Department of Statistics, Mathematical Statistics and Applications in Industry, TU Dortmund University, Germany.
Br J Math Stat Psychol. 2022 Feb;75(1):1-22. doi: 10.1111/bmsp.12242. Epub 2021 May 2.
Meta-analyses of correlation coefficients are an important technique to integrate results from many cross-sectional and longitudinal research designs. Uncertainty in pooled estimates is typically assessed with the help of confidence intervals, which can double as hypothesis tests for two-sided hypotheses about the underlying correlation. A standard approach to construct confidence intervals for the main effect is the Hedges-Olkin-Vevea Fisher-z (HOVz) approach, which is based on the Fisher-z transformation. Results from previous studies (Field, 2005, Psychol. Meth., 10, 444; Hafdahl and Williams, 2009, Psychol. Meth., 14, 24), however, indicate that in random-effects models the performance of the HOVz confidence interval can be unsatisfactory. To this end, we propose improvements of the HOVz approach, which are based on enhanced variance estimators for the main effect estimate. In order to study the coverage of the new confidence intervals in both fixed- and random-effects meta-analysis models, we perform an extensive simulation study, comparing them to established approaches. Data were generated via a truncated normal and beta distribution model. The results show that our newly proposed confidence intervals based on a Knapp-Hartung-type variance estimator or robust heteroscedasticity consistent sandwich estimators in combination with the integral z-to-r transformation (Hafdahl, 2009, Br. J. Math. Stat. Psychol., 62, 233) provide more accurate coverage than existing approaches in most scenarios, especially in the more appropriate beta distribution simulation model.
元分析相关系数是整合来自多个横断面和纵向研究设计结果的重要技术。聚合估计的不确定性通常通过置信区间来评估，置信区间可以作为关于基础相关的双边假设的假设检验。构建主要效应置信区间的标准方法是 Hedges-Olkin-Vevea Fisher-z（HOVz）方法，该方法基于 Fisher-z 变换。然而，先前研究（Field，2005，Psychol. Meth.，10，444；Hafdahl 和 Williams，2009，Psychol. Meth.，14，24）的结果表明，在随机效应模型中，HOVz 置信区间的性能可能不尽如人意。为此，我们提出了对 HOVz 方法的改进，这些改进基于对主要效应估计的增强方差估计。为了研究新置信区间在固定效应和随机效应荟萃分析模型中的覆盖范围，我们进行了广泛的模拟研究，将其与已建立的方法进行了比较。数据是通过截断正态分布和贝塔分布模型生成的。结果表明，我们新提出的置信区间基于 Knapp-Hartung 型方差估计或稳健异方差一致三明治估计器，并结合积分 z 到 r 变换（Hafdahl，2009，Br. J. Math. Stat. Psychol.，62，233），在大多数情况下，尤其是在更合适的贝塔分布模拟模型中，比现有方法提供更准确的覆盖范围。
