally, we also provide an example of application using real-world data. Supplementary materials for this article are available online.

本文提出了一种带稀疏性诱导的贝叶斯因果森林（Bayesian Causal Forests）变体。贝叶斯因果森林是近年提出的非参数因果回归模型，采用贝叶斯可加回归树（Bayesian Additive Regression Trees），专为利用观测数据估计异质性处理效应而设计。我们引入的稀疏性诱导组件，其设计动机来自实证研究场景：并非所有可用协变量均具有相关性，这导致个体处理效应估计中所关注的曲面存在不同程度的稀疏性。本文提出的扩展模型我们命名为收缩型贝叶斯因果森林（Shrinkage Bayesian Causal Forest），该模型新增了一组先验，使得模型可通过树集成的对应分裂次数调整每个协变量的权重。这类先验提升了模型对稀疏数据生成过程的适配能力，同时可在处理效应估计框架内实现完整的贝叶斯特征收缩，进而揭示驱动异质性的调节因素。此外，该方法还支持将关于相关混淆协变量及其对结果变量影响相对强度的先验知识融入模型。我们通过模拟研究验证了所提方法的性能，并与贝叶斯因果森林及其他当前最优模型进行对比，展示了其随协变量数量增加的扩展性，以及在强混淆场景下的处理能力。本文还提供了一个基于真实世界数据的应用示例。本文的补充材料可在线获取。