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There is ample research on false discovery rate (FDR) control for testing hypotheses classified according to one criterion. However, scenarios of hypotheses partitioned via two different criteria are often encountered in practice. Such two-way classification encodes more structural information in the associated multiple testing of the hypotheses than its one-way or un-classified counterparts. Unfortunately, there seems to be very little research tailored for multiple testing under that classification setting. This article proposes weighted versions of the Benjamini–Hochberg (BH) method, both in their oracle and data-adaptive forms, efficiently capturing one- or two-way classified structure of hypotheses through appropriately chosen weights. The proposed methods control FDR non-asymptotically in their oracle forms under positive regression dependence on subset (PRDS) of null p-values and in their data-adaptive forms for independent p-values. The one-way data-adaptive methods are asymptotically conservative under weak dependence. Simulations demonstrate these methods’ superior power performances over some contemporary procedures and provide evidence of their non-asymptotic conservativeness under certain dependence scenarios. The proposed two-way adaptive procedure is effectively applied to a data set from microbial abundance study.

Multiple testing with discrete p -values routinely arises in various scientific endeavors. However, procedures, including the false discovery rate (FDR) controlling Benjamini–Hochberg (BH) procedure, often used in such settings, being developed originally for p -values with continuous distributions, are too conservative, and so may not be as powerful as one would hope for. Therefore, improving the BH procedure by suitably adapting it to discrete p -values without losing its FDR control is currently an important path of research. This paper studies the FDR control of the BH procedure when it is applied to mid p -values and derive conditions under which it is conservative. Our simulation study reveals that the BH procedure applied to mid p -values may be conservative under much more general settings than characterized in this work, and that an adaptive version of the BH procedure applied to mid p -values is as powerful as an existing adaptive procedure based on randomized p -values.

For multiple testing based on discrete p-values, we propose a false discovery rate (FDR) procedure "BH+" with proven conservativeness. BH+ is at least as powerful as the BH (i.e., Benjamini-Hochberg) procedure when they are applied to superuniform p-values. Further, when applied to mid-p-values, BH+ can be more powerful than it is applied to conventional p-values. An easily verifiable necessary and sufficient condition for this is provided. BH+ is perhaps the first conservative FDR procedure applicable to mid-p-values and to p-values with general distributions. It is applied to multiple testing based on discrete p-values in a methylation study, an HIV study and a clinical safety study, where it makes considerably more discoveries than the BH procedure. In addition, we propose an adaptive version of the BH+ procedure, prove its conservativeness under certain conditions, and provide evidence on its excellent performance via simulation studies.

The objective of this foundational study was to develop and evaluate the efficacy of an affordable hyperspectral imaging (HSI) system to identify single and mixed strains of foodborne pathogens in dairy products. This study was designed as a completely randomized design with three replications. Three strains each of

We propose a ranking and selection procedure to prioritize relevant predictors and control false discovery proportion (FDP) in variable selection. Our procedure utilizes a new ranking method built upon the de-sparsified Lasso estimator. We show that the new ranking method achieves the optimal order of minimum non-zero effects in ranking relevant predictors ahead of irrelevant ones. Adopting the new ranking method, we develop a variable selection procedure to asymptotically control FDP at a user-specified level. We show that our procedure can consistently estimate the FDP of variable selection as long as the de-sparsified Lasso estimator is asymptotically normal. In simulations, our procedure compares favorably to existing methods in ranking efficiency and FDP control when the regression model is relatively sparse.

We show that, when a random variable has a parametric distribution as a member of an infinitely divisible natural exponential family whose induced measure is absolutely continuous with respect to its basis measure, there exists a deterministic function, referred to as “reduction function”, such that the random variable transformed by this function is an unbiased estimator of the variance of the random variable. Our result can be used in estimating latent structure in high-dimensional data and in implementing iterative reweighted least squares for generalized linear models.

Dysregulation or crosstalk of signal transduction pathways contributes to disease development. Despite the initial success of identifying causal links between source and target proteins in simple or well-studied biological systems, it remains challenging to investigate alternative pathways specifically associated with a disease. We develop a Gene network-based integrative approach for Inferring disease-associated signaling Pathways (GIP). Specifically, we identify alternative pathways given source and target proteins. GIP was applied to human breast cancer data. Experimental results showed that GIP identified biologically meaningful pathway modules associated with antiestrogen resistance.

Deep sequencing of bulk RNA enables the differential expression analysis at transcript level. We develop a Bayesian approach to directly identify differentially expressed transcripts from RNA-seq data, which features a novel joint model of the sample variability and the differential state of individual transcripts. For each transcript, to minimize the inaccuracy of differential state caused by transcription abundance estimation, we estimate its expression abundance together with the differential state iteratively and enable the differential analysis of weakly expressed transcripts. Simulation analysis demonstrates that the proposed approach has a superior performance over conventional methods (estimating transcription expression first and then identifying differential state), particularly for lowly expressed transcripts. We further apply the proposed approach to a breast cancer RNA-seq data of patients treated by tamoxifen and identified a set of differentially expressed transcripts, providing insights into key signaling pathways associated with breast cancer recurrence.

The proportion of false null hypotheses is a very important quantity in statistical modelling and inference based on the two-component mixture model and its extensions, and in control and estimation of the false discovery rate and false non-discovery rate. Most existing estimators of this proportion threshold p-values, deconvolve the mixture model under constraints on its components, or depend heavily on the location-shift property of distributions. Hence, they usually are not consistent, applicable to non-location-shift distributions, or applicable to discrete statistics or p-values. To eliminate these shortcomings, we construct uniformly consistent estimators of the proportion as solutions to Lebesgue-Stieltjes integral equations. In particular, we provide such estimators respectively for random variables whose distributions have Riemann-Lebesgue type characteristic functions, form discrete natural exponential families with infinite supports, and form natural exponential families with separable moment sequences. We provide the speed of convergence and uniform consistency class for each such estimator under independence. In addition, we provide example distribution families for which a consistent estimator of the proportion cannot be constructed using our techniques., 44 pages in single spacing; 5 figures; proofs moved to supplementary materials; extended Introduction and Discussion; added a Simulation Study; accepted by Journal of Multivariate Analysis

Variable selection methods have been developed in linear regression to provide sparse solutions. Recent studies have focused on further interpretations on the sparse solutions in terms of false positive control. In this paper, we consider false negative control for variable selection with the goal to efficiently select a high proportion of relevant predictors. Different from existing studies in power analysis and sure screening, we propose to directly estimate the false negative proportion (FNP) of a decision rule and select the smallest subset of predictors that has the estimated FNP less than a user-specified control level. The proposed method is adaptive to the user-specified control level on FNP by selecting less candidates if a higher level is implemented. On the other hand, when data has stronger effect size or larger sample size, the proposed method controls FNP more efficiently with less false positives. New analytic techniques are developed to cope with the major challenge of FNP control when relevant predictors cannot be consistently separated from irrelevant ones. Our numerical results are in line with the theoretical findings., Comment: 27 pages and 1 figure; to appear in Electronic Journal of Statistics

The false discovery rate measures the proportion of false discoveries among a set of hypothesis tests called significant. This quantity is typically estimated based on p-values or test statistics. In some scenarios, there is additional information available that may be used to more accurately estimate the false discovery rate. We develop a new framework for formulating and estimating false discovery rates and q-values when an additional piece of information, which we call an “informative variable”, is available. For a given test, the informative variable provides information about the prior probability a null hypothesis is true or the power of that particular test. The false discovery rate is then treated as a function of this informative variable. We consider two applications in genomics. Our first is a genetics of gene expression (eQTL) experiment in yeast where every genetic marker and gene expression trait pair are tested for associations. The informative variable in this case is the distance between each genetic marker and gene. Our second application is to detect differentially expressed genes in an RNA-seq study carried out in mice. The informative variable in this study is the per-gene read depth. The framework we develop is quite general, and it should be useful in a broad range of scientific applications.

We prove a conjecture of Bar-Lev, Bshouty and Enis stating that a polynomial with a simple root at 0 and a complex root with positive imaginary part is the variance function of a one-parameter natural exponential family with mean domain ( 0 , ∞ ) if and only if the real part of the complex root is not positive.

Multiple testing with false discovery rate (FDR) control has been widely conducted in the ``discrete paradigm" where p-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 non-asymptotically conservative. We propose a weighted FDR procedure for multiple testing in the discrete paradigm that efficiently adapts to both the heterogeneity and discreteness of p-value distributions. We theoretically justify the non-asymptotic conservativeness of the weighted FDR procedure under independence, and show via simulation studies that, for multiple testing based on p-values of Binomial test or Fisher's exact test, it is more powerful than six other procedures. The weighted FDR procedure is applied to a drug safety study and a differential methylation study based on discrete data, where it makes more discoveries than two existing methods., Comment: 29 pages; in this version: (1) new weights from arXiv:1812.06551v2 are employed by the wFDR procedure to ensure its conservativeness under independence; (2) non-asymptotic upper bound is provided for the wFDR procedure that uses plug-in weights that are induced by the proportion estimator of arxiv:1410.4274v2; (3) simulation study under dependence uses more a complicated block dependence structure

We consider multiple testing with false discovery rate (FDR) control when p-values have discrete and heterogeneous null distributions. We propose a new estimator of the proportion of true null hypotheses and demonstrate that it is less upwardly biased than Storey's estimator and two other estimators. The new estimator induces two adaptive procedures, i.e., an adaptive Benjamini-Hochberg (BH) procedure and an adaptive Benjamini-Hochberg-Heyse (BHH) procedure. We prove that the the adaptive BH procedure is conservative non-asymptotically. Through simulation studies, we show that these procedures are usually more powerful than their non-adaptive counterparts and that the adaptive BHH procedure is usually more powerful than the adaptive BH procedure and a procedure based on randomized p-value. The adaptive procedures are applied to a study of HIV vaccine efficacy, where they identify more differentially polymorphic positions than the BH procedure at the same FDR level., Comment: This version is essentially a different paper than the previous one. A new estimator of the proportion of true null hypotheses has been developed, and it induces two adaptive FDR procedures. One such procedure has been proved to be conservative non-asymptotically, and the other has been empirically shown to be conservative