One of the reasons for the popularity of meta‐analysis is the notion that these analyses will possess more power to detect effects than individual studies. This is inevitably the case under a fixed‐effect model. However, the inclusion of the between‐study variance in the random‐effects model, and the need to estimate this parameter, can have unfortunate implications for this power. We develop methods for assessing the power of random‐effects meta‐analyses, and the average power of the individual studies that contribute to meta‐analyses, so that these powers can be compared. In addition to deriving new analytical results and methods, we apply our methods to 1991 meta‐analyses taken from the Cochrane Database of Systematic Reviews to retrospectively calculate their powers. We find that, in practice, 5 or more studies are needed to reasonably consistently achieve powers from random‐effects meta‐analyses that are greater than the studies that contribute to them. Not only is statistical inference under the random‐effects model challenging when there are very few studies but also less worthwhile in such cases. The assumption that meta‐analysis will result in an increase in power is challenged by our findings.

中文翻译：

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随机效应荟萃分析的功效分析。

荟萃分析流行的原因之一是这些分析比个别研究更有能力检测效果。在固定效应模型下，这是不可避免的情况。然而，随机效应模型中包含研究间方差以及估计该参数的需要可能会对这种功效产生不幸的影响。我们开发了评估随机效应荟萃分析功效的方法，以及有助于荟萃分析的各个研究的平均功效，以便可以对这些功效进行比较。除了得出新的分析结果和方法之外，我们还将我们的方法应用于从 Cochrane 系统评价数据库中获取的 1991 年荟萃分析，以回顾性地计算其功效。我们发现，在实践中，需要 5 项或更多研究才能合理一致地获得随机效应荟萃分析的功效，这些功效大于对它们做出贡献的研究。当研究很少时，随机效应模型下的统计推断不仅具有挑战性，而且在这种情况下也不太有价值。我们的研究结果对荟萃分析会导致功效增加的假设提出了挑战。