Network meta-analysis (NMA) is a useful tool to compare multiple interventions simultaneously in a single meta-analysis, it can be very helpful for medical decision making when the study aims to find the best therapy among several active candidates. However, the validity of its results is threatened by the publication bias issue. Existing methods to handle the publication bias issue in the standard pairwise meta-analysis are hard to extend to this area with the complicated data structure and the underlying assumptions for pooling the data. In this paper, we aimed to provide a flexible inverse probability weighting (IPW) framework along with several t-type selection functions to deal with the publication bias problem in the NMA context. To solve these proposed selection functions, we recommend making use of the additional information from the unpublished studies from multiple clinical trial registries. A comprehensive numerical study and a real example showed that our methodology can help obtain more accurate estimates and higher coverage probabilities, and improve other properties of an NMA (e.g., ranking the interventions).

翻译：网络荟萃分析（NMA）是一种可在单次荟萃分析中同时比较多种干预措施的有效工具，当研究旨在从多个候选方案中寻找最优疗法时，对医疗决策具有重要价值。然而，发表偏倚问题威胁着其结果的效度。在标准配对荟萃分析中处理发表偏倚的现有方法，因数据结构的复杂性及数据合并的隐含假设，难以拓展至该领域。本文旨在提供一种灵活的逆概率加权（IPW）框架，结合多种t型选择函数，以处理NMA情境下的发表偏倚问题。为求解所提出的选择函数，我们建议利用来自多个临床试验注册库中未发表研究的额外信息。全面的数值模拟与真实案例表明，本方法有助于获得更准确的估计值、更高的覆盖概率，并改善NMA的其他特性（如干预措施排序）。