Meta-regression with categorical moderators and dependent effect sizes: A simulation study

Categorical moderators are often found in meta-analysis and examined using meta-regression models. When multiple effect sizes are present within studies, several methods can be used for meta-regression: multivariate models, three-level models, correlated-effects models with robust variance estimation (RVE), three-level models with RVE, and correlated-effects models with RVE and cluster wild bootstrapping (CWB). This study aimed to compare the performance of these methods through a simulation study. Cohen's d values were generated under a multivariate model, incorporating a binary variable that could represent either study-level or effect size-level characteristics. When the moderator referred to an effect size-level characteristic, its effect was allowed to vary across studies. Factors manipulated in the simulation included number of studies, number of outcomes per study, and the distribution of effect sizes across the categories of the moderator variable, ranging from balanced to highly unbalanced. The methods were applied and compared in terms of bias, Type I error, and power. The results showed that all methods exhibited lower power to detect effects when the moderator variable referred to study-level characteristics and the effect size distribution was very unbalanced. Methods based on RVE (correlated-effects with RVE or with RVE and CWB, and three-level models with RVE) effectively controlled Type I error rates but tended to be overconservative. In contrast, three-level models achieved higher power but at the cost of inflated Type I error. The best balance between Type I error control and power was observed when using a combination of three-level models and RVE.