Université Paris Cité, Research Center of Epidemiology and Statistics (CRESS-U1153), INSERM, Paris, France.
MRC Clinical Trials Unit, University College London, London, UK.
Stat Med. 2022 Nov 20;41(26):5203-5219. doi: 10.1002/sim.9562. Epub 2022 Aug 26.
Network meta-analysis (NMA) of rare events has attracted little attention in the literature. Until recently, networks of interventions with rare events were analyzed using the inverse-variance NMA approach. However, when events are rare the normal approximations made by this model can be poor and effect estimates are potentially biased. Other methods for the synthesis of such data are the recent extension of the Mantel-Haenszel approach to NMA or the use of the noncentral hypergeometric distribution. In this article, we suggest a new common-effect NMA approach that can be applied even in networks of interventions with extremely low or even zero number of events without requiring study exclusion or arbitrary imputations. Our method is based on the implementation of the penalized likelihood function proposed by Firth for bias reduction of the maximum likelihood estimate to the logistic expression of the NMA model. A limitation of our method is that heterogeneity cannot be taken into account as an additive parameter as in most meta-analytical models. However, we account for heterogeneity by incorporating a multiplicative overdispersion term using a two-stage approach. We show through simulation that our method performs consistently well across all tested scenarios and most often results in smaller bias than other available methods. We also illustrate the use of our method through two clinical examples. We conclude that our "penalized likelihood NMA" approach is promising for the analysis of binary outcomes with rare events especially for networks with very few studies per comparison and very low control group risks.
网络荟萃分析（NMA）对罕见事件的关注较少。直到最近，罕见事件干预措施的网络仍采用逆方差 NMA 方法进行分析。然而，当事件很少时，该模型的正态逼近可能很差，并且效果估计可能存在偏差。分析此类数据的其他方法是 Mantel-Haenszel 方法在 NMA 中的最新扩展，或者使用非中心超几何分布。在本文中，我们提出了一种新的通用效应 NMA 方法，即使在干预措施网络中罕见事件甚至零事件的情况下也可以应用，而无需排除研究或任意插补。我们的方法基于 Firth 提出的惩罚似然函数的实施，该函数可减少最大似然估计对 NMA 模型逻辑表达式的偏差。我们方法的一个局限性是，由于大多数荟萃分析模型中都将异质性作为附加参数来考虑，因此不能将异质性作为附加参数来考虑。但是，我们通过使用两阶段方法结合乘法过离散项来考虑异质性。通过模拟，我们证明我们的方法在所有测试场景中都表现良好，并且通常比其他可用方法产生的偏差更小。我们还通过两个临床示例说明了我们方法的使用。我们得出结论，我们的“惩罚似然 NMA”方法对于分析罕见事件的二分类结局很有前途，特别是对于每比较研究很少且对照组风险很低的网络。
