Meta-analysis is a powerful tool to synthesize findings from multiple studies. The normal-normal random-effects model is widely used to account for between-study heterogeneity. However, meta-analysis of sparse data, which may arise when the event rate is low for binary or count outcomes, poses a challenge to the normal-normal random-effects model in the accuracy and stability in inference since the normal approximation in the within-study model may not be good. To reduce bias arising from data sparsity, the generalized linear mixed model can be used by replacing the approximate normal within-study model with an exact model. Publication bias is one of the most serious threats in meta-analysis. Several quantitative sensitivity analysis methods for evaluating the potential impacts of selective publication are available for the normal-normal random-effects model. We propose a sensitivity analysis method by extending the likelihood-based sensitivity analysis with the t-statistic selection function of Copas to several generalized linear mixed-effects models. Through applications of our proposed method to several real-world meta-analysis and simulation studies, the proposed method was proven to outperform the likelihood-based sensitivity analysis based on the normal-normal model. The proposed method would give useful guidance to address publication bias in meta-analysis of sparse data.

翻译：荟萃分析是综合多项研究结果的有力工具。正态-正态随机效应模型被广泛用于解释研究间的异质性。然而，当二元或计数结局的事件发生率较低时，可能产生稀疏数据，此类数据的荟萃分析对正态-正态随机效应模型在推断的准确性和稳定性方面构成了挑战，因为研究内模型的正态近似可能效果不佳。为减少由数据稀疏性引起的偏倚，可通过用精确模型替代近似正态的研究内模型来使用广义线性混合模型。发表偏倚是荟萃分析中最严重的威胁之一。已有多种定量敏感性分析方法可用于评估正态-正态随机效应模型中选择性发表可能产生的影响。我们通过将基于似然的敏感性分析与Copas的t统计量选择函数扩展到几种广义线性混合效应模型，提出了一种敏感性分析方法。通过将所提方法应用于多个真实世界荟萃分析和模拟研究，证明该方法优于基于正态-正态模型的基于似然敏感性分析。所提方法将为处理稀疏数据荟萃分析中的发表偏倚提供有用的指导。