Applied Bayesian Modelling, 2nd Edition

Chapter 5Meta-analysis and multilevel models

5.1 Introduction

Meta-analysis and multilevel analysis are related techniques seeking to draw inferences regarding individual clusters or subjects from a broader collection of observations. The focus in Section 5.2 of this chapter is on hierarchical meta-analysis, namely methods for combining the results of independent studies to provide an estimate of a presumed common effect (e.g. treatment gain, environmental risk), while recognising heterogeneity between studies. Meta-analysis uses findings from sets of studies, assumed similar enough to be considered exchangeable, and typically uses summary statistics from originally multilevel or longitudinal studies, where subjects and clusters are analysed jointly.

The remaining sections in this chapter consider multilevel techniques (with longitudinal studies discussed in Chapter 7). Multilevel studies also adopt a hierarchical random effects approach (e.g. Goldstein, 2011), though fixed effects models for clustered data, particularly the varying intercept case, are sometimes used. The dual aims are then to allow for contextual or cluster effects on individual level outcomes, and conversely adjust contextual effects to fully reflect individual subject variation (e.g. Courgeau and Baccaini, 1997; Blakely and Woodward, 2000; Diez-Roux, 2004; Clarke, 2008). Multilevel analysis seeks to avoid ecological bias potentially present in studies simply of aggregate unit data, including meta-analysis ...