Local False Discovery Rate Research Articles

Multiple testing under dependence via graphical models

Large-scale multiple testing tasks often exhibit dependence. Leveraging the dependence between individual tests is still one challenging and important problem in statistics. With recent advances in graphical models, it is feasible to use them to capture the dependence among multiple hypotheses. We propose a multiple testing procedure which is based on a Markov-random-field-coupled mixture model. The underlying true states of hypotheses are represented by a latent binary Markov random field, and the observed test statistics appear as the coupled mixture variables. The model can be learned by a novel EM algorithm. The next step is to infer the posterior probability that each hypothesis is null (termed local index of significance), and the false discovery rate can be controlled accordingly. We also provide a semiparametric variation of the graphical model which is useful in the situation where $f_{1}$ (the density function of the test statistic under the alternative hypothesis) is heterogeneous among multiple hypotheses. This semiparametric approach exactly generalizes the local FDR procedure [J. Amer. Statist. Assoc. 96 (2001) 1151–1160] and connects with the BH procedure [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300]. Simulations show that the numerical performance of multiple testing can be improved substantially by using our procedure. We apply the procedure to a real-world genome-wide association study on breast cancer, and we identify several SNPs with strong association evidence.

Nonlinear Network Reconstruction from Gene Expression Data Using Marginal Dependencies Measured by DCOL.

Reconstruction of networks from high-throughput expression data is an important tool to identify new regulatory relations. Given that nonlinear and complex relations exist between biological units, methods that can utilize nonlinear dependencies may yield insights that are not provided by methods using linear associations alone. We have previously developed a distance to measure predictive nonlinear relations, the Distance based on Conditional Ordered List (DCOL), which is sensitive and computationally efficient on large matrices. In this study, we explore the utility of DCOL in the reconstruction of networks, by combining it with local false discovery rate (lfdr)–based inference. We demonstrate in simulations that the new method named nlnet is effective in recovering hidden nonlinear modules. We also demonstrate its utility using a single cell RNA seq dataset. The method is available as an R package at https://cran.r-project.org/web/packages/nlnet.

An improvement on local FDR analysis applied to functional MRI data

BackgroundDiscovering effective connectivity between brain regions gained a lot of attention recently. A vector autoregressive model is a simple and flexible approach for exploratory structural modeling where the involvement of a large number of brain regions is crucial to avoid confounding. The non-zero coefficients of the VAR model are interpreted as actual effective connectivity between brain regions. Thus methods for a higher correct discovery rate are crucial for neuroscience. New methodWe propose an improved version of the FDR analysis procedure which would be more suitable to fMRI data. The estimates of the VAR coefficients are often not symmetric about 0 with non-zero modes. In this case, we suggest to estimate the null distribution of the estimates which is assumed symmetric about 0 in two steps: use one side of the estimates and then both sides under some condition. ResultsA theoretical argument is provided for the proposed procedure with a theorem and two types of experiments are made. In a simulation experiment, we show via ROC curves improvement over previous methods. We apply the proposed method to analyze real fMRI data with results interpreted in the language of cognitive neuroscience. Comparison with existing method(s)The proposed method outperforms the standard method in the simulation experiment with a VAR model of dimension up to 100 over a wide range of sample sizes. The improvement is made in the context of the true positive rate and performance consistency. ConclusionsThe proposed method is more appropriate for analyzing fMRI data with VAR models when the estimates of the VAR coefficients are not symmetric about 0 and have non-zero modes.

Increased resting-state EEG functional connectivity in benign childhood epilepsy with centro-temporal spikes

PurposeTo explore intrahemispheric, cortico-cortical EEG functional connectivity (EEGfC) in benign childhood epilepsy with rolandic spikes (BECTS). Methods21-channel EEG was recorded in 17 non-medicated BECTS children and 19 healthy controls. 180s of spike- and artifact-free activity was selected for EEGfC analysis. Correlation of Low Resolution Electromagnetic Tomography- (LORETA-) defined current source density time series were computed between two cortical areas (region of interest, ROI). Analyses were based on broad-band EEGfC results. Groups were compared by statistical parametric network (SPN) method. Statistically significant differences between group EEGfC values were emphasized at p<0.05 corrected for multiple comparison by local false discovery rate (FDR). Results(1) Bilaterally increased beta EEGfC occurred in the BECTS group as compared to the controls. Greatest beta abnormality emerged between frontal and frontal, as well as frontal and temporal ROIs. (2) Locally increased EEGfC emerged in all frequency bands in the right parietal area. ConclusionsAreas of increased EEGfC topographically correspond to cortical areas that, based on relevant literature, are related to speech and attention deficit in BECTS children.

An Empirical Bayes Mixture Model for Effect Size Distributions in Genome-Wide Association Studies.

Characterizing the distribution of effects from genome-wide genotyping data is crucial for understanding important aspects of the genetic architecture of complex traits, such as number or proportion of non-null loci, average proportion of phenotypic variance explained per non-null effect, power for discovery, and polygenic risk prediction. To this end, previous work has used effect-size models based on various distributions, including the normal and normal mixture distributions, among others. In this paper we propose a scale mixture of two normals model for effect size distributions of genome-wide association study (GWAS) test statistics. Test statistics corresponding to null associations are modeled as random draws from a normal distribution with zero mean; test statistics corresponding to non-null associations are also modeled as normal with zero mean, but with larger variance. The model is fit via minimizing discrepancies between the parametric mixture model and resampling-based nonparametric estimates of replication effect sizes and variances. We describe in detail the implications of this model for estimation of the non-null proportion, the probability of replication in de novo samples, the local false discovery rate, and power for discovery of a specified proportion of phenotypic variance explained from additive effects of loci surpassing a given significance threshold. We also examine the crucial issue of the impact of linkage disequilibrium (LD) on effect sizes and parameter estimates, both analytically and in simulations. We apply this approach to meta-analysis test statistics from two large GWAS, one for Crohn’s disease (CD) and the other for schizophrenia (SZ). A scale mixture of two normals distribution provides an excellent fit to the SZ nonparametric replication effect size estimates. While capturing the general behavior of the data, this mixture model underestimates the tails of the CD effect size distribution. We discuss the implications of pervasive small but replicating effects in CD and SZ on genomic control and power. Finally, we conclude that, despite having very similar estimates of variance explained by genotyped SNPs, CD and SZ have a broadly dissimilar genetic architecture, due to differing mean effect size and proportion of non-null loci.

Quantitative analysis of the murine lipid droplet-associated proteome during diet-induced hepatic steatosis

Hepatic steatosis is characterized by the accumulation of lipid droplets (LDs), which are composed of a neutral lipid core surrounded by a phospholipid monolayer embedded with many proteins. Although the LD-associated proteome has been investigated in multiple tissues and organisms, the dynamic changes in the murine LD-associated proteome in response to obesity and hepatic steatosis have not been studied. We characterized the hepatic LD-associated proteome of C57BL/6J male mouse livers following high-fat feeding using isobaric tagging for relative and absolute quantification. Of the 1,520 proteins identified with a 5% local false discovery rate, we report a total of 48 proteins that were increased and 52 proteins that were decreased on LDs in response to high-fat feeding. Most notably, ribosomal and endoplasmic reticulum proteins were increased and extracellular and cytosolic proteins were decreased in response to high-fat feeding. Additionally, many proteins involved in fatty acid catabolism or xenobiotic metabolism were enriched in the LD fraction following high-fat feeding. In contrast, proteins involved in glucose metabolism and liver X receptor or retinoid X receptor activation were decreased on LDs of high-fat-fed mice. This study provides insights into unique biological functions of hepatic LDs under normal and steatotic conditions.

Local false discovery rate estimation using feature reliability in LC/MS metabolomics data.

False discovery rate (FDR) control is an important tool of statistical inference in feature selection. In mass spectrometry-based metabolomics data, features can be measured at different levels of reliability and false features are often detected in untargeted metabolite profiling as chemical and/or bioinformatics noise. The traditional false discovery rate methods treat all features equally, which can cause substantial loss of statistical power to detect differentially expressed features. We propose a reliability index for mass spectrometry-based metabolomics data with repeated measurements, which is quantified using a composite measure. We then present a new method to estimate the local false discovery rate (lfdr) that incorporates feature reliability. In simulations, our proposed method achieved better balance between sensitivity and controlling false discovery, as compared to traditional lfdr estimation. We applied our method to a real metabolomics dataset and were able to detect more differentially expressed metabolites that were biologically meaningful.

Beyond the E-Value: Stratified Statistics for Protein Domain Prediction.

E-values have been the dominant statistic for protein sequence analysis for the past two decades: from identifying statistically significant local sequence alignments to evaluating matches to hidden Markov models describing protein domain families. Here we formally show that for “stratified” multiple hypothesis testing problems—that is, those in which statistical tests can be partitioned naturally—controlling the local False Discovery Rate (lFDR) per stratum, or partition, yields the most predictions across the data at any given threshold on the FDR or E-value over all strata combined. For the important problem of protein domain prediction, a key step in characterizing protein structure, function and evolution, we show that stratifying statistical tests by domain family yields excellent results. We develop the first FDR-estimating algorithms for domain prediction, and evaluate how well thresholds based on q-values, E-values and lFDRs perform in domain prediction using five complementary approaches for estimating empirical FDRs in this context. We show that stratified q-value thresholds substantially outperform E-values. Contradicting our theoretical results, q-values also outperform lFDRs; however, our tests reveal a small but coherent subset of domain families, biased towards models for specific repetitive patterns, for which weaknesses in random sequence models yield notably inaccurate statistical significance measures. Usage of lFDR thresholds outperform q-values for the remaining families, which have as-expected noise, suggesting that further improvements in domain predictions can be achieved with improved modeling of random sequences. Overall, our theoretical and empirical findings suggest that the use of stratified q-values and lFDRs could result in improvements in a host of structured multiple hypothesis testing problems arising in bioinformatics, including genome-wide association studies, orthology prediction, and motif scanning.

Optimization of Search Engines and Postprocessing Approaches to Maximize Peptide and Protein Identification for High-Resolution Mass Data.

The two key steps for analyzing proteomic data generated by high-resolution MS are database searching and postprocessing. While the two steps are interrelated, studies on their combinatory effects and the optimization of these procedures have not been adequately conducted. Here, we investigated the performance of three popular search engines (SEQUEST, Mascot, and MS Amanda) in conjunction with five filtering approaches, including respective score-based filtering, a group-based approach, local false discovery rate (LFDR), PeptideProphet, and Percolator. A total of eight data sets from various proteomes (e.g., E. coli, yeast, and human) produced by various instruments with high-accuracy survey scan (MS1) and high- or low-accuracy fragment ion scan (MS2) (LTQ-Orbitrap, Orbitrap-Velos, Orbitrap-Elite, Q-Exactive, Orbitrap-Fusion, and Q-TOF) were analyzed. It was found combinations involving Percolator achieved markedly more peptide and protein identifications at the same FDR level than the other 12 combinations for all data sets. Among these, combinations of SEQUEST-Percolator and MS Amanda-Percolator provided slightly better performances for data sets with low-accuracy MS2 (ion trap or IT) and high accuracy MS2 (Orbitrap or TOF), respectively, than did other methods. For approaches without Percolator, SEQUEST-group performs the best for data sets with MS2 produced by collision-induced dissociation (CID) and IT analysis; Mascot-LFDR gives more identifications for data sets generated by higher-energy collisional dissociation (HCD) and analyzed in Orbitrap (HCD-OT) and in Orbitrap Fusion (HCD-IT); MS Amanda-Group excels for the Q-TOF data set and the Orbitrap Velos HCD-OT data set. Therefore, if Percolator was not used, a specific combination should be applied for each type of data set. Moreover, a higher percentage of multiple-peptide proteins and lower variation of protein spectral counts were observed when analyzing technical replicates using Percolator-associated combinations; therefore, Percolator enhanced the reliability for both identification and quantification. The analyses were performed using the specific programs embedded in Proteome Discoverer, Scaffold, and an in-house algorithm (BuildSummary). These results provide valuable guidelines for the optimal interpretation of proteomic results and the development of fit-for-purpose protocols under different situations.

Importance of presenting the variability of the false discovery rate control.

BackgroundMultiple hypothesis testing is a pervasive problem in genomic data analysis. The conventional Bonferroni method which controls the family-wise error rate is conservative and with low power. The current paradigm is to control the false discovery rate.ResultsWe characterize the variability of the false discovery rate indices (local false discovery rates, q-value and false discovery proportion) using the bootstrapped method. A colon cancer gene-expression data and a visual refractive errors genome-wide association study data are analyzed as demonstration. We found a high variability in false discovery rate controls for typical genomic studies.ConclusionsWe advise researchers to present the bootstrapped standard errors alongside with the false discovery rate indices.Electronic supplementary materialThe online version of this article (doi:10.1186/s12863-015-0259-z) contains supplementary material, which is available to authorized users.

Proteomic profiling of hyperplasia/atypia and adenoma-induced by NNK in mouse lung identified multiple proteins as potential biomarkers for early detection

We used a proteomics approach (iTRAQ) to identify differentially expressed lung proteins during early stages of the tobacco carcinogen, NNK-induced lung tumorigenesis (hyperplasia/atypia, 4–10 weeks and adenoma, 25 week) prior to the detection of adenocarcinoma in A/J mice. We identified 790 proteins at week 4 and 710 proteins at weeks 10 and 25 with >95% confidence and a Local False Discovery Rate estimation less than 5%. We have demonstrated that NNK altered multiple protein (e.g., Carbonyl Reductase, Annexin A5/6, Selenbp1, Hmgb1 and Hsp90b1) expressions in early lesions which can be used as potential biomarkers for early detection of lung cancer.

SWATH analysis of the synaptic proteome in Alzheimer's disease

Brain tissue from Alzheimer's disease patients exhibits synaptic degeneration in selected regions. Synaptic dysfunction occurs early in the disease and is a primary pathological target for treatment. The molecular mechanisms underlying this degeneration remain unknown. Quantifying the synaptic proteome in autopsy brain and comparing tissue from Alzheimer's disease cases and subjects with normal aging are critical to understanding the molecular mechanisms associated with Alzheimer pathology. We isolated synaptosomes from hippocampus and motor cortex so as to reduce sample complexity relative to whole-tissue homogenates. Synaptosomal extracts were subjected to strong cation exchange (SCX) fractionation to further partition sample complexity; each fraction received SWATH-based information-dependent acquisition to generate a comprehensive peptide-ion library. The expression of synaptic proteins from AD hippocampus and motor cortex was then compared between groups. A total of 2077 unique proteins were identified at a critical local false discovery rate <5%. Thirty of these, including 17 novel proteins, exhibited significant expression differences between cases and controls; these proteins are involved in cellular functions including structural maintenance, signal transduction, autophagy, oxidative stress, and proteasome activity, or they have synaptic-vesicle related or energy-related functions. Differentially expressed proteins were subjected to pathway analysis to identify protein–protein interactions. This revealed that the most perturbed molecular and cellular functions were cellular assembly and organization. Core analysis revealed RhoA signaling to be the top canonical pathway. Network analysis showed that differentially expressed proteins were related to cellular assembly and organization, and cellular function and maintenance. This is the first study to combine SCX fractionation with SWATH analysis. SWATH is a promising new technique that can greatly enhance protein identification in any proteome, and has many other benefits; however, there are limitations yet to be resolved.

Leveraging Multi-Ethnic Evidence for Mapping Complex Traits in Minority Populations: An Empirical Bayes Approach

Elucidating the genetic basis of complex traits and diseases in non-European populations is particularly challenging because U.S. minority populations have been under-represented in genetic association studies. We developed an empirical Bayes approach named XPEB (Cross-Population Empirical Bayes), designed to improve the power for mapping complex trait loci in a minority population by exploiting information from genome-wide association studies (GWAS) from another ethnic population. Taking as input summary statistics from two GWAS, a target-GWAS from an ethnic minority population of primary interest and an auxiliary base-GWAS (such as a larger GWAS in Europeans), our XPEB approach reprioritizes SNPs in the target population to compute local false discovery rates. We demonstrated, through simulations, that whenever the base-GWAS harbors relevant information, XPEB gains efficiency. Moreover, XPEB has the ability to discard irrelevant auxiliary information, providing a safeguard against inflated false discovery rates due to genetic heterogeneity between populations. Applied to a blood lipids study in African Americans, XPEB more than quadrupled the discoveries compared to the conventional approach that uses target-GWAS alone, bringing the number of significant loci from 14 to 65. Thus, XPEB offers a flexible framework for mapping complex traits in minority populations.

Statistical detection of EEG synchrony using empirical bayesian inference.

There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.

Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing

The proposed minimax procedure blends strict Bayesian methods with p values and confidence intervals or with default-prior methods. Two applications to hypothesis testing bring some implications to light. First, the blended probability that a point null hypothesis is true is equal to the p value or a lower bound of an unknown posterior probability, whichever is greater. As a result, the p value is reported instead of any posterior probability in the case of complete prior ignorance but is ignored in the case of a fully known prior. In the case of partial knowledge about the prior, the possible posterior probability that is closest to the p value is used for inference. The second application provides guidance on the choice of methods used for small numbers of tests as opposed to those appropriate for large numbers. Whereas statisticians tend to prefer a multiple comparison procedure that adjusts each p value for small numbers of tests, large numbers instead lead many to estimate the local false discovery rate (LFDR), a posterior probability of hypothesis truth. Each blended probability reduces to the LFDR estimate if it can be estimated with sufficient accuracy or to the adjusted p value otherwise.

Bayesian semiparametric copula estimation with application to psychiatric genetics.

This paper proposes a semiparametric methodology for modeling multivariate and conditional distributions. We first build a multivariate distribution whose dependence structure is induced by a Gaussian copula and whose marginal distributions are estimated nonparametrically via mixtures of B-spline densities. The conditional distribution of a given variable is obtained in closed form from this multivariate distribution. We take a Bayesian approach, using Markov chain Monte Carlo methods for inference. We study the frequentist properties of the proposed methodology via simulation and apply the method to estimation of conditional densities of summary statistics, used for computing conditional local false discovery rates, from genetic association studies of schizophrenia and cardiovascular disease risk factors.

K-core decomposition of a protein domain co-occurrence network reveals lower cancer mutation rates for interior cores.

BackgroundNetwork biology currently focuses primarily on metabolic pathways, gene regulatory, and protein-protein interaction networks. While these approaches have yielded critical information, alternative methods to network analysis will offer new perspectives on biological information. A little explored area is the interactions between domains that can be captured using domain co-occurrence networks (DCN). A DCN can be used to study the function and interaction of proteins by representing protein domains and their co-existence in genes and by mapping cancer mutations to the individual protein domains to identify signals.ResultsThe domain co-occurrence network was constructed for the human proteome based on PFAM domains in proteins. Highly connected domains in the central cores were identified using the k-core decomposition technique. Here we show that these domains were found to be more evolutionarily conserved than the peripheral domains. The somatic mutations for ovarian, breast and prostate cancer diseases were obtained from the TCGA database. We mapped the somatic mutations to the individual protein domains and the local false discovery rate was used to identify significantly mutated domains in each cancer type. Significantly mutated domains were found to be enriched in cancer disease pathways. However, we found that the inner cores of the DCN did not contain any of the significantly mutated domains. We observed that the inner core protein domains are highly conserved and these domains co-exist in large numbers with other protein domains.ConclusionMutations and domain co-occurrence networks provide a framework for understanding hierarchal designs in protein function from a network perspective. This study provides evidence that a majority of protein domains in the inner core of the DCN have a lower mutation frequency and that protein domains present in the peripheral regions of the k-core contribute more heavily to the disease. These findings may contribute further to drug development.Electronic supplementary materialThe online version of this article (doi:10.1186/s13336-015-0016-6) contains supplementary material, which is available to authorized users.

Proteomic analysis revealed the altered kidney protein profile of a Cyld knockout mouse model.

The aim of this study was to compare the proteomics pattern of the kidneys from Cyld knockout mice with that from normal mouse kidneys and establish a preliminary understanding of the role of Cyld in the kidney. Proteins from the kidneys of knockout Cyld mice and wild-type mice were extracted, isobaric tags for relative and absolute quantitation (iTRAQ) was performed, and the proteomics patterns of the two groups were compared. The genotypes of the mice were verified by polymerase chain reaction. A total of 1748 proteins with a local false discovery rate of ≤5% were identified, among which 1437 proteins were reliably recognized and quantified. The expression of two dysregulated proteins was confirmed by Western blotting. Gene ontology and pathway analyses indicated that the proteins identified were involved in biological processes, cell components, and molecular functions, and participated in different pathways. Some of the proteins identified were relevant to renal function or kidney diseases. The difference between the proteomics profiles of kidneys from Cyld knockout mice and wild-type mice was prominent, which correlates to kidney dysfunction and the development of renal diseases.

Genomic regions influencing coat color saturation and facial markings in Fleckvieh cattle.

Genomic regions associated with coat color and pigmented areas of the head were identified for Fleckvieh (dual-purpose Simmental), a red-spotted and white-headed cattle breed. Coat color was measured with a chromameter, implementing the CIELAB color space and resulting in numerical representation of lightness, color intensity, red/green and blue/yellow color components, rather than subjective classification. Single marker regression analyses with fixed effects of the sex and barn were applied, and significant regions were determined with the local false discovery rate methodology. The PMEL and ERBB3 genes on chromosome 5 were in the most significant region for the color measurements. In addition to the blue/yellow color component and color intensity, the AP3B2 gene on chromosome 21 was identified. Its function was confirmed for similar traits in a range of model species. The KIT gene on chromosome 6 was found to be strongly associated with the inhibition of circum-ocular pigmentation and pigmented spots on the cheek.

Small‐scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison

SummaryEmpirical Bayes methods of estimating the local false discovery rate (LFDR) by maximum likelihood estimation (MLE), originally developed for large numbers of comparisons, are applied to a single comparison. Specifically, when assuming a lower bound on the mixing proportion of true null hypotheses, the LFDR MLE can yield reliable hypothesis tests and confidence intervals given as few as one comparison. Simulations indicate that constrained LFDR MLEs perform markedly better than conventional methods, both in testing and in confidence intervals, for high values of the mixing proportion, but not for low values. (A decision‐theoretic interpretation of the confidence distribution made those comparisons possible.) In conclusion, the constrained LFDR estimators and the resulting effect‐size interval estimates are not only effective multiple comparison procedures but also they might replace p‐values and confidence intervals more generally. The new methodology is illustrated with the analysis of proteomics data.