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

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.