Multiple hypothesis testing is an integral component of data analysis for large-scale technologies such as proteomics, transcriptomics, or metabolomics, for which the false discovery rate (FDR) and positive FDR (pFDR) have been accepted as error estimation and control measures. The pFDR is the expectation of false discovery proportion (FDP), which refers to the ratio of the number of null hypotheses to that of all rejected hypotheses. In practice, the expectation of ratio is approximated by the ratio of expectation; however, the conditions for transforming the former into the latter have not been investigated. This work derives exact integral expressions for the expectation (pFDR) and variance of FDP. The widely used approximation (ratio of expectations) is shown to be a particular case (in the limit of a large sample size) of the integral formula for pFDR. A recurrence formula is provided to compute the pFDR for a predefined number of null hypotheses. The variance of FDP was approximated for a practical application in peptide identification using forward and reversed protein sequences. The simulations demonstrate that the integral expression exhibits better accuracy than the approximate formula in the case of a small number of hypotheses. For large sample sizes, the pFDRs obtained by the integral expression and approximation do not differ substantially. Applications to proteomics data sets are included.

Replicability is the cornerstone of modern scientific research. Reliable identifications of genotype-phenotype associations that are significant in multiple genome-wide association studies (GWASs) provide stronger evidence for the findings. Current replicability analysis relies on the independence assumption among single-nucleotide polymorphisms (SNPs) and ignores the linkage disequilibrium (LD) structure. We show that such a strategy may produce either overly liberal or overly conservative results in practice. We develop an efficient method, ReAD, to detect replicable SNPs associated with the phenotype from two GWASs accounting for the LD structure. The local dependence structure of SNPs across two heterogeneous studies is captured by a four-state hidden Markov model (HMM) built on two sequences of p values. By incorporating information from adjacent locations via the HMM, our approach provides more accurate SNP significance rankings. ReAD is scalable, platform independent, and more powerful than existing replicability analysis methods with effective false discovery rate control. Through analysis of datasets from two asthma GWASs and two ulcerative colitis GWASs, we show that ReAD can identify replicable genetic loci that existing methods might otherwise miss.

We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model the nested structure as a directed acyclic graph, including chain and tree graphs as special cases. Each node in the graph is a hypothesis and rejecting a node requires also rejecting all of its ancestors. We propose a general framework for adjusting node-level test statistics using the known logical constraints. Within this framework, we study a smoothing procedure that combines each node with all of its descendants to form a more powerful statistic. We prove a broad class of smoothing strategies can be used with existing selection procedures to control the familywise error rate, false discovery exceedance rate, or false discovery rate, so long as the original test statistics are independent under the null. When the null statistics are not independent but are derived from positively-correlated normal observations, we prove control for all three error rates when the smoothing method is arithmetic averaging of the observations. Simulations and an application to a real biology dataset demonstrate that smoothing leads to substantial power gains.

This paper develops a method based on model-X knockoffs to find conditional associations that are consistent across environments, controlling the false discovery rate. The motivation for this problem is that large data sets may contain numerous associations that are statistically significant and yet misleading, as they are induced by confounders or sampling imperfections. However, associations replicated under different conditions may be more interesting. In fact, consistency sometimes provably leads to valid causal inferences even if conditional associations do not. While the proposed method is widely applicable, this paper highlights its relevance to genome-wide association studies, in which robustness across populations with diverse ancestries mitigates confounding due to unmeasured variants. The effectiveness of this approach is demonstrated by simulations and applications to the UK Biobank data.

BACKGROUND: Expression quantitative trait locus (eQTL) analysis aims to detect the genetic variants that influence the expression of one or more genes. Gene-level eQTL testing forms a natural grouped-hypothesis testing strategy with clear biological importance. Methods to control family-wise error rate or false discovery rate for group testing have been proposed earlier, but may not be powerful or easily apply to eQTL data, for which certain structured alternatives may be defensible and may enable the researcher to avoid overly conservative approaches.
RESULTS: In an empirical Bayesian setting, we propose a new method to control the false discovery rate (FDR) for grouped hypotheses. Here, each gene forms a group, with SNPs annotated to the gene corresponding to individual hypotheses. The heterogeneity of effect sizes in different groups is considered by the introduction of a random effects component. Our method, entitled Random Effects model and testing procedure for Group-level FDR control (REG-FDR), assumes a model for alternative hypotheses for the eQTL data and controls the FDR by adaptive thresholding. As a convenient alternate approach, we also propose Z-REG-FDR, an approximate version of REG-FDR, that uses only Z-statistics of association between genotype and expression for each gene-SNP pair. The performance of Z-REG-FDR is evaluated using both simulated and real data. Simulations demonstrate that Z-REG-FDR performs similarly to REG-FDR, but with much improved computational speed.
CONCLUSIONS: Our results demonstrate that the Z-REG-FDR method performs favorably compared to other methods in terms of statistical power and control of FDR. It can be of great practical use for grouped hypothesis testing for eQTL analysis or similar problems in statistical genomics due to its fast computation and ability to be fit using only summary data.

The false discovery rate (FDR) is a widely used metric of statistical significance for genomic data analyses that involve multiple hypothesis testing. Power and sample size considerations are important in planning studies that perform these types of genomic data analyses. Here, we propose a three-rectangle approximation of a p-value histogram to derive a formula to compute the statistical power and sample size for analyses that involve the FDR. We also introduce the R package FDRsamplesize2, which incorporates these and other power calculation formulas to compute power for a broad variety of studies not covered by other FDR power calculation software. A few illustrative examples are provided. The FDRsamplesize2 package is available on CRAN.

A growing number of modern scientific problems in areas such as genomics, neurobiology, and spatial epidemiology involve the measurement and analysis of thousands of related features that may be stochastically dependent at arbitrarily strong levels. In this work, we consider the scenario where the features follow a multivariate Normal distribution. We demonstrate that dependence is manifested as random variation shared among features, and that standard methods may yield highly unstable inference due to dependence, even when the dependence is fully parameterized and utilized in the procedure. We propose a \"cross-dimensional inference\" framework that alleviates the problems due to dependence by modeling and removing the variation shared among features, while also properly regularizing estimation across features. We demonstrate the framework on both simultaneous point estimation and multiple hypothesis testing in scenarios derived from the scientific applications of interest.

Estimating the false discovery rate (FDR) of peptide identifications is a key step in proteomics data analysis, and many methods have been proposed for this purpose. Recently, an entrapment-inspired protocol to validate methods for FDR estimation appeared in articles showcasing new spectral library search tools. That validation approach involves generating incorrect spectral matches by searching spectra from evolutionarily distant organisms (entrapment queries) against the original target search space. Although this approach may appear similar to the solutions using entrapment databases, it represents a distinct conceptual framework whose correctness has not been verified yet. In this viewpoint, we first discussed the background of the entrapment-based validation protocols and then conducted a few simple computational experiments to verify the assumptions behind them. The results reveal that entrapment databases may, in some implementations, be a reasonable choice for validation, while the assumptions underpinning validation protocols based on entrapment queries are likely to be violated in practice. This article also highlights the need for well-designed frameworks for validating FDR estimation methods in proteomics.

Assigning statistical confidence estimates to discoveries produced by a tandem mass spectrometry proteomics experiment is critical to enabling principled interpretation of the results and assessing the cost/benefit ratio of experimental follow-up. The most common technique for computing such estimates is to use target-decoy competition (TDC), in which observed spectra are searched against a database of real (target) peptides and a database of shuffled or reversed (decoy) peptides. TDC procedures for estimating the false discovery rate (FDR) at a given score threshold have been developed for application at the level of spectra, peptides, or proteins. Although these techniques are relatively straightforward to implement, it is common in the literature to skip over the implementation details or even to make mistakes in how the TDC procedures are applied in practice. Here we present Crema, an open-source Python tool that implements several TDC methods of spectrum-, peptide- and protein-level FDR estimation. Crema is compatible with a variety of existing database search tools and provides a straightforward way to obtain robust FDR estimates.

This paper explores the exposome concept and its role in elucidating the interplay between environmental exposures and human health. We introduce two key concepts critical for exposomics research. Firstly, we discuss the joint impact of genetics and environment on phenotypes, emphasizing the variance attributable to shared and nonshared environmental factors, underscoring the complexity of quantifying the exposome\'s influence on health outcomes. Secondly, we introduce the importance of advanced data-driven methods in large cohort studies for exposomic measurements. Here, we introduce the exposome-wide association study (ExWAS), an approach designed for systematic discovery of relationships between phenotypes and various exposures, identifying significant associations while controlling for multiple comparisons. We advocate for the standardized use of the term \"exposome-wide association study, ExWAS,\" to facilitate clear communication and literature retrieval in this field. The paper aims to guide future health researchers in understanding and evaluating exposomic studies. Our discussion extends to emerging topics, such as FAIR Data Principles, biobanked healthcare datasets, and the functional exposome, outlining the future directions in exposomic research. This abstract provides a succinct overview of our comprehensive approach to understanding the complex dynamics of the exposome and its significant implications for human health.