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

Keming Zhang1, Yaoyao Li2, Jungang Zou3

  • 1Department of Biostatistics, Brown University, Providence, Rhode Island, USA.

Statistics in Medicine
|May 18, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a novel Bayesian framework for selecting important predictors in complex healthcare data with multiple clusters. The method enhances variable selection accuracy for both individual and group levels, improving multilevel modeling.

Keywords:
Bayesian machine learningDirichlet distributionMetropolis importancenear‐collinearitypermutation‐basedspike and slab prior

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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.