Meta-regression estimates of the percentage of meaningfully strong population effects

Meta-regression analyses usually focus on estimating and testing differences in average effect sizes between individual levels of each meta-regressive effect modifier in turn. These metrics are useful but have limitations: they consider each effect modifier individually, rather than in combination, and they characterize only the mean of a potentially heterogeneous distribution of effects. We propose additional metrics that address both limitations. Given a chosen threshold representing a meaningfully strong effect size, these metrics address the questions: (1) “For a given joint level of the effect modifiers, what percentage of the population effects are meaningfully strong?'' and (2) “For any two joint levels of the effect modifiers, what is the difference between these percentages of meaningfully strong effects?'' We provide nonparametric methods for estimation and inference and validate their performance in a simulation study. We apply the proposed methods to a meta-regression on memory consolidation, illustrating how the methods can provide more information than standard reporting alone. The methods are straightforward to implement in practice, and we provide simple example code in R to do so.