Bayesian additive regression trees for multivariate skewed responses.

Area of Science:

• Biostatistics
• Statistical modeling
• Machine learning in healthcare

Background:

• Bayesian additive regression trees (BART) are popular for accurate prediction but typically assume Gaussian errors.
• Gaussian error assumptions are often violated in biomedical applications, limiting BART's utility.
• Existing methods lack flexibility for skewed or multivariate response data.

Purpose of the Study:

• To introduce a novel nonparametric regression approach for univariate and multivariate skewed response data.
• To extend Bayesian additive regression trees (BART) to accommodate non-Gaussian error distributions, specifically skewed responses.
• To develop a flexible model for analyzing complex, associated skewed data within subjects.

Main Methods:

• Developed the skewBART model, an extension of BART for skewed response variables.
• Extended skewBART to handle multivariate skewed responses, enabling information sharing across decision trees for different responses.
• The methodology accounts for within-subject associations and allows for varying skewness parameters.

Main Results:

• Demonstrated the effectiveness of the multivariate skewBART model through simulation studies.
• Applied the model to a bivariate, highly skewed oral health dataset, showcasing its advantages over existing methods.
• The skewBART model provides a robust alternative for analyzing skewed biomedical data.

Conclusions:

• The skewBART model offers a significant advancement for regression with skewed and multivariate responses in biomedical research.
• This flexible approach improves upon standard BART by relaxing restrictive distributional assumptions.
• The R package skewBART is available, facilitating the implementation of this advanced statistical methodology.