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

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 (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.We 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.Outcome measures in a single randomised trial or a meta-analysis of several randomised trials are typically dichotomous, especially for important clinical outcomes such as death, acute myocardial infarction, etc. Although meta-analysts cannot directly influence the number of participants in a meta-analysis like trialists conducting a single trial, the assessment of the meta-analytic result depends heavily on the amount of information provided. A limited number of events from a few small trials and the associated random error may be under-recognised sources of spurious findings. If a meta-analysis is conducted before reaching a required inform