Novel approaches for random-effects meta-analysis of a small number of studies under normality

Random-effects meta-analyses with only a few studies often face challenges in accurately estimating between-study heterogeneity, leading to biased effect estimates and confidence intervals with poor coverage. This issue is especially the case when dealing with rare diseases. To address this problem for normally distributed outcomes, two new approaches have been proposed to provide confidence limits of the global mean: one based on fiducial inference, and the other involving two modifications of the signed log-likelihood ratio test statistic in order to have improved performance with small numbers of studies. The performance of the proposed methods was evaluated numerically and compared with the Hartung-Knapp-Sidik-Jonkman approach and its modification to handle small numbers of studies. The simulation results indicated that the proposed methods achieved coverage probabilities closer to the nominal level and produced shorter confidence intervals compared to those based on existing methods. Two real examples are used to illustrate the proposed methods.