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Multivariate meta-analysis: the effect of ignoring within-study correlation

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Summary. 

Multivariate meta-analysis allows the joint synthesis of summary estimates from multiple end points and accounts for their within-study and between-study correlation. Yet practitioners usually meta-analyse each end point independently. I examine the role of within-study correlation in multivariate meta-analysis, to elicit the consequences of ignoring it. Using analytic reasoning and a simulation study, the within-study correlation is shown to influence the ‘borrowing of strength’ across end points, and wrongly ignoring it gives meta-analysis results with generally inferior statistical properties; for example, on average it increases the mean-square error and standard error of pooled estimates, and for non-ignorable missing data it increases their bias. The influence of within-study correlation is only negligible when the within-study variation is small relative to the between-study variation, or when very small differences exist across studies in the within-study covariance matrices. The findings are demonstrated by applied examples within medicine, dentistry and education. Meta-analysts are thus encouraged to account for the correlation between end points. To facilitate this, I conclude by reviewing options for multivariate meta-analysis when within-study correlations are unknown; these include obtaining individual patient data, using external information, performing sensitivity analyses and using alternatively parameterized models.
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Keywords: Bivariate random-effects meta-analysis; Multiple end points; Multiple outcomes; Multivariate meta-analysis; Unknown within-study correlation

Document Type: Research Article

Affiliations: University of Birmingham, UK

Publication date: 2009-10-01

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