  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.
