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Bivariate random-effects meta-analysis and the estimation of between-study correlation
BACKGROUND: When multiple endpoints are of interest in evidence synthesis, a multivariate meta-analysis can jointly synthesise those endpoints and utilise their correlation. A multivariate random-effects meta-analysis must incorporate and estimate the between-study correlation (ρ(B)). METHODS: In th...
Autores principales: | , , , , |
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Formato: | Texto |
Lenguaje: | English |
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BioMed Central
2007
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1800862/ https://www.ncbi.nlm.nih.gov/pubmed/17222330 http://dx.doi.org/10.1186/1471-2288-7-3 |
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author | Riley, Richard D Abrams, Keith R Sutton, Alexander J Lambert, Paul C Thompson, John R |
author_facet | Riley, Richard D Abrams, Keith R Sutton, Alexander J Lambert, Paul C Thompson, John R |
author_sort | Riley, Richard D |
collection | PubMed |
description | BACKGROUND: When multiple endpoints are of interest in evidence synthesis, a multivariate meta-analysis can jointly synthesise those endpoints and utilise their correlation. A multivariate random-effects meta-analysis must incorporate and estimate the between-study correlation (ρ(B)). METHODS: In this paper we assess maximum likelihood estimation of a general normal model and a generalised model for bivariate random-effects meta-analysis (BRMA). We consider two applied examples, one involving a diagnostic marker and the other a surrogate outcome. These motivate a simulation study where estimation properties from BRMA are compared with those from two separate univariate random-effects meta-analyses (URMAs), the traditional approach. RESULTS: The normal BRMA model estimates ρ(B )as -1 in both applied examples. Analytically we show this is due to the maximum likelihood estimator sensibly truncating the between-study covariance matrix on the boundary of its parameter space. Our simulations reveal this commonly occurs when the number of studies is small or the within-study variation is relatively large; it also causes upwardly biased between-study variance estimates, which are inflated to compensate for the restriction on [Formula: see text] (B). Importantly, this does not induce any systematic bias in the pooled estimates and produces conservative standard errors and mean-square errors. Furthermore, the normal BRMA is preferable to two normal URMAs; the mean-square error and standard error of pooled estimates is generally smaller in the BRMA, especially given data missing at random. For meta-analysis of proportions we then show that a generalised BRMA model is better still. This correctly uses a binomial rather than normal distribution, and produces better estimates than the normal BRMA and also two generalised URMAs; however the model may sometimes not converge due to difficulties estimating ρ(B). CONCLUSION: A BRMA model offers numerous advantages over separate univariate synthesises; this paper highlights some of these benefits in both a normal and generalised modelling framework, and examines the estimation of between-study correlation to aid practitioners. |
format | Text |
id | pubmed-1800862 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2007 |
publisher | BioMed Central |
record_format | MEDLINE/PubMed |
spelling | pubmed-18008622007-02-26 Bivariate random-effects meta-analysis and the estimation of between-study correlation Riley, Richard D Abrams, Keith R Sutton, Alexander J Lambert, Paul C Thompson, John R BMC Med Res Methodol Research Article BACKGROUND: When multiple endpoints are of interest in evidence synthesis, a multivariate meta-analysis can jointly synthesise those endpoints and utilise their correlation. A multivariate random-effects meta-analysis must incorporate and estimate the between-study correlation (ρ(B)). METHODS: In this paper we assess maximum likelihood estimation of a general normal model and a generalised model for bivariate random-effects meta-analysis (BRMA). We consider two applied examples, one involving a diagnostic marker and the other a surrogate outcome. These motivate a simulation study where estimation properties from BRMA are compared with those from two separate univariate random-effects meta-analyses (URMAs), the traditional approach. RESULTS: The normal BRMA model estimates ρ(B )as -1 in both applied examples. Analytically we show this is due to the maximum likelihood estimator sensibly truncating the between-study covariance matrix on the boundary of its parameter space. Our simulations reveal this commonly occurs when the number of studies is small or the within-study variation is relatively large; it also causes upwardly biased between-study variance estimates, which are inflated to compensate for the restriction on [Formula: see text] (B). Importantly, this does not induce any systematic bias in the pooled estimates and produces conservative standard errors and mean-square errors. Furthermore, the normal BRMA is preferable to two normal URMAs; the mean-square error and standard error of pooled estimates is generally smaller in the BRMA, especially given data missing at random. For meta-analysis of proportions we then show that a generalised BRMA model is better still. This correctly uses a binomial rather than normal distribution, and produces better estimates than the normal BRMA and also two generalised URMAs; however the model may sometimes not converge due to difficulties estimating ρ(B). CONCLUSION: A BRMA model offers numerous advantages over separate univariate synthesises; this paper highlights some of these benefits in both a normal and generalised modelling framework, and examines the estimation of between-study correlation to aid practitioners. BioMed Central 2007-01-12 /pmc/articles/PMC1800862/ /pubmed/17222330 http://dx.doi.org/10.1186/1471-2288-7-3 Text en Copyright © 2007 Riley et al; licensee BioMed Central Ltd. http://creativecommons.org/licenses/by/2.0 This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( (http://creativecommons.org/licenses/by/2.0) ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Research Article Riley, Richard D Abrams, Keith R Sutton, Alexander J Lambert, Paul C Thompson, John R Bivariate random-effects meta-analysis and the estimation of between-study correlation |
title | Bivariate random-effects meta-analysis and the estimation of between-study correlation |
title_full | Bivariate random-effects meta-analysis and the estimation of between-study correlation |
title_fullStr | Bivariate random-effects meta-analysis and the estimation of between-study correlation |
title_full_unstemmed | Bivariate random-effects meta-analysis and the estimation of between-study correlation |
title_short | Bivariate random-effects meta-analysis and the estimation of between-study correlation |
title_sort | bivariate random-effects meta-analysis and the estimation of between-study correlation |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1800862/ https://www.ncbi.nlm.nih.gov/pubmed/17222330 http://dx.doi.org/10.1186/1471-2288-7-3 |
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