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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...

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Detalles Bibliográficos
Autores principales: Lunn, David, Barrett, Jessica, Sweeting, Michael, Thompson, Simon
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Blackwell Publishing Ltd 2013
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.
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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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