Permutation inference methods for multivariate meta-analysis
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Multivariate meta-analysis is gaining prominence in evidence synthesis research as it enables synthesis of multiple correlated outcome data simultaneously, and random effects models have been generally used for addressing between-studies heterogeneities. However, coverage probabilities of confidence regions or intervals for standard inference methods for the random effects models (e.g., restricted maximum likelihood estimation) cannot retain their nominal confidence levels in general, especially when the number of synthesized studies is moderate or small because their validities depend on large sample approximations. In this article, we provide permutation-based inference methods that enable exact joint inferences for the average outcome measures without large sample approximations. We also provide accurate marginal inference methods under general settings of multivariate meta-analyses. We propose two effective approaches for the permutation inferences, one using an optimal weighting method based on the efficient score statistic, and another using a computationally efficient method of moments estimator. The effectiveness of the proposed methods is illustrated via applications to bivariate meta-analyses of diagnostic accuracy studies for minimally invasive markers of airway eosinophilia in asthma, as well as through simulation experiments. In the numerical evaluations via simulations, the developed methods generally provided accurate confidence regions or intervals under broad settings, while the current standard inference methods showed serious undercoverage properties.
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