Small sample adjustments for robust variance estimation with meta-regression

Although primary studies often report multiple outcomes, the covariances between these outcomes are rarely reported. This leads to difficulties when combining studies in a meta-analysis. This problem was recently addressed with the introduction of robust variance estimation. This new method enables the estimation of meta-regression models with dependent effect sizes, even when the dependence structure is unknown. Although robust variance estimation has been shown to perform well when the number of studies in the meta-analysis is large, previous simulation studies suggest that the associated tests often have Type I error rates that are much larger than nominal. In this article, I introduce 6 estimators with better small sample properties and study the effectiveness of these estimators via 2 simulation studies. The results of these simulations suggest that the best estimator involves correcting both the residuals and degrees of freedom used in the robust variance estimator. These studies also suggest that the degrees of freedom depend on not only the number of studies but also the type of covariates in the meta-regression. The fact that the degrees of freedom can be small, even when the number of studies is large, suggests that these small-sample corrections should be used more generally. I conclude with an example comparing the results of a meta-regression with robust variance estimation with the results from the corrected estimator.