Publication bias (PB) is one of the serious issues in meta-analysis. Many existing methods dealing with PB are based on the normal-normal (NN) random-effects model assuming normal models in both the within-study and the between-study levels. For rare-event meta-analysis where the data contain rare occurrences of event, the standard NN random-effects model may perform poorly. Instead, the generalized linear mixed effects model (GLMM) using the exact within-study model is recommended. However, no method has been proposed for dealing with PB in rare-event meta-analysis using the GLMM. In this paper, we propose sensitivity analysis methods for evaluating the impact of PB on the GLMM based on the famous Copas-Heckman-type selection model. The proposed methods can be easily implemented with the standard software coring the nonlinear mixed-effects model. We use a real-world example to show how the usefulness of the proposed methods in evaluating the potential impact of PB in meta-analysis of the log-transformed odds ratio based on the GLMM using the non-central hypergeometric or binomial distribution as the within-study model. An extension of the proposed method is also introduced for evaluating PB in meta-analysis of proportion based on the GLMM with the binomial within-study model.

翻译：发表偏倚（PB）是荟萃分析中的严重问题之一。现有处理PB的诸多方法均基于正态-正态（NN）随机效应模型，该模型假设研究内与研究间水平均服从正态分布。对于包含罕见事件发生的数据的罕见事件荟萃分析，标准NN随机效应模型表现欠佳。此时，推荐采用精确研究内模型的广义线性混合模型（GLMM）。然而，目前尚无基于GLMM处理罕见事件荟萃分析中PB的方法。本文基于著名的Copas-Heckman型选择模型，提出评估PB对GLMM影响的敏感性分析方法。所提方法可通过标准软件调用非线性混合效应模型轻松实现。我们通过一个真实案例展示了所提方法在评估基于GLMM的对数转换优势比荟萃分析中潜在PB影响时的实用性，该GLMM采用非中心超几何分布或二项分布作为研究内模型。此外，还介绍了所提方法的扩展，用于评估基于二项研究内模型的GLMM比例荟萃分析中的PB。