Bivariate Hierarchical Bayesian Model for Combining Summary Measures and their Uncertainties from Multiple Sources

TL;DR

This paper introduces a bivariate hierarchical Bayesian model that jointly analyzes estimates and their variances, accounting for correlation, to improve data synthesis across multiple sources in various applications.

Contribution

It presents a novel Bayesian model that jointly models estimates and variances with correlation, enhancing data integration methods.

Findings

The model performs well across different correlation scenarios.

Simulation studies show improved accuracy over traditional methods.

Applications demonstrate versatility in diverse fields.

Abstract

It is often of interest to combine available estimates of a similar quantity from multiple data sources. When the corresponding variances of each estimate are also available, a model should take into account the uncertainty of the estimates themselves as well as the uncertainty in the estimation of variances. In addition, if there exists a strong association between estimates and their variances, the correlation between these two quantities should also be considered. In this paper, we propose a bivariate hierarchical Bayesian model that jointly models the estimates and their estimated variances assuming a correlation between these two measures. We conduct simulations to explore the performance of the proposed bivariate Bayesian model and compare it to other commonly used methods under different correlation scenarios. The proposed bivariate Bayesian model has a wide range of applications. We illustrate its application in three very different areas: PET brain imaging studies, meta-analysis, and small area estimation.