The Annals of Applied Statistics

A semiparametric modeling approach using Bayesian Additive Regression Trees with an application to evaluate heterogeneous treatment effects

Bret Zeldow, Vincent Lo Re III, and Jason Roy

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Bayesian Additive Regression Trees (BART) is a flexible machine learning algorithm capable of capturing nonlinearities between an outcome and covariates and interactions among covariates. We extend BART to a semiparametric regression framework in which the conditional expectation of an outcome is a function of treatment, its effect modifiers, and confounders. The confounders are allowed to have unspecified functional form, while treatment and effect modifiers that are directly related to the research question are given a linear form. The result is a Bayesian semiparametric linear regression model where the posterior distribution of the parameters of the linear part can be interpreted as in parametric Bayesian regression. This is useful in situations where a subset of the variables are of substantive interest and the others are nuisance variables that we would like to control for. An example of this occurs in causal modeling with the structural mean model (SMM). Under certain causal assumptions, our method can be used as a Bayesian SMM. Our methods are demonstrated with simulation studies and an application to dataset involving adults with HIV/Hepatitis C coinfection who newly initiate antiretroviral therapy. The methods are available in an R package called semibart.

Article information

Ann. Appl. Stat., Volume 13, Number 3 (2019), 1989-2010.

Received: June 2018
Revised: May 2019
First available in Project Euclid: 17 October 2019

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Mathematical Reviews number (MathSciNet)

Bayesian Additive Regression Trees structural mean model antiretrovirals


Zeldow, Bret; Lo Re III, Vincent; Roy, Jason. A semiparametric modeling approach using Bayesian Additive Regression Trees with an application to evaluate heterogeneous treatment effects. Ann. Appl. Stat. 13 (2019), no. 3, 1989--2010. doi:10.1214/19-AOAS1266.

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  • Zeldow, B., Lo Re III, V. and Roy, J. (2019). Supplement to “A semiparametric modeling approach using Bayesian Additive Regression Trees with an application to evaluate heterogeneous treatment effects.” DOI:10.1214/19-AOAS1266SUPP.

Supplemental materials

  • Supplement A: R code for semi-BART manuscript. The supplement contains R code for the simulations, analysis code for our data application, and R code for some additional simulations performed.