  Systematic reviews aim to summarize all the available evidence relevant to a
particular research question. If appropriate, the data from identified studies
are quantitatively combined in a meta-analysis. Often only few studies
regarding a particular research question exist. In these settings the
estimation of the between-study heterogeneity is challenging. Furthermore, the
assessment of publication bias is difficult as standard methods such as visual
inspection or formal hypothesis tests in funnel plots do not provide adequate
guidance. Previously, Henmi and Copas (Statistics in Medicine 2010, 29:
2969--2983) proposed a confidence interval for the overall effect in
random-effects meta-analysis that is robust to publication bias to some extent.
As is evident from their simulations, the confidence intervals have improved
coverage compared with standard methods. To our knowledge, the properties of
their method has never been assessed for meta-analyses including fewer than
five studies. In this manuscript, we propose a variation of the method by Henmi
and Copas employing an improved estimator of the between-study heterogeneity,
in particular when dealing with few studies only. In a simulation study, the
proposed method is compared to several competitors. Overall, we found that our
method outperforms the others in terms of coverage probabilities. In
particular, an improvement compared with the proposal by Henmi and Copas is
demonstrated. The work is motivated and illustrated by a systematic review and
meta-analysis in paediatric immunosuppression following liver transplantations.
