  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.
