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Fully Bayesian hierarchical modelling in two stages, with application to meta‐analysis

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Summary. Meta‐analysis is often undertaken in two stages, with each study analysed separately in stage 1 and estimates combined across studies in stage 2. The study‐specific estimates are assumed to arise from normal distributions with known variances equal to their corresponding estimates. In contrast, a one‐stage analysis estimates all parameters simultaneously. A Bayesian one‐stage approach offers additional advantages, such as the acknowledgement of uncertainty in all parameters and greater flexibility. However, there are situations when a two‐stage strategy is compelling, e.g. when study‐specific analyses are complex and/or time consuming. We present a novel method for fitting the full Bayesian model in two stages, hence benefiting from its advantages while retaining the convenience and flexibility of a two‐stage approach. Using Markov chain Monte Carlo methods, posteriors for the parameters of interest are derived separately for each study. These are then used as proposal distributions in a computationally efficient second stage. We illustrate these ideas on a small binomial data set; we also analyse motivating data on the growth and rupture of abdominal aortic aneurysms. The two‐stage Bayesian approach closely reproduces a one‐stage analysis when it can be undertaken, but can also be easily carried out when a one‐stage approach is difficult or impossible.

Document Type: Research Article


Affiliations: Medical Research Council Biostatistics Unit, Cambridge, UK

Publication date: 2013-08-01

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