  Meta-analyses frequently include trials that report multiple effect sizes
based on a common set of study participants. These effect sizes will generally
be correlated. Cluster-robust variance-covariance estimators are a fruitful
approach for synthesizing dependent effects. However, when the number of
studies is small, state-of-the-art robust estimators can yield inflated Type 1
errors. We present two new cluster-robust estimators, 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. Our proposals are asymptotically equivalent to previously suggested
cluster-robust estimators such as the bias reduced linearization approach. We
apply the methods to real world data and compare and contrast their performance
in an extensive simulation study. We focus on bivariate meta-regression,
although the approaches can be applied more generally.
