Combining correlated p -values from multiple hypothesis testing is a most frequently used method for integrating information in genetic and genomic data analysis. However, most existing methods for combining independent p -values from individual component problems into a single unified p -value are unsuitable for the correlational structure among p -values from multiple hypothesis testing. Although some existing p -value combination methods had been modified to overcome the potential limitations, there is no uniformly most powerful method for combining correlated p -values in genetic data analysis. Therefore, providing a p -value combination method that can robustly control type I errors and keep the good power rates is necessary. In this paper, we propose an empirical method based on the gamma distribution (EMGD) for combining dependent p -values from multiple hypothesis testing. The proposed test, EMGD, allows for flexible accommodating the highly correlated p -values from the multiple hypothesis testing into a unified p -value for examining the combined hypothesis that we are interested in. The EMGD retains the robustness character of the empirical Brown’s method (EBM) for pooling the dependent p -values from multiple hypothesis testing. Moreover, the EMGD keeps the character of the method based on the gamma distribution that simultaneously retains the advantages of the z -transform test and the gamma-transform test for combining dependent p -values from multiple statistical tests. The two characters lead to the EMGD that can keep the robust power for combining dependent p -values from multiple hypothesis testing. The performance of the proposed method EMGD is illustrated with simulations and real data applications by comparing with the existing methods, such as Kost and McDermott’s method, the EBM and the harmonic mean p -value method.

中文翻译：

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通过伽马分布组合相关 p 值


结合多个假设检验的相关 p 值是遗传和基因组数据分析中整合信息最常用的方法。然而，大多数现有的将来自各个分量问题的独立 p 值组合成单个统一 p 值的方法不适合来自多个假设检验的 p 值之间的相关结构。尽管一些现有的 p 值组合方法已被修改以克服潜在的局限性，但在遗传数据分析中还没有统一的最强大的方法来组合相关的 p 值。因此，有必要提供能够鲁棒地控制I类误差并保持良好功率率的p值组合方法。在本文中，我们提出了一种基于伽玛分布（EMGD）的经验方法，用于组合来自多个假设检验的相关 p 值。所提出的检验 EMGD 允许灵活地将多个假设检验中的高度相关的 p 值容纳为统一的 p 值，以检查我们感兴趣的组合假设。EMGD 保留了经验布朗方法的鲁棒性特征（ EBM）用于汇集来自多个假设检验的相关 p 值。此外，EMGD 保留了基于伽玛分布的方法的特征，同时保留了 z 变换检验和用于组合来自多个统计检验的相关 p 值的伽玛变换检验的优点。这两个特征导致 EMGD 可以保持组合来自多个假设检验的相关 p 值的稳健能力。 通过与现有方法（如 Kost 和 McDermott 方法、EBM 和调和平均 p 值方法）的比较，通过仿真和实际数据应用说明了所提出的方法 EMGD 的性能。