Meta-analyses are commonly used to provide solid evidence across numerous studies. Traditional moment methods, such as the DerSimonian-Laird method, remain popular in spite of the availability of more accurate alternatives. While moment estimators are simple and intuitive, they are known to underestimate the variance of the overall treatment effect, particularly when the number of studies is small. This underestimation can lead to excessively narrow confidence intervals that do not meet the nominal confidence level, potentially resulting in misleading conclusions. In this study, we improve traditional moment-based meta-analysis methods by incorporating Huber's M-estimation to more accurately capture the distributional characteristics of between-study variance. Our approach enables conservative parameter estimation, even when almost all existing methods lead to underestimation of between-study variance under a small number of studies. Additionally, by deriving the simultaneous distribution of overall treatment effect and between-study variance, we propose facilitating a visual exploration of the relationship between these two quantities. Our method provides more reliable estimators for the overall treatment effect and between-study variance, particularly in situations with few studies. Using simulations and real data analysis, we demonstrate that our approach always yields more conservative results compared to traditional moment methods, and ensures more accurate confidence intervals in meta-analyses.

翻译：元分析通常用于在众多研究中提供坚实证据。尽管存在更精确的替代方法，传统的矩方法（如DerSimonian-Laird方法）仍然广受欢迎。虽然矩估计量简单直观，但已知它们会低估总体治疗效应的方差，特别是在研究数量较少时。这种低估可能导致置信区间过窄，无法达到名义置信水平，从而可能产生误导性结论。在本研究中，我们通过引入Huber M估计来改进传统的基于矩的元分析方法，以更准确地捕捉研究间方差的分布特征。即使在几乎所有现有方法都会因研究数量较少而低估研究间方差的情况下，我们的方法仍能实现保守的参数估计。此外，通过推导总体治疗效应与研究间方差的联合分布，我们提出了一种促进对这两个量之间关系进行可视化探索的方法。我们的方法为总体治疗效应和研究间方差提供了更可靠的估计量，特别是在研究数量较少的情况下。通过模拟和实际数据分析，我们证明与传统矩方法相比，我们的方法始终产生更保守的结果，并确保元分析中更准确的置信区间。