Robust metrics and sensitivity analyses for meta-analyses of heterogeneous effects

We recently suggested new statistical metrics for routine reporting in random-effects meta-analyses to convey evidence strength for scientifically meaningful effects under effect heterogeneity. First, given a chosen threshold of meaningful effect size, we suggested reporting the estimated proportion of true effect sizes above this threshold. Second, we suggested reporting the proportion of effect sizes below a second, possibly symmetric, threshold in the opposite direction from the estimated mean. Our previous methods applied when the true effects are approximately normal, when the number of studies is relatively large, and when the proportion is between approximately 0.15 and 0.85. Here, we additionally describe robust methods for point estimation and inference that perform well under considerably more general conditions, as we validate in an extensive simulation study. The methods are implemented in the R package MetaUtility (function prop_stronger). We describe application of the robust methods to conducting sensitivity analyses for unmeasured confounding in meta-analyses.