Abstract

We introduce a Bayesian approach which estimates and adjusts for selection bias in a set of studies used in a meta-analysis. We use a hierarchical model for study outcome, and propose an additional model component to account for publication bias, which is the possibility that studies of interest are not equally likely to be published and hence observed studies are not a random sample. Estimation is based on the data augmentation principle and the number and outcomes of unobserved studies are simulated using Gibbs sampling methods. After examining simulation performance, we apply our techniques to a meta-analysis of 35 studies of the relationship between lung cancer and spousal exposure to environmental tobacco smoke. We find that the 95% posterior probability interval for relative risk is shifted downward after allowing for this. These results are consistent with earlier, ad hoc, approaches to this problem. Keywords and phrases: Meta-analysis, publication bias, missing studies, Markov...

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