Rilling Joseph, Tang Cheng Yong
Department of Statistics, Operations, and Data Science, Temple University, Philadelphia, PA 19122 USA.
Stat Comput. 2025;35(3):69. doi: 10.1007/s11222-025-10600-2. Epub 2025 Mar 16.
This study introduces a novel -value-based multiple testing approach tailored for generalized linear models. Despite the crucial role of generalized linear models in statistics, existing methodologies face obstacles arising from the heterogeneous variance of response variables and complex dependencies among estimated parameters. Our aim is to address the challenge of controlling the false discovery rate (FDR) amidst arbitrarily dependent test statistics. Through the development of efficient computational algorithms, we present a versatile statistical framework for multiple testing. The proposed framework accommodates a range of tools developed for constructing a new model matrix in regression-type analysis, including random row permutations and Model-X knockoffs. We devise efficient computing techniques to solve the encountered non-trivial quadratic matrix equations, enabling the construction of paired -values suitable for the two-step multiple testing procedure proposed by Sarkar and Tang (Biometrika 109(4): 1149-1155, 2022). Theoretical analysis affirms the properties of our approach, demonstrating its capability to control the FDR at a given level. Empirical evaluations further substantiate its promising performance across diverse simulation settings.
The online version contains supplementary material available at 10.1007/s11222-025-10600-2.
本研究介绍了一种专门为广义线性模型量身定制的基于p值的新型多重检验方法。尽管广义线性模型在统计学中起着关键作用，但现有方法面临着响应变量异质方差以及估计参数之间复杂相关性所带来的障碍。我们的目标是应对在任意相关检验统计量中控制错误发现率（FDR）的挑战。通过开发高效的计算算法，我们提出了一个用于多重检验的通用统计框架。所提出的框架容纳了一系列为回归类型分析中构建新模型矩阵而开发的工具，包括随机行排列和模型X替代。我们设计了高效的计算技术来解决遇到的非平凡二次矩阵方程，从而能够构建适用于Sarkar和Tang（《生物统计学》109(4): 1149 - 1155, 2022）提出的两步多重检验程序的配对p值。理论分析证实了我们方法的性质，表明其能够在给定水平上控制FDR。实证评估进一步证实了其在各种模拟设置下的良好性能。
在线版本包含可在10.1007/s11222-025-10600-2获取的补充材料。
