Cluster-robust estimators for multivariate mixed-effects meta-regression

Meta-analyses frequently include trials that report multiple outcomes based on a common set of study participants. These outcomes will generally be correlated. Cluster-robust variance-covariance estimators are a fruitful approach for synthesizing dependent outcomes. However, when the number of studies is small, state-of-the-art robust estimators can yield inflated Type 1 errors. Therefore, two new cluster-robust estimators are presented, in order to improve small sample performance. For both new estimators the idea is to transform the estimated variances of the residuals using only the diagonal entries of the hat matrix. The proposals are asymptotically equivalent to previously suggested cluster-robust estimators such as the bias reduced linearization approach. The methods are applied to a dataset of 81 trials examining overall and disease-free survival in neuroblastoma patients with amplified versus normal MYC-N genes. Furthermore, their performance is compared and contrasted in an extensive simulation study. The focus is on bivariate meta-regression, although the approaches can be applied more generally.