A SEMIPARAMETRIC MODELING APPROACH USING BAYESIAN ADDITIVE REGRESSION TREES WITH AN APPLICATION TO EVALUATE...

Area of Science:

• Statistics
• Machine Learning
• Biostatistics

Background:

• Bayesian Additive Regression Trees (BART) is a powerful machine learning algorithm for modeling complex relationships.
• Existing BART methods may not adequately handle situations requiring specific modeling of treatment effects and confounders.

Purpose of the Study:

• To extend BART to a semiparametric regression framework for improved causal inference.
• To develop a Bayesian semiparametric linear regression model that allows for unspecified functional forms of confounders while maintaining a linear form for treatment and effect modifiers.

Main Methods:

• Developed a semiparametric extension of BART.
• Integrated a linear component for treatment and effect modifiers with a flexible component for confounders.
• The model allows for interpretable posterior distributions for the linear parameters, akin to parametric Bayesian regression.

Main Results:

• The proposed semiparametric BART model effectively captures nonlinearities and interactions.
• Demonstrated utility in causal modeling, potentially serving as a Bayesian Structural Mean Model (SMM).
• Validated through simulation studies and an application to HIV/Hepatitis C coinfection data.

Conclusions:

• The semiparametric BART framework offers a flexible and interpretable approach for regression and causal inference.
• The `semibart` R package provides practical implementation of these advanced statistical methods.
• This method is particularly useful when controlling for nuisance variables while focusing on specific variables of interest.