Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects

By By P. Richard Hahn, Jared S. Murray, Carlos M. Carvalho. 2017

277 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

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Citations in the corpus

Metalearners for estimating heterogeneous treatment effects using machine learning (2017, background): “For example, if F0 is the family of distributions P such that X ∼Unif[0, 1], Y =βX + ε, ε∼N (0, 1), and β ∈R, then it is well known that the ordinary least squares (OLS) estimator achieves the optimal parametric rate.”
Quasi-oracle estimation of heterogeneous treatment effects (2017, methodology): “Some notable recent advances include proposals based on the lasso (Imai and Ratkovic, 2013), recursive partitioning (Athey and Imbens, 2016; Su et al., 2009), BART (Hahn, Murray, and Carvalho, 2017; Hill, 2011), random forests (Athey, Tibshirani, and Wager, 2018; Wager and Athey, 2017), boosting (Po”
Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion) (2020, unknown): “As previously noted, the Bayesian causal forest model directly extends ideas from two earlier papers: Hill (2011) and Hahn et al. (2016). Specifically, this paper studies the “regularization-induced confounding” of Hahn et al. (2016) in the context of Bayesian additive regression tree (BART) models ”
MALTS: Matching After Learning to Stretch (2018, background): “Machine learning approaches generalize regression approaches and can create models that are extremely flexible and predict outcomes accurately for both treatment and control groups [2, 9, 10].”
Bayesian regression tree ensembles that adapt to smoothness and sparsity (2017, methodology): “…variable selection (Bleich et al., 2014; Linero, 2016), analysis of loglinear model (Murray, 2017), and survival analysis (Sparapani et al., 2016), and was among the best performing methodologies in the 2016 Atlantic Causal Inference Conference Competition (Hill, 2011, 2016; Hahn et al., 2017).”
Limits of Estimating Heterogeneous Treatment Effects: Guidelines for Practical Algorithm Design (2018, methodology): “We considered: tree-based algorithms (BART (Hill, 2011), Causal forests (Wager & Athey, 2017), Bayesian causal forests (Hahn et al., 2017)), methods based on deep learning (CFR Wass.”
A Survey of Learning Causality with Data (2018, background): “BART has several advantages [59, 65]: (1) it is good at capturing non-linearity and discontinuity, (2) it needs little hyperparameter tuning and (3) it infers posterior distribution of outcomes, which allows uncertainty quantification.”
A Survey of Learning Causality with Data: Problems and Methods (2018, methodology): “To justify the usage of BART, in [55, 59], authors mentioned that BART has shown to have several advantages over other models: BART is good at capture of non-linearities and discontinuity, it frees”