Abstract
BackgroundThere is increasing awareness that meta-analyses require a sufficiently large information size to detect or reject an anticipated intervention effect. The required information size in a meta-analysis may be calculated from an anticipated a priori intervention effect or from an intervention effect suggested by trials with low-risk of bias.MethodsInformation size calculations need to consider the total model variance in a meta-analysis to control type I and type II errors. Here, we derive an adjusting factor for the required information size under any random-effects model meta-analysis.ResultsWe devise a measure of diversity (D2) in a meta-analysis, which is the relative variance reduction when the meta-analysis model is changed from a random-effects into a fixed-effect model. D2 is the percentage that the between-trial variability constitutes of the sum of the between-trial variability and a sampling error estimate considering the required information size. D2 is different from the intuitively obvious adjusting factor based on the common quantification of heterogeneity, the inconsistency (I2), which may underestimate the required information size. Thus, D2 and I2 are compared and interpreted using several simulations and clinical examples. In addition we show mathematically that diversity is equal to or greater than inconsistency, that is D2 ≥ I2, for all meta-analyses.ConclusionWe conclude that D2 seems a better alternative than I2 to consider model variation in any random-effects meta-analysis despite the choice of the between trial variance estimator that constitutes the model. Furthermore, D2 can readily adjust the required information size in any random-effects model meta-analysis.
Highlights
There is increasing awareness that meta-analyses require a sufficiently large information size to detect or reject an anticipated intervention effect
2.1 Deriving the required meta-analysis information size and diversity If the required IS needed to detect or reject an intervention effect in a meta-analysis should be at least the sample size needed to detect or reject a similar effect in a single trial, the following scenario applies: Let μF denote the weighted mean intervention effect to be detected in a fixed-effect model meta-analysis and let μR denote the weighted mean intervention effect to be detected in a in a random-effects model meta-analysis using generic inverse variance weighting
3.1 The relationship between diversity, D2, and heterogeneity, I2 We want to show that D2 ≥ I2 for all meta-analyses
Summary
There is increasing awareness that meta-analyses require a sufficiently large information size to detect or reject an anticipated intervention effect. The reliability of a conclusion drawn from a meta-analysis, despite standardly calculated confidence limits, may depend even more on the number of events and the total number of participants included than hitherto perceived [2,3,4,5,6,7,8]. The information size (IS) required for a reliable and conclusive meta-analysis may be assumed to be at least as large as the sample size (SS) of a single well-powered randomised clinical trial to detect or reject an anticipated intervention effect [2,3,4]
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