Meta-regression analyses usually focus on estimating and testing differences in average effect sizes between individual levels of each meta-regression covariate in turn. These metrics are useful but have limitations: they consider each covariate 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: "For a given joint level of the covariates, what percentage of the population effects are meaningfully strong?" and "For any two joint levels of the covariates, what is the difference between these percentages of meaningfully strong effects?" We provide semiparametric methods for estimation and inference and assess their performance in a simulation study. We apply the proposed methods to meta-regression analyses on memory consolidation and on dietary behavior interventions, illustrating how the methods can provide more information than standard reporting alone. To facilitate implementing the methods in practice, we provide reporting guidelines and simple R code.
Keywords: bootstrapping; effect sizes; heterogeneity; meta-analysis; meta-regression; semiparametric.
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