skip to main content

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

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.

more » « less
Award ID(s):
Author(s) / Creator(s):
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Journal of the Royal Statistical Society Series B: Statistical Methodology
Page Range / eLocation ID:
1886 to 1946
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Multiple testing (MT) with false discovery rate (FDR) control has been widely conducted in the “discrete paradigm” wherep‐values have discrete and heterogeneous null distributions. However, in this scenario existing FDR procedures often lose some power and may yield unreliable inference, and for this scenario there does not seem to be an FDR procedure that partitions hypotheses into groups, employs data‐adaptive weights and is nonasymptotically conservative. We propose a weightedp‐value‐based FDR procedure, “weighted FDR (wFDR) procedure” for short, for MT in the discrete paradigm that efficiently adapts to both heterogeneity and discreteness ofp‐value distributions. We theoretically justify the nonasymptotic conservativeness of the wFDR procedure under independence, and show via simulation studies that, for MT based onp‐values of binomial test or Fisher's exact test, it is more powerful than six other procedures. The wFDR procedure is applied to two examples based on discrete data, a drug safety study, and a differential methylation study, where it makes more discoveries than two existing methods.

    more » « less
  2. Combining SNP p -values from GWAS summary data is a promising strategy for detecting novel genetic factors. Existing statistical methods for the p -value-based SNP-set testing confront two challenges. First, the statistical power of different methods depends on unknown patterns of genetic effects that could drastically vary over different SNP sets. Second, they do not identify which SNPs primarily contribute to the global association of the whole set. We propose a new signal-adaptive analysis pipeline to address these challenges using the omnibus thresholding Fisher’s method (oTFisher). The oTFisher remains robustly powerful over various patterns of genetic effects. Its adaptive thresholding can be applied to estimate important SNPs contributing to the overall significance of the given SNP set. We develop efficient calculation algorithms to control the type I error rate, which accounts for the linkage disequilibrium among SNPs. Extensive simulations show that the oTFisher has robustly high power and provides a higher balanced accuracy in screening SNPs than the traditional Bonferroni and FDR procedures. We applied the oTFisher to study the genetic association of genes and haplotype blocks of the bone density-related traits using the summary data of the Genetic Factors for Osteoporosis Consortium. The oTFisher identified more novel and literature-reported genetic factors than existing p -value combination methods. Relevant computation has been implemented into the R package TFisher to support similar data analysis. 
    more » « less
  3. 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. 
    more » « less
  4. Summary

    In multiple-testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well-known Benjamini–Hochberg procedure, which a(0, 1]dapts to the amount of signal in the data, under certain distributional assumptions. Many modifications of this procedure have been proposed to improve power in scenarios where the hypotheses are organized into groups or into a hierarchy, as well as other structured settings. Here we introduce the ‘structure-adaptive Benjamini–Hochberg algorithm’ (SABHA) as a generalization of these adaptive testing methods. The SABHA method incorporates prior information about any predetermined type of structure in the pattern of locations of the signals and nulls within the list of hypotheses, to reweight the p-values in a data-adaptive way. This raises the power by making more discoveries in regions where signals appear to be more common. Our main theoretical result proves that the SABHA method controls the FDR at a level that is at most slightly higher than the target FDR level, as long as the adaptive weights are constrained sufficiently so as not to overfit too much to the data—interestingly, the excess FDR can be related to the Rademacher complexity or Gaussian width of the class from which we choose our data-adaptive weights. We apply this general framework to various structured settings, including ordered, grouped and low total variation structures, and obtain the bounds on the FDR for each specific setting. We also examine the empirical performance of the SABHA method on functional magnetic resonance imaging activity data and on gene–drug response data, as well as on simulated data.

    more » « less
  5. Summary

    Many methods for estimation or control of the false discovery rate (FDR) can be improved by incorporating information about π0, the proportion of all tested null hypotheses that are true. Estimates of π0 are often based on the number of p-values that exceed a threshold λ. We first give a finite sample proof for conservative point estimation of the FDR when the λ-parameter is fixed. Then we establish a condition under which a dynamic adaptive procedure, whose λ-parameter is determined by data, will lead to conservative π0- and FDR estimators. We also present asymptotic results on simultaneous conservative FDR estimation and control for a class of dynamic adaptive procedures. Simulation results show that a novel dynamic adaptive procedure achieves more power through smaller estimation errors for π0 under independence and mild dependence conditions. We conclude by discussing the connection between estimation and control of the FDR and show that several recently developed FDR control procedures can be cast in a unifying framework where the strength of the procedures can be easily evaluated.

    more » « less