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Non-Gaussian normative modelling with hierarchical Bayesian regression.

Augustijn A A de Boer1,2, Johanna M M Bayer1,2, Seyed Mostafa Kia1,2,3

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Summary
This summary is machine-generated.

This study introduces a flexible Bayesian regression model for normative modeling, improving analysis of diverse clinical data by handling non-Gaussian distributions and site variations effectively.

Keywords:
hierarchical Bayesian regressionneuroimagingnormative modellingprecision psychiatry

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Area of Science:

  • Biostatistics
  • Neuroimaging Analysis
  • Machine Learning in Healthcare

Background:

  • Normative modeling analyzes clinical cohort heterogeneity.
  • Hierarchical Bayesian regression handles site variation in federated learning.
  • Existing methods often assume Gaussian distributions, limiting applicability.

Purpose of the Study:

  • Extend hierarchical Bayesian regression for non-Gaussian data.
  • Incorporate flexible distributions (sinh-arcsinh family) for skewness and kurtosis.
  • Improve normative modeling for complex clinical and imaging data.

Main Methods:

  • Developed a novel reparameterization for the sinh-arcsinh (SHASH) distribution.
  • Implemented a Markov chain Monte Carlo (MCMC) sampling approach for inference.
  • Applied the extended framework to a large neuroimaging dataset from 82 sites.

Main Results:

  • The extended model achieved equivalent or superior results compared to a warped Bayesian linear regression baseline.
  • Demonstrated enhanced control over distribution shape parameters.
  • Successfully modeled highly nonlinear relationships between aging and imaging phenotypes.

Conclusions:

  • The flexible Bayesian regression framework advances normative modeling capabilities.
  • This extension is crucial for accurately analyzing complex, non-Gaussian clinical and neuroimaging data.
  • The methods are available in the open-source pcntoolkit for broader application.