  Bayesian Additive Regression Trees (BART) is a flexible machine learning
algorithm capable of capturing nonlinearities between an outcome and covariates
and interaction 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, not of
scientific interest, are allowed to have unspecified functional form, while
treatment and other covariates that do have scientific importance are given the
usual linear form from parametric regression. 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 semibart.
