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.

中文翻译：

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固定效应和随机效应荟萃分析中基于Fisher变换的相关置信区间

相关系数的荟萃分析是整合许多横断面和纵向研究设计结果的重要技术。汇总估计的不确定性通常在置信区间的帮助下进行评估，置信区间可以兼作关于潜在相关性的双边假设的假设检验。构建主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。先前研究的结果（Field, 2005, Psychol. Meth ., 10, 444; Hafdahl and Williams, 2009, Psychol. Meth., 14, 24)，然而，表明在随机效应模型中，HOVz 置信区间的性能可能不令人满意。为此，我们提出了对 HOVz 方法的改进，该方法基于对主效应估计的增强方差估计。为了研究固定效应和随机效应荟萃分析模型中新置信区间的覆盖率，我们进行了广泛的模拟研究，将它们与已建立的方法进行比较。数据是通过截断的正态分布和 beta 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 型方差估计量或稳健的异方差一致三明治估计量，并结合积分 z 到 r 变换 (Hafdahl, 2009, Br. J. Math. Stat. Psychol., 62, 233) 在大多数情况下提供比现有方法更准确的覆盖率，尤其是在更合适的 beta 分布模拟模型中。