Zhang Ming, Xiao Olivia Y, Lim Johan, Wang Xinlei
Department of Statistics and Data Science, Southern Methodist University, Dallas, Texas, 75205, USA.
Highland Park High School, Dallas, Texas, 75205, USA.
Sci Rep. 2023 Oct 18;13(1):17712. doi: 10.1038/s41598-023-44638-x.
Random-effects (RE) meta-analysis is a crucial approach for combining results from multiple independent studies that exhibit heterogeneity. Recently, two frequentist goodness-of-fit (GOF) tests were proposed to assess the fit of RE model. However, they tend to perform poorly when assessing rare binary events. Under a general binomial-normal framework, we propose a novel GOF test for the meta-analysis of rare events. Our method is based on pivotal quantities that play an important role in Bayesian model assessment. It further adopts the Cauchy combination idea proposed in a 2019 JASA paper, to combine dependent p-values computed using posterior samples from Markov Chain Monte Carlo. The advantages of our method include clear conception and interpretation, incorporation of all data including double zeros without the need for artificial correction, well-controlled Type I error, and generally improved ability in detecting model misfits compared to previous GOF methods. We illustrate the proposed method via simulation and three real data applications.
随机效应（RE）荟萃分析是整合多个存在异质性的独立研究结果的关键方法。最近，有人提出了两种频率主义拟合优度（GOF）检验来评估RE模型的拟合情况。然而，在评估罕见二元事件时，它们往往表现不佳。在一般的二项式正态框架下，我们提出了一种用于罕见事件荟萃分析的新型GOF检验。我们的方法基于在贝叶斯模型评估中起重要作用的枢轴量。它进一步采用了2019年发表于《美国统计学会杂志》一篇论文中提出的柯西组合思想，来组合使用马尔可夫链蒙特卡罗后验样本计算出的相关p值。我们方法的优点包括概念清晰且易于解释、纳入了所有数据（包括双零数据）而无需人工校正、I型错误得到良好控制，并且与之前的GOF方法相比，在检测模型不拟合方面的能力普遍有所提高。我们通过模拟和三个实际数据应用来说明所提出的方法。
