Robust confidence intervals for meta-regression with interaction effects

Meta-analysis is an important statistical technique for synthesizing the results of multiple studies regarding the same or closely related research question. So-called meta-regression extends meta-analysis models by accounting for study-level covariates. Mixed-effects meta-regression models provide a powerful tool for evidence synthesis, by appropriately accounting for between-study heterogeneity. In fact, modelling the study effect in terms of random effects and moderators not only allows to examine the impact of the moderators, but often leads to more accurate estimates of the involved parameters. Nevertheless, due to the often small number of studies on a specific research topic, interactions are often neglected in meta-regression. In this work we consider the research questions (i) how moderator interactions influence inference in mixed-effects meta-regression models and (ii) whether some inference methods are more reliable than others. Here we review robust methods for confidence intervals in meta-regression models including interaction effects. These methods are based on the application of robust sandwich estimators of Hartung-Knapp-Sidik-Jonkman (HKSJ) or heteroscedasticity-consistent (HC)-type for estimating the variance-covariance matrix of the vector of model coefficients. Furthermore, we compare different versions of these robust estimators in an extensive simulation study. We thereby investigate coverage and width of seven different confidence intervals under varying conditions. Our simulation study shows that the coverage rates as well as the interval widths of the parameter estimates are only slightly affected by adjustment of the parameters. It also turned out that using the Satterthwaite approximation for the degrees of freedom seems to be advantageous for accurate coverage rates. In addition, different to previous analyses for simpler models, the $$\textbf{HKSJ}$$ HKSJ -estimator shows a worse performance in this more complex setting compared to some of the $$\textbf{HC}$$ HC -estimators.