Department of Fisheries and Wildlife, Michigan State University, East Lansing, Michigan, 48824, USA.
Odum School of Ecology, University of Georgia, Athens, Georgia, 30602, USA.
Ecology. 2020 Dec;101(12):e03184. doi: 10.1002/ecy.3184. Epub 2020 Oct 7.
In ecological meta-analyses, nonindependence among observed effect sizes from the same source paper is common. If not accounted for, nonindependence can seriously undermine inferences. We compared the performance of four meta-analysis methods that attempt to address such nonindependence and the standard random-effect model that ignores nonindependence. We simulated data with various types of within-paper nonindependence, and assessed the standard deviation of the estimated mean effect size and Type I error rate of each method. Although all four methods performed substantially better than the standard random-effects model that assumes independence, there were differences in performance among the methods. A two-step method that first summarizes the multiple observed effect sizes per paper using a weighted mean and then analyzes the reduced data in a standard random-effects model, and a robust variance estimation method performed consistently well. A hierarchical model with both random paper and study effects gave precise estimates but had a higher Type I error rates, possibly reflecting limitations of currently available meta-analysis software. Overall, we advocate the use of the two-step method with a weighted paper mean and the robust variance estimation method as reliable ways to handle within-paper nonindependence in ecological meta-analyses.
在生态元分析中，从同一来源论文中观察到的效应大小之间的非独立性是常见的。如果不考虑这种非独立性，它可能会严重破坏推论。我们比较了四种试图解决这种非独立性的元分析方法和忽略非独立性的标准随机效应模型的性能。我们模拟了具有不同类型的论文内非独立性的数据，并评估了每种方法估计的平均效应大小的标准偏差和 I 型错误率。尽管所有四种方法的性能都明显优于假设独立性的标准随机效应模型，但这些方法之间的性能存在差异。一种两步法，首先使用加权平均值总结每篇论文中的多个观察到的效应大小，然后在标准随机效应模型中分析简化数据，以及一种稳健方差估计方法，表现一致良好。具有随机论文和研究效应的层次模型给出了精确的估计，但 I 型错误率较高，这可能反映了当前可用的元分析软件的局限性。总的来说，我们提倡使用两步法，用加权论文均值和稳健方差估计方法作为处理生态元分析中论文内非独立性的可靠方法。
