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

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.