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Borrowing Strength and Borrowing Index for Bayesian Hierarchical Models.

Ganggang Xu1, Huirong Zhu2, J Jack Lee3

  • 1Department of Management Science, University of Maimi, FL, 33146, USA.

Computational Statistics & Data Analysis
|April 29, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces new methods to measure borrowing strength in Bayesian hierarchical models. These tools help understand prior influences on statistical inferences in various applications, including clinical trials.

Keywords:
Bayesian Hierarchical ModelBorrowing IndexBorrowing StrengthClinical TrialsMallow’s Distance

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Computational Statistics

Background:

  • Bayesian hierarchical models are widely used in statistical inference.
  • Understanding prior influence on posterior distributions is crucial but often ambiguous.
  • Existing methods for quantifying borrowing strength are limited.

Purpose of the Study:

  • To propose novel measures for quantifying borrowing strength in Bayesian hierarchical models.
  • To develop an overall borrowing index for subgroup analysis.
  • To enhance understanding of prior-posterior relationships in statistical modeling.

Main Methods:

  • Developed a novel borrowing strength measure and an overall borrowing index.
  • Constructed indexes based on Mallow's distance.
  • Utilized Markov Chain Monte Carlo (MCMC) samples for computation of univariate and multivariate posterior distributions.

Main Results:

  • The proposed indexes provide meaningful exploratory tools for Bayesian hierarchical models.
  • The methods effectively quantify the strength of borrowing behaviors among subgroups.
  • Demonstrated applicability to continuous and binary outcome variables.

Conclusions:

  • The novel borrowing strength measures offer valuable insights into prior influence in hierarchical models.
  • The proposed approach is adaptable to diverse settings, including clinical trials.
  • The methods facilitate better statistical inference by clarifying prior-posterior relationships.