Bayesian biomarker effect estimate for combining data from multiple biomarker studies

Pooling data from multiple studies enhances statistical power and precision for quantifying biomarker-disease associations. However, inter-study variability in biomarker measurements exists, requiring calibration to a reference assay to standardize biomarker data across contributing studies before pooling. In this study, we develop a novel Bayesian Biomarker Pooling (BBP) method to aggregate biomarker data from multiple study sources, which considers the reference measurements of biospecimens that have not been re-assayed as unobservable latent variables. We establish a two-level model of studies and biospecimens to delineate the relationships among reference measurements, local measurements, and outcomes. Furthermore, we compare the proposed BBP method with several prevalent methodologies: the internalized method, the full calibration method, the two-stage method, the naïve method, and the x-only method. Our results demonstrate that the BBP method outperforms the other methods. This advantage is particularly pronounced in scenarios involving high noise and strong effects. As an illustrative example, we apply these methods in a pooling analysis to evaluate the association between Human Epidermal Growth Factor Receptor 2 (HER2) gene expression levels and breast cancer risk. The full package is available online at https://github.com/luyiyun/bayesian_biomark_pooling.