Estimating required information size by quantifying diversity in random-effects model meta-analyses

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Abstract
There 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. Information 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. We devise a measure of diversity (D 2) 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. D 2 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. D 2 is different from the intuitively obvious adjusting factor based on the common quantification of heterogeneity, the inconsistency (I 2), which may underestimate the required information size. Thus, D 2 and I 2 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 D 2 ≥ I 2, for all meta-analyses. We conclude that D 2 seems a better alternative than I 2 to consider model variation in any random-effects meta-analysis despite the choice of the between trial variance estimator that constitutes the model. Furthermore, D 2 can readily adjust the required information size in any random-effects model meta-analysis.