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Case Studies in Bayesian Statistical Modelling and Analysis by Anthony N. Pettitt, Kerrie L. Mengersen, Clair L. Alston

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7

Bayesian Meta-Analysis

Jegar O. Pitchforth and Kerrie L. Mengersen

Queensland University of Technology, Brisbane, Australia

7.1 Introduction

Meta-analysis is the process of quantitatively combining a set of estimates about an outcome of interest. Typically, these estimates are obtained from a set of studies identified through a systematic review of relevant literature on the topic. The combined analysis reduces dependence on any one finding or narrative and ‘borrows strength’ across studies which may each provide inconclusive, or conclusive but conflicting evidence. Bayesian meta-analysis has advantages over frequentist approaches in that it provides a more flexible modelling framework, allows more appropriate quantification of the uncertainty around effect estimates, and facilitates a clearer understanding of sources of variation within and between studies (Sutton and Abrams 2001).

In this chapter, we describe Bayesian meta-analysis models and their attributes through two substantive case studies.

The first study is illustrative of a very wide range of univariate meta-analyses that can be described using a standard random effects model. Extensions to this model are also described. These include the extension of the hierarchical structure of the model to allow for dependencies between the studies, incorporation of covariates via meta-regression, and analysis of multiple effects via a full multivariate meta-analysis model. Although not all of these extensions are employed in ...

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