In meta-analysis, hypothesis testing is one of the commonly used approaches for assessing whether heterogeneity exists in effects between studies. The literature concluded that the Q-statistic is clearly the best choice and criticized the performance of the likelihood ratio test in terms of the type I error control and power. However, all the criticism for the likelihood ratio test is based on the use of a mixture of two chi-square distributions with 0 and 1 degrees of freedom, which is justified only asymptotically. In this study, we develop a novel method to derive the finite sample distribution of the likelihood ratio test and restricted likelihood ratio test statistics for testing the zero variance component in the random effects model for meta-analysis. We also extend this result to the heterogeneity test when metaregression is applied. A numerical study shows that the proposed statistics have superior performance to the Q-statistic, especially when the number of studies collected for meta-analysis is small to moderate.

中文翻译：

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荟萃分析中检验异质性的似然比统计量的有限样本分布

在荟萃分析中，假设检验是评估研究之间的效应是否存在异质性的常用方法之一。文献得出的结论是，Q 统计量显然是最佳选择，并批评了似然比检验在 I 类误差控制和功效方面的性能。然而，对似然比检验的所有批评都是基于使用具有 0 和 1 自由度的两个卡方分布的混合，这仅在渐近方面是合理的。在本研究中，我们开发了一种新颖的方法来推导似然比检验和限制似然比检验统计量的有限样本分布，以测试随机效应模型中的零方差分量以进行荟萃分析。当应用元回归时，我们还将这个结果扩展到异质性测试。数值研究表明，所提出的统计量具有优于 Q 统计量的性能，特别是当为荟萃分析收集的研究数量较少到中等时。