title: Power analysis for random-effects meta-analysis.
abstract: 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.
authors.affiliation: MRC Biostatistics Unit, Cambridge, UK.
authors.forename: Dan
authors.identifier: http://orcid.org/0000-0002-4963-8123
authors.initials: D
authors.lastname: Jackson
authors.affiliation: MRC Biostatistics Unit, Cambridge, UK.
authors.forename: Rebecca
authors.initials: R
authors.lastname: Turner
mesh_terms: D015982:Bias; D016208:Databases, Factual; D006801:Humans; D015201:Meta-Analysis as Topic; D015233:Models, Statistical
keywords: cochrane; empirical evaluation; power calculations; random-effects meta-analysis