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Robust confidence intervals for trend estimation in meta-analysis with publication bias

Confidence interval (CI) is very useful for trend estimation in meta-analysis. It provides a type of interval estimate of the regression slope as well as an indicator of the reliability of the estimate. Thus a precise calculation of confidence interval at an expected level is important. It is always difficult to explicitly quantify the CIs when there is publication bias in meta-analysis. Various CIs have been proposed, including the most widely used DerSimonian–Laird CI and the recently proposed Henmi–Copas CI. The latter provides a robust solution when there are non-ignorable missing data due to publication bias. In this paper we extended the idea into meta-analysis for trend estimation. We applied the method in different scenarios and showed that this type of CI is more robust than the others.