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Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis
Article first published online: 4 APR 2013
© 2013 Royal Statistical Society
Journal of the Royal Statistical Society: Series C (Applied Statistics)
Volume 62, Issue 4, pages 551–572, August 2013
How to Cite
Lunn, D., Barrett, J., Sweeting, M. and Thompson, S. (2013), Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis. Journal of the Royal Statistical Society: Series C (Applied Statistics), 62: 551–572. doi: 10.1111/rssc.12007
- Issue published online: 11 JUL 2013
- Article first published online: 4 APR 2013
- [Received February 2012. Final revision November 2012]
- Abdominal aortic aneurysm;
- Bayesian hierarchical modelling;
- Markov chain Monte Carlo methods;
- Random-effects meta-analysis
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.