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However, coverage probabilities of confidence regions or intervals for standard inference methods for random\u2010effects models (eg, restricted maximum likelihood estimation) cannot retain their nominal confidence levels in general, especially when the number of synthesized studies is small because their validities depend on large sample approximations. In this article, we provide permutation\u2010based inference methods that enable exact joint inferences for average outcome measures without large sample approximations. We also provide accurate marginal inference methods under general settings of multivariate meta\u2010analyses. We propose effective approaches for permutation inferences using optimal weighting based on the efficient score statistic. The effectiveness of the proposed methods is illustrated via applications to bivariate meta\u2010analyses of diagnostic accuracy studies for airway eosinophilia in asthma and a network meta\u2010analysis for antihypertensive drugs on incident diabetes, as well as through simulation experiments. In numerical evaluations performed via simulations, our methods generally provided accurate confidence regions or intervals under a broad range of settings, whereas the current standard inference methods exhibited serious undercoverage properties.<\/jats:p>","DOI":"10.1111\/biom.13134","type":"journal-article","created":{"date-parts":[[2019,8,10]],"date-time":"2019-08-10T08:59:24Z","timestamp":1565427564000},"page":"337-347","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Permutation inference methods for multivariate meta\u2010analysis"],"prefix":"10.1093","volume":"76","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2520-9949","authenticated-orcid":false,"given":"Hisashi","family":"Noma","sequence":"first","affiliation":[{"name":"Department of Data Science The Institute of Statistical Mathematics Tokyo 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