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1. Differentially private false discovery rate control

   https://doi.org/10.29012/jpc.755  

   Dwork, Cynthia; Su, Weijie; Zhang, Li (September 2021, Journal of Privacy and Confidentiality)

   Differential privacy provides a rigorous framework for privacy-preserving data analysis. This paper proposes the first differentially private procedure for controlling the false discovery rate (FDR) in multiple hypothesis testing. Inspired by the Benjamini-Hochberg procedure (BHq), our approach is to first repeatedly add noise to the logarithms of the p-values to ensure differential privacy and to select an approximately smallest p-value serving as a promising candidate at each iteration; the selected p-values are further supplied to the BHq and our private procedure releases only the rejected ones. Moreover, we develop a new technique that is based on a backward submartingale for proving FDR control of a broad class of multiple testing procedures, including our private procedure, and both the BHq step- up and step-down procedures. As a novel aspect, the proof works for arbitrary dependence between the true null and false null test statistics, while FDR control is maintained up to a small multiplicative factor. 

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2. Joint mirror procedure: controlling false discovery rate for identifying simultaneous signals

   https://doi.org/10.1093/biomtc/ujae142  

   Deng, Linsui; He, Kejun; Zhang, Xianyang (October 2024, Biometrics)

   ABSTRACT 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. 

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3. ZAP: Z -Value Adaptive Procedures for False Discovery Rate Control with Side Information

   https://doi.org/10.1111/rssb.12557  

   Leung, Dennis; Sun, Wenguang (November 2022, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract Adaptive multiple testing with covariates is an important research direction that has gained major attention in recent years. It has been widely recognised that leveraging side information provided by auxiliary covariates can improve the power of false discovery rate (FDR) procedures. Currently, most such procedures are devised with p-values as their main statistics. However, for two-sided hypotheses, the usual data processing step that transforms the primary statistics, known as p-values, into p-values not only leads to a loss of information carried by the main statistics, but can also undermine the ability of the covariates to assist with the FDR inference. We develop a p-value based covariate-adaptive (ZAP) methodology that operates on the intact structural information encoded jointly by the p-values and covariates. It seeks to emulate the oracle p-value procedure via a working model, and its rejection regions significantly depart from those of the p-value adaptive testing approaches. The key strength of ZAP is that the FDR control is guaranteed with minimal assumptions, even when the working model is misspecified. We demonstrate the state-of-the-art performance of ZAP using both simulated and real data, which shows that the efficiency gain can be substantial in comparison with p-value-based methods. Our methodology is implemented in the R package zap. 

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4. A generalized knockoff procedure for FDR control in structural change detection

   https://doi.org/10.1016/j.jeconom.2022.07.008  

   Liu, Jingyuan; Sun, Ao; Ke, Yuan (February 2024, Journal of Econometrics)

   Controlling false discovery rate (FDR) is crucial for variable selection, multiple testing, among other signal detection problems. In literature, there is certainly no shortage of FDR control strategies when selecting individual features, but the relevant works for structural change detection, such as profile analysis for piecewise constant coefficients and integration analysis with multiple data sources, are limited. In this paper, we propose a generalized knockoff procedure (GKnockoff) for FDR control under such problem settings. We prove that the GKnockoff possesses pairwise exchangeability, and is capable of controlling the exact FDR under finite sample sizes. We further explore GKnockoff under high dimensionality, by first introducing a new screening method to filter the high-dimensional potential structural changes. We adopt a data splitting technique to first reduce the dimensionality via screening and then conduct GKnockoff on the refined selection set. Furthermore, the powers of proposed methods are systematically studied. Numerical comparisons with other methods show the superior performance of GKnockoff, in terms of both FDR control and power. We also implement the proposed methods to analyze a macroeconomic dataset for detecting changes of driven effects of economic development on the secondary industry. 

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5. Ultra-high-dimensional threshold selection for quantile feature screening with false discovery rate error rate control: a case study on high blood pressure analysis

   https://doi.org/10.1093/biomtc/ujag035  

   Sanni, Saidat Abidemi; Yu, Yan; Zhao, Zhigen (January 2026, Biometrics)

   Abstract Identifying important genetic risk factors for high blood pressure is paramount for targeted interventions and comprehensive management strategies for this prevalent health condition. With ultra-high-dimensional genetic factors, feature screening plays a vital role in retaining the important risk factors and screening out the unimportant ones. However, its efficacy depends on selecting the appropriate threshold in different data contexts. We propose a novel quantile mirror (QM) approach for data-adaptive threshold selection with false discovery rate (FDR) control in quantile feature screening, where abnormally high blood pressure levels are of the most interest. The symmetric QM statistics enable the estimation of the FDR. Multiple data splitting is employed for result stability, and different thresholds are allowed for different quantiles. Additionally, we introduce the Quantile REflection via Data Splitting (QREDS) and the Hard Threshold with QREDS feature screening procedures. We apply our proposed methods to the Framingham Heart Study data. While many of the retained high-blood-pressure-related genetic features are validated from medical literature, some new risk factors are discovered. We show that our proposed procedures asymptotically control the FDR under suitable conditions. We further demonstrate the performance of the proposed methods through extensive numerical analysis and simulation studies. 

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