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

<p>Abstract</p> <p>Background</p> <p>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 <it>a priori </it>intervention effect or from an intervention effect suggested by trials with low-risk of bias.</p> <p>Methods</p> <p>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.</p> <p>Results</p> <p>We devise a measure of diversity (<it>D</it>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. <it>D</it>²is 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. <it>D</it>²is different from the intuitively obvious adjusting factor based on the common quantification of heterogeneity, the inconsistency (<it>I</it>²), which may underestimate the required information size. Thus, <it>D</it>²and <it>I</it>²are 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 <it>D</it>²≥ <it>I</it>², for all meta-analyses.</p> <p>Conclusion</p> <p>We conclude that <it>D</it>²seems a better alternative than <it>I</it>²to consider model variation in any random-effects meta-analysis despite the choice of the between trial variance estimator that constitutes the model. Furthermore, <it>D</it>²can readily adjust the required information size in any random-effects model meta-analysis.</p