Improving the Accuracy of Confidence Intervals and Regions in Multivariate Random-effects Meta-analysis
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Multivariate random-effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations since they ignore the variability in the estimation of variance parameters. In this article, we propose new improved inference methods without any repeated calculations such as Bootstrap or Monte Carlo methods. We employ distributional properties of ordinary least squares and residuals under random-effects models, and provide relatively simple and closed form expressions of confidence intervals and regions whose coverages are more accurate than conventional methods such as restricted maximum likelihood methods. As specific applications, we consider two multivariate meta-analysis: bivariate meta-analysis of diagnostic test accuracy and multiple treatment comparisons via network meta-analysis. We also illustrate the practical effectiveness of these methods via real data applications and simulation studies.
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