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September 2019 A semiparametric modeling approach using Bayesian Additive Regression Trees with an application to evaluate heterogeneous treatment effects
Bret Zeldow, Vincent Lo Re III, Jason Roy
Ann. Appl. Stat. 13(3): 1989-2010 (September 2019). DOI: 10.1214/19-AOAS1266

Abstract

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.

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Bret Zeldow. Vincent Lo Re III. Jason Roy. "A semiparametric modeling approach using Bayesian Additive Regression Trees with an application to evaluate heterogeneous treatment effects." Ann. Appl. Stat. 13 (3) 1989 - 2010, September 2019. https://doi.org/10.1214/19-AOAS1266

Information

Received: 1 June 2018; Revised: 1 May 2019; Published: September 2019
First available in Project Euclid: 17 October 2019

zbMATH: 07145982
MathSciNet: MR4019164
Digital Object Identifier: 10.1214/19-AOAS1266

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.13 • No. 3 • September 2019
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