Bayesian Hierarchical Models With Calibrated Mixtures of g‐priors for Assessing Treatment Effect Moderation in Meta‐Analysis

ABSTRACT Assessing treatment effect moderation is critical in biomedical science and many other fields, as it guides personalized interventions to improve individual health outcomes. Individual participant‐level data meta‐analysis (IPD‐MA) offers a robust framework for such assessments by leveraging data from multiple studies. However, its performance is often compromised by real‐world challenges, including but not limited to high between‐study variability or small magnitude of moderation effect. Traditional Bayesian shrinkage methods have gained popularity in addressing these challenges, but are less suitable in MA, as their priors do not discern heterogeneous studies. In this paper, we propose calibrated mixtures of g‐priors in IPD‐MA to enhance efficiency and reduce risks in estimating moderation effects, providing a novel series of priors tailored for multiple studies by incorporating a study‐level calibration parameter and a moderator‐level shrinkage. This design offers a flexible range of shrinkage levels, allowing practitioners to evaluate moderator importance from conservative and optimistic perspectives. Compared with existing Bayesian shrinkage methods, our simulation studies demonstrate that calibrated mixtures of g‐priors exhibit equivalent or superior performances in estimating moderation effects. The benefits of the proposed methods are particularly pronounced in scenarios with high between‐study variability, high model sparsity, weak moderation effects, and correlated design matrices. We illustrate their application in assessing moderators of two treatments for major depressive disorder, using IPD from four randomized controlled trials.