Multi-Level Variable Selection Using a BART-Enhanced Mixed-Effects Framework

Area of Science:

• Biostatistics
• Health Data Science
• Statistical Modeling

Background:

• Healthcare data often has hierarchical structures, requiring multilevel variable selection.
• Existing methods using mixed-effects models have limitations with nonlinear relationships and interactions.
• Nonparametric methods for multilevel data are less studied and often focus on prediction, not simultaneous selection.

Purpose of the Study:

• To develop a flexible, Bayesian framework for simultaneous variable selection of fixed and random effects in multilevel data.
• To integrate nonparametric flexibility with hierarchical Bayesian modeling for robust predictor identification.
• To address collinearity and instability issues common in multilevel cluster-level predictors.

Main Methods:

• A unified Bayesian framework combining Bayesian Additive Regression Trees (BART) for fixed effects.
• Hierarchical Bayesian component for random-effect predictor identification using covariance decomposition and permutation.
• A computationally efficient two-step procedure to disentangle individual- and cluster-level predictor contributions.

Main Results:

• The proposed methods demonstrate effectiveness and robustness across diverse simulation scenarios.
• The framework successfully identifies relevant predictors at both individual and cluster levels.
• The two-step procedure effectively mitigates collinearity and enhances selection stability.

Conclusions:

• The developed Bayesian framework offers a flexible and powerful approach for simultaneous variable selection in multilevel data.
• This method overcomes limitations of existing parametric and nonparametric techniques.
• The approach is applicable to complex health research, as shown in an Alzheimer's disease dataset analysis.