Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands.
Preventive Medicine and Epidemiology, Department of Medicine, Boston University, USA.
Biom J. 2022 Oct;64(7):1340-1360. doi: 10.1002/bimj.202100108. Epub 2022 Jun 26.
The DerSimonian-Laird (DL) weighted average method for aggregated data meta-analysis has been widely used for the estimation of overall effect sizes. It is criticized for its underestimation of the standard error of the overall effect size in the presence of heterogeneous effect sizes. Due to this negative property, many alternative estimation approaches have been proposed in the literature. One of the earliest alternative approaches was developed by Hardy and Thompson (HT), who implemented a profile likelihood instead of the moment-based approach of DL. Others have further extended this likelihood approach and proposed higher-order likelihood inferences (e.g., Bartlett-type corrections). In addition, corrections factors for the estimated DL standard error, like the Hartung-Knapp-Sidik-Jonkman (HKSJ) adjustment, and the restricted maximum likelihood (REML) estimation have been suggested too. Although these improvements address the uncertainty in estimating the between-study variance better than the DL method, they all assume that the true within-study standard errors are known and equal to the observed standard errors of the effect sizes. Here, we will treat the observed standard errors as estimators for the within-study variability and we propose a bivariate likelihood approach that jointly estimates the overall effect size, the between-study variance, and the potentially heteroskedastic within-study variances. We study the performance of the proposed method by means of simulation, and compare it to DL (with and without HKSJ), HT, their higher-order likelihood methods, and REML. Our proposed approach seems to have better or similar coverages compared to the other approaches and it appears to be less biased in the case of heteroskedastic within-study variances when this heteroskedasticty is correlated with the effect size.
用于聚合数据荟萃分析的 DerSimonian-Laird（DL）加权平均法已被广泛用于估计总体效应大小。由于其在存在异质效应大小的情况下低估了总体效应大小的标准误差，因此受到了批评。由于这种负面特性，文献中提出了许多替代的估计方法。最早的替代方法之一是由 Hardy 和 Thompson（HT）提出的，他们实施了轮廓似然而不是 DL 的基于矩的方法。其他人进一步扩展了这种似然方法，并提出了更高阶的似然推断（例如，Bartlett 型校正）。此外，还提出了用于估计 DL 标准误差的校正因子，例如 Hartung-Knapp-Sidik-Jonkman（HKSJ）调整和受限最大似然（REML）估计。尽管这些改进比 DL 方法更好地解决了估计组间方差的不确定性，但它们都假设真实的组内标准误差是已知的并且等于效应大小的观测标准误差。在这里，我们将观测标准误差视为组内变异性的估计值，并提出了一种二元似然方法，该方法联合估计总体效应大小、组间方差和潜在的异方差组内方差。我们通过模拟研究了所提出方法的性能，并将其与 DL（带和不带 HKSJ）、HT、它们的高阶似然方法和 REML 进行了比较。与其他方法相比，我们提出的方法似乎具有更好或相似的覆盖率，并且在组内方差存在异方差且这种异方差与效应大小相关时，它的偏差似乎较小。
