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

Questionnaires are widely used in clinical research and mental health studies, but their responses are usually more subjective than clinical biomarkers. Researchers may use latent variable models such as the item response theory (IRT) model to characterize individual ability, but response instability and small sample sizes can lead to increased uncertainty in estimation. Historical data from similar questionnaires may help reduce variation, but they must be incorporated adaptively. The challenge is further compounded by the need to ensure computational efficiency in IRT models with a large number of parameters. In this work, we develop a Bayesian framework for adaptive borrowing in IRT models based on an approximated normalized power prior (NPP) that treats the borrowing weight as a random parameter. The proposed method makes NPP feasible for general IRT models and is coupled with a full Bayesian data augmentation strategy that enables joint estimation of ability and item parameters through an efficient Gibbs sampler. In simulations, the approach adaptively increases borrowing when historical and current data are compatible and automatically downweights conflicting information. Relative to analyzes without borrowing, the method reduces variance and mean squared error while maintaining coverage across a range of test lengths, item discrimination profiles, and historical-current concordance scenarios. We illustrate the method by integrating historical mental health surveys into current assessments, yielding more precise ability estimates with preserved calibration. An efficient implementation is provided in our updated package NPP available on the Comprehensive R Archive Network.