Random-Effect Meta-Analysis with Robust Between-Study Variance

Meta-analyses are widely employed to demonstrate strong evidence across numerous studies. On the other hand, in the context of rare diseases, meta-analyses are often conducted with a limited number of studies in which the analysis methods are based on theoretical frameworks assuming that the between-study variance is known. That is, the estimate of between-study variance is substituted for the true value, neglecting the randomness with the between-study variance estimated from the data. Consequently, excessively narrow confidence intervals for the overall treatment effect for meta-analyses have been constructed in only a few studies. In the present study, we propose overcoming this problem by estimating the distribution of between-study variance using the maximum likelihood-like estimator. We also suggest an approach for estimating the overall treatment effect via the distribution of the between-study variance. Our proposed method can extend many existing approaches to allow more adequate estimation under a few studies. Through simulation and analysis of real data, we demonstrate that our method remains consistently conservative compared to existing methods, which enables meta-analyses to consider the randomness of the between-study variance.