Department of Basic Psychology and Methodology, Faculty of Psychology, University of Murcia, Murcia, Spain.
Department of Social Psychology and Methodology, Faculty of Psychology, Autonomous University of Madrid, Madrid, Spain.
BMC Med Res Methodol. 2023 Jan 17;23(1):19. doi: 10.1186/s12874-022-01809-0.
Advantages of meta-analysis depend on the assumptions underlying the statistical procedures used being met. One of the main assumptions that is usually taken for granted is the normality underlying the population of true effects in a random-effects model, even though the available evidence suggests that this assumption is often not met. This paper examines how 21 frequentist and 24 Bayesian methods, including several novel procedures, for computing a point estimate of the heterogeneity parameter ([Formula: see text]) perform when the distribution of random effects departs from normality compared to normal scenarios in meta-analysis of standardized mean differences.
A Monte Carlo simulation was carried out using the R software, generating data for meta-analyses using the standardized mean difference. The simulation factors were the number and average sample size of primary studies, the amount of heterogeneity, as well as the shape of the random-effects distribution. The point estimators were compared in terms of absolute bias and variance, although results regarding mean squared error were also discussed.
Although not all the estimators were affected to the same extent, there was a general tendency to obtain lower and more variable [Formula: see text] estimates as the random-effects distribution departed from normality. However, the estimators ranking in terms of their absolute bias and variance did not change: Those estimators that obtained lower bias also showed greater variance. Finally, a large number and sample size of primary studies acted as a bias-protective factor against a lack of normality for several procedures, whereas only a high number of studies was a variance-protective factor for most of the estimators analyzed.
Although the estimation and inference of the combined effect have proven to be sufficiently robust, our work highlights the role that the deviation from normality may be playing in the meta-analytic conclusions from the simulation results and the numerical examples included in this work. With the aim to exercise caution in the interpretation of the results obtained from random-effects models, the tau2() R function is made available for obtaining the range of [Formula: see text] values computed from the 45 estimators analyzed in this work, as well as to assess how the pooled effect, its confidence and prediction intervals vary according to the estimator chosen.
荟萃分析的优势取决于所使用的统计程序的假设得到满足。通常默认的一个主要假设是随机效应模型中真实效应的总体呈正态分布，尽管现有证据表明这种假设并不总是成立。本文比较了 21 种频率派和 24 种贝叶斯方法（包括几种新方法）在计算异质性参数（[公式：见正文]）点估计值时的表现，这些方法在荟萃分析标准化均数差时，与随机效应分布偏离正态分布的情况相比。
使用 R 软件进行蒙特卡罗模拟，使用标准化均数差生成荟萃分析数据。模拟因素包括初级研究的数量和平均样本量、异质性程度以及随机效应分布的形状。点估计值的比较考虑了绝对偏差和方差，尽管也讨论了均方误差的结果。
虽然并非所有的估计值都受到相同程度的影响，但当随机效应分布偏离正态分布时，[公式：见正文]的估计值通常会降低且更具变异性。然而，在绝对偏差和方差方面的估计值排名并没有改变：那些获得较低偏差的估计值也显示出更大的方差。最后，大量和大样本的初级研究成为了对某些程序缺乏正态性的偏倚保护因素，而只有大量的研究才是大多数分析的估计值的方差保护因素。
尽管综合效应的估计和推断已经被证明足够稳健，但我们的工作强调了偏离正态性可能在从模拟结果和包括在这项工作中的数值示例得出的荟萃分析结论中所起的作用。为了谨慎解释从随机效应模型获得的结果，tau2()R 函数可用于获得从这项工作中分析的 45 个估计值计算得到的[公式：见正文]值的范围，以及评估选择的估计值如何影响汇总效应、置信区间和预测区间。
