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.

翻译：元分析被广泛应用于展示众多研究中的有力证据。另一方面，在罕见疾病领域，元分析通常基于有限数量的研究进行，其分析方法建立在假定研究间方差已知的理论框架之上。也就是说，用研究间方差的估计值替代了真实值，忽略了从数据中估计出的研究间方差本身所具有的随机性。因此，在仅包含少数研究的元分析中，所构建的总体治疗效应的置信区间往往过窄。在本研究中，我们提出通过使用类最大似然估计量来估计研究间方差的分布，以克服这一问题。我们还提出了一种通过研究间方差的分布来估计总体治疗效应的方法。我们提出的方法可以扩展许多现有方法，使其在少数研究的情况下也能进行更充分的估计。通过模拟和真实数据分析，我们证明，与现有方法相比，我们的方法始终保持保守性，这使得元分析能够考虑研究间方差的随机性。