  Random-effects models are frequently used to synthesise information from
different studies in meta-analysis. While likelihood-based inference is
attractive both in terms of limiting properties and of implementation, its
application in random-effects meta-analysis may result in misleading
conclusions, especially when the number of studies is small to moderate. The
current paper shows how methodology that reduces the asymptotic bias of the
maximum likelihood estimator of the variance component can also substantially
improve inference about the mean effect size. The results are derived for the
more general framework of random-effects meta-regression, which allows the mean
effect size to vary with study-specific covariates.
