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

A confidence interval robust to publication bias for random-effects meta-analysis of few studies