A Unified Method for Exact Inference in Random-effects Meta-analysis via Monte Carlo Conditioning
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Random-effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies to adequately address between-studies heterogeneity. However, standard inference methods for average treatment effects (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. Also, random-effects models typically include nuisance parameters, and these methods ignore variability in the estimation of such parameters. In this article we solve this problem using a unified inference method without large sample approximation for broad application to random-effects meta-analysis. The developed method provides accurate confidence intervals with coverage probabilities that are exactly the same as the nominal level. The exact confidence intervals are constructed based on the likelihood ratio test for an average treatment effect, and the exact p-value can be defined based on the conditional distribution given the maximum likelihood estimator of the nuisance parameters via the Monte Carlo conditioning method. As specific applications, we provide exact 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.
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