New metrics for meta-analyses of heterogeneous effects

We provide two simple metrics that could be reported routinely in random-effects meta-analyses to convey evidence strength for scientifically meaningful effects under effect heterogeneity (i.e., a nonzero estimated variance of the true effect distribution). First, given a chosen threshold of meaningful effect size, meta-analyses could report the estimated proportion of true effect sizes above this threshold. Second, meta-analyses could estimate the proportion of effect sizes below a second, possibly symmetric, threshold in the opposite direction from the estimated mean. These metrics could help identify if: (1) there are few effects of scientifically meaningful size despite a "statistically significant" pooled point estimate; (2) there are some large effects despite an apparently null point estimate; or (3) strong effects in the direction opposite the pooled estimate regularly also occur (and thus, potential effect modifiers should be examined). These metrics should be presented with confidence intervals, which can be obtained analytically or, under weaker assumptions, using bias-corrected and accelerated (BCa) bootstrapping. Additionally, these metrics inform relative comparison of evidence strength across related meta-analyses. We illustrate with applied examples and provide an R package to compute the metrics and confidence intervals.