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A Modified Normalized Power Prior Approach for Bayesian Adaptive Borrowing in Item Response Theory Models.

Qiang Zhang1, Wei Xiong2, Min Wang3

  • 1School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China.

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|April 30, 2026
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Summary
This summary is machine-generated.

This study introduces a Bayesian framework for adaptive borrowing in item response theory (IRT) models. The method improves estimation accuracy by adaptively using historical data, reducing uncertainty in clinical and mental health research.

Keywords:
Bayesian data augmentationadaptive borrowinghistorical informationitem response theorynormalized power prior

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Clinical Research Methodology

Background:

  • Questionnaire responses in clinical research are often subjective, leading to estimation uncertainty in item response theory (IRT) models, especially with small sample sizes.
  • Adaptive incorporation of historical data can reduce response variation but poses computational challenges for complex IRT models.
  • Existing methods struggle with computational efficiency and adaptively downweighting conflicting historical information.

Purpose of the Study:

  • To develop a computationally efficient Bayesian framework for adaptive borrowing in IRT models.
  • To enhance the precision of ability and item parameter estimation by leveraging historical data.
  • To create a method that adaptively adjusts the influence of historical data based on its compatibility with current data.

Main Methods:

  • Developed a Bayesian framework using an approximated normalized power prior (NPP) for adaptive borrowing in IRT models.
  • Treated the borrowing weight as a random parameter, making NPP applicable to general IRT models.
  • Employed a Bayesian data augmentation strategy with a Gibbs sampler for joint estimation of parameters.

Main Results:

  • The proposed method adaptively borrows information, increasing weight for compatible historical data and downweighting conflicting data.
  • Simulations demonstrated reduced variance and mean squared error compared to analyses without borrowing, while maintaining statistical coverage.
  • The approach proved effective across various test lengths, item discrimination profiles, and levels of historical-current data concordance.

Conclusions:

  • The Bayesian adaptive borrowing framework offers a robust and efficient solution for improving parameter estimation in IRT models.
  • Integrating historical data via this method leads to more precise ability estimates and preserved calibration in mental health assessments.
  • An efficient implementation is available in the updated NPP package on CRAN, facilitating broader application.