Bayesian hierarchical models with calibrated mixtures of g-priors for assessing treatment effect moderation in meta–analysis

Music City Center 

Assessing treatment effect moderation is critical in biomedical research and many other fields, as it guides personalized intervention strategies to improve participant's 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 challenges such as high between-study variability or small magnitude of moderation effect. Traditional Bayesian shrinkage methods have gained popularity, but are less suitable in MA, as their priors do not discern heterogeneous studies. In this paper, we propose the calibrated mixtures of g–priors in IPD–MA to enhance efficiency and reduce risks in the estimation of 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 both conservative and optimistic perspectives. Compared with existing Bayesian shrinkage methods, our extensive simulation studies demonstrate that the calibrated mixtures of g–priors exhibit superior performances in terms of efficiency and risk metrics, particularly under high between–study variability, high model sparsity, weak moderation effects and correlated design matrices. We further illustrate their application in assessing effect moderators of two active treatments for major depressive disorder, using IPD from four randomized controlled trials.

Calibrated mixtures of g–priors

Treatment effect moderation

Individual participant-level data

Shrinkage method

Meta-analysis

Major depression disorder