Deng Linsui, He Kejun, Zhang Xianyang
School of Data Science, The Chinese University of Hong Kong, Shenzhen 518172, China.
Center for Applied Statistics, Institute of Statistics and Big Data, Renmin University of China, Beijing 100872, China.
Biometrics. 2024 Oct 3;80(4). doi: 10.1093/biomtc/ujae142.
In many applications, the process of identifying a specific feature of interest often involves testing multiple hypotheses for their joint statistical significance. Examples include mediation analysis, which simultaneously examines the existence of the exposure-mediator and the mediator-outcome effects, and replicability analysis, aiming to identify simultaneous signals that exhibit statistical significance across multiple independent studies. In this work, we present a new approach called the joint mirror (JM) procedure that effectively detects such features while maintaining false discovery rate (FDR) control in finite samples. The JM procedure employs an iterative method that gradually shrinks the rejection region based on progressively revealed information until a conservative estimate of the false discovery proportion is below the target FDR level. Additionally, we introduce a more stringent error measure known as the composite FDR (cFDR), which assigns weights to each false discovery based on its number of null components. We use the leave-one-out technique to prove that the JM procedure controls the cFDR in finite samples. To implement the JM procedure, we propose an efficient algorithm that can incorporate partial ordering information. Through extensive simulations, we show that our procedure effectively controls the cFDR and enhances statistical power across various scenarios, including the case that test statistics are dependent across the features. Finally, we showcase the utility of our method by applying it to real-world mediation and replicability analyses.
在许多应用中，识别感兴趣的特定特征的过程通常涉及检验多个假设的联合统计显著性。例如包括中介分析，它同时考察暴露-中介效应和中介-结果效应的存在情况，以及可重复性分析，旨在识别在多个独立研究中呈现统计显著性的同时信号。在这项工作中，我们提出了一种称为联合镜像（JM）程序的新方法，该方法能在有限样本中有效检测此类特征，同时保持对错误发现率（FDR）的控制。JM程序采用一种迭代方法，基于逐步揭示的信息逐渐缩小拒绝区域，直到对错误发现比例的保守估计低于目标FDR水平。此外，我们引入了一种更严格的误差度量，称为复合FDR（cFDR），它根据每个错误发现的零分量数量为其分配权重。我们使用留一法来证明JM程序在有限样本中控制cFDR。为了实现JM程序，我们提出了一种可以纳入偏序信息的高效算法。通过广泛的模拟，我们表明我们的程序在各种情况下都能有效控制cFDR并提高统计功效，包括检验统计量在各特征间相关的情况。最后，我们通过将其应用于实际的中介分析和可重复性分析来展示我们方法的实用性。
