Objective Bayesian meta-analysis based on generalized multivariate random effects model

TL;DR

This paper develops objective Bayesian methods for multivariate meta-analysis using generalized multivariate random effects models with elliptically contoured distributions, providing proper posterior conditions and applying to hypertension treatment data.

Contribution

It introduces analytical Bayesian inference procedures for the multivariate random effects model with noninformative priors under weak assumptions, ensuring posterior propriety.

Findings

Posterior is proper if sample size exceeds data dimension.

Method applied successfully to hypertension treatment data.

Analytical expressions derived for noninformative priors.

Abstract

Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data-generating model, independently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated.