Bayesian methods in meta-analysis

Meta-analysis refers to the collection and subsequent statistical analysis of results from numerous studies. The purpose of a meta-analysis is to arrive at an overall conclusion about an issue of interest based on the available data. Meta-analysis has a long history, but it has enjoyed a surge of interest and corresponding rapid methodological development in the past two decades. Philosophical and practical problems surround the combination of studies with discrepancies in aims, study designs and quality, sampling frames, populations, and reported information. Other concerns include dealing with studies of small sample size or with peculiar results, inclusion of predictors at study level, methods by which results are updated as new information is available, and accounting for the impact of other biases because of publication, selection, and so on. A Bayesian approach to meta-analysis has been advocated as a way to address many of these issues. A Bayesian model describes the structural relationship between data and unknown parameters, whereby both data and parameters are considered random variables with uncertainty. The full posterior distributions of parameters borrow strength from all studies and enable direct inference regarding probabilities about expectations and, perhaps more notably in a pharmacology context, comparisons such as the probability with which subjects receiving a particular medication are better on average recovery, symptom level, or survival, than those on an alternative medication. Moreover, by their construction, these distributions are not confined to "usual" (normal) representations or based on asymptotic assumptions, and give substantially more information than single point estimates. The article begins with a description of some applications of Bayesian approaches in meta-analysis. The steps involved in a meta-analysis are discussed next, followed by a description of Bayesian models for meta-analysis and selection of prior distributions. Computer implementation of Bayesian models for meta-analysis next, followed by extensions to the simple Bayesian model and dealing with publication bias in the Bayesian framework.2nd ed