  Multivariate meta-analysis is gaining prominence in evidence synthesis
research because it enables simultaneous synthesis of multiple correlated
outcome data, and random-effects models have generally been used for addressing
between-studies heterogeneities. However, coverage probabilities of confidence
regions or intervals for standard inference methods for 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 small because their validities depend on large sample approximations. In
this article, we provide permutation-based 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-analyses. 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-analyses of diagnostic accuracy studies for
airway eosinophilia in asthma and a network meta-analysis 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.
