Random effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations; for instance, coverage probabilities of confidence intervals can be substantially below the nominal level. The main reason is that these inference methods rely on large sample approximations even though the number of synthesized studies is usually small or moderate in practice. In this article, we solve this problem using a unified inference method based on Monte Carlo conditioning for broad application to random effects meta-analysis. The developed method provides improved confidence intervals with coverage probabilities that are closer to the nominal level than standard methods. As specific applications, we provide new inference procedures for three types of meta-analysis: conventional univariate meta-analysis for pairwise treatment comparisons, 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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