Bayesian Random-Effects Meta-Analysis Integrating Individual Participant Data and Aggregate Data

Meta-analysis using individual participant data (IPD) offers many benefits, including greater analytical flexibility, compared to conventional analyses based on aggregate data (AD). However, it is often hindered by restricted access to IPD. Relying solely on available IPD may introduce “data availability bias,” compromising external validity. Integrating IPD with relevant AD addresses this concern, but existing methods are restrictive, requiring precise knowledge of the IPD-to-AD parameter mapping or relying on fixed-effect models that fail to account for study-level heterogeneity. We propose a Bayesian random-effects framework to overcome these limitations. Building on existing methods, we use estimating equations to derive the conditional distributions of AD parameters, given the corresponding IPD model parameters. We then apply the multiplier bootstrap method and density ratio models to approximate these conditional distributions based on the observed data, without requiring homogeneity in the covariate distributions. Both theoretical and empirical results demonstrate that our method reduces mean squared error compared to IPD-only analysis when IPD availability is independent of the data, and reduces bias when data availability is dependent. We apply this integrated approach to complement the IPD-only analysis in the International Weight Management in Pregnancy (i-WIP) Collaborative Group study.