Fox Jeremy W
Department of Biological Sciences University of Calgary Calgary Alberta Canada.
Ecol Evol. 2022 Nov 15;12(11):e9521. doi: 10.1002/ece3.9521. eCollection 2022 Nov.
Many primary research studies in ecology are underpowered, providing very imprecise estimates of effect size. Meta-analyses partially mitigate this imprecision by combining data from different studies. But meta-analytic estimates of mean effect size may still remain imprecise, particularly if the meta-analysis includes a small number of studies. Imprecise, large-magnitude estimates of mean effect size from small meta-analyses likely would shrink if additional studies were conducted (regression towards the mean). Here, I propose a way to estimate and correct this regression to the mean, using meta-meta-analysis (meta-analysis of meta-analyses). Hierarchical random effects meta-meta-analysis shrinks estimated mean effect sizes from different meta-analyses towards the grand mean, bringing those estimated means closer on average to their unknown true values. The intuition is that, if a meta-analysis reports a mean effect size much larger in magnitude than that reported by other meta-analyses, that large mean effect size likely is an overestimate. This intuition holds even if different meta-analyses of different topics have different true mean effect sizes. Drawing on a compilation of data from hundreds of ecological meta-analyses, I find that the typical (median) ecological meta-analysis overestimates the absolute magnitude of the true mean effect size by ~10%. Some small ecological meta-analyses overestimate the magnitude of the true mean effect size by >50%. Meta-meta-analysis is a promising tool for improving the accuracy of meta-analytic estimates of mean effect size, particularly estimates based on just a few studies.
生态学领域的许多基础研究功效不足，对效应量的估计非常不精确。荟萃分析通过合并不同研究的数据，部分缓解了这种不精确性。但是，平均效应量的荟萃分析估计可能仍然不够精确，特别是当荟萃分析纳入的研究数量较少时。如果进行更多研究，基于少量研究的小型荟萃分析得出的平均效应量的不精确、大幅度估计可能会缩小（向均值回归）。在此，我提出一种方法，即使用元荟萃分析（对荟萃分析的荟萃分析）来估计和校正这种向均值的回归。分层随机效应元荟萃分析会将不同荟萃分析得出的估计平均效应量向总均值收缩，使这些估计均值平均而言更接近其未知的真实值。其直观理解是，如果一项荟萃分析报告的平均效应量在幅度上比其他荟萃分析报告的大得多，那么这个大的平均效应量很可能是高估了。即使对不同主题的不同荟萃分析有不同的真实平均效应量，这种直观理解仍然成立。基于数百项生态荟萃分析的数据汇编，我发现典型的（中位数）生态荟萃分析将真实平均效应量的绝对幅度高估了约10%。一些小型生态荟萃分析将真实平均效应量的幅度高估了50%以上。元荟萃分析是提高平均效应量荟萃分析估计准确性的一种很有前景的工具，特别是对于基于少量研究的估计。
