Please use this identifier to cite or link to this item:
Title: Bivariate random-effects meta-analysis and the estimation of between-study correlation
Authors: Riley, Richard D.
Abrams, Keith R.
Sutton, Alex J.
Lambert, Paul C.
Thompson, John R.
First Published: 12-Jan-2007
Publisher: BioMed Central Ltd
Citation: BMC Medical Research Methodology, 2007, 7 : 3
Abstract: 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[subscript 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[subscript 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 ρ^[subscript 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[subscript 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.
DOI Link: 10.1186/1471-2288-7-3
eISSN: 1471-2288
Version: Publisher Version
Status: Peer-reviewed
Type: Article
Rights: Copyright © 2007 Riley et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Appears in Collections:Published Articles, Dept. of Health Sciences

Files in This Item:
File Description SizeFormat 
1471-2288-7-3.pdfPublished (publisher PDF)395.98 kBAdobe PDFView/Open

Items in LRA are protected by copyright, with all rights reserved, unless otherwise indicated.