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Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis
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 on...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Blackwell Publishing Ltd
2013
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3814003/ https://www.ncbi.nlm.nih.gov/pubmed/24223435 http://dx.doi.org/10.1111/rssc.12007 |
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author | Lunn, David Barrett, Jessica Sweeting, Michael Thompson, Simon |
author_facet | Lunn, David Barrett, Jessica Sweeting, Michael Thompson, Simon |
author_sort | Lunn, David |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-3814003 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2013 |
publisher | Blackwell Publishing Ltd |
record_format | MEDLINE/PubMed |
spelling | pubmed-38140032013-11-06 Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis Lunn, David Barrett, Jessica Sweeting, Michael Thompson, Simon J R Stat Soc Ser C Appl Stat Original Articles 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. Blackwell Publishing Ltd 2013-08 /pmc/articles/PMC3814003/ /pubmed/24223435 http://dx.doi.org/10.1111/rssc.12007 Text en © 2013 Royal Statistical Society http://creativecommons.org/licenses/by/2.5/ Re-use of this article is permitted in accordance with the Creative Commons Deed, Attribution 2.5, which does not permit commercial exploitation. |
spellingShingle | Original Articles Lunn, David Barrett, Jessica Sweeting, Michael Thompson, Simon Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis |
title | Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis |
title_full | Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis |
title_fullStr | Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis |
title_full_unstemmed | Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis |
title_short | Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis |
title_sort | fully bayesian hierarchical modelling in two stages, with application to meta-analysis |
topic | Original Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3814003/ https://www.ncbi.nlm.nih.gov/pubmed/24223435 http://dx.doi.org/10.1111/rssc.12007 |
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