Exact inference on meta-analysis with generalized fixed-effects and random-effects models

ABSTRACT Meta-analysis with fixed-effects and random-effects models provides a general framework for quantitatively summarizing multiple comparative studies. However, a majority of the conventional methods rely on large-sample approximations to justify their inference, which may be invalid and lead to erroneous conclusions, especially when the number of studies is not large, or sample sizes of the individual studies are small. In this article, we propose a set of ‘exact’ confidence intervals for the overall effect, where the coverage probabilities of the intervals can always be achieved. We start with conventional parametric fixed-effects and random-effects models, and then extend the exact methods beyond the commonly postulated Gaussian assumptions. Efficient numerical algorithms for implementing the proposed methods are developed. We also conduct simulation studies to compare the performance of our proposal to existing methods, indicating our proposed procedures are better in terms of coverage level and robustness. The new proposals are then illustrated with the data from meta-analyses for estimating the efficacy of statins and BCG vaccination.