Local False Discovery Rate Research Articles

MHCVision: estimation of global and local false discovery rate for MHC class I peptide binding prediction.

MotivationMHC-peptide binding prediction has been widely used for understanding the immune response of individuals or populations, each carrying different MHC molecules as well as for the development of immunotherapeutics. The results from MHC-peptide binding prediction tools are mostly reported as a predicted binding affinity (IC50) and the percentile rank score, and global thresholds e.g. IC50 value < 500 nM or percentile rank < 2% are generally recommended for distinguishing binding peptides from non-binding peptides. However, it is difficult to evaluate statistically the probability of an individual peptide binding prediction to be true or false solely considering predicted scores. Therefore, statistics describing the overall global false discovery rate (FDR) and local FDR, also called posterior error probability (PEP) are required to give statistical context to the natively produced scores.ResultWe have developed an algorithm and code implementation, called MHCVision, for estimation of FDR and PEP values for the predicted results of MHC-peptide binding prediction from the NetMHCpan tool. MHCVision performs parameter estimation using a modified expectation maximization framework for a two-component beta mixture model, representing the distribution of true and false scores of the predicted dataset. We can then estimate the PEP of an individual peptide’s predicted score, and conversely the probability that it is true. We demonstrate that the use of global FDR and PEP estimation can provide a better trade-off between sensitivity and precision over using currently recommended thresholds from tools.Availability and implementation https://github.com/PGB-LIV/MHCVision.Supplementary information Supplementary data are available at Bioinformatics online.

A simple yet efficient method of local false discovery rate estimation designed for genome-wide association data analysis

A simple yet efficient method of local false discovery rate estimation designed for genome-wide association data analysis

Where to find needles in a haystack?

In many existing methods of multiple comparison, one starts with either Fisher’s p value or the local fdr. One commonly used p value, defined as the tail probability exceeding the observed test statistic under the null distribution, fails to use information from the distribution under the alternative hypothesis. The targeted region of signals could be wrong when the likelihood ratio is not monotone. The oracle local fdr based approaches could be optimal because they use the probability density functions of the test statistic under both the null and alternative hypotheses. However, the data-driven version could be problematic because of the difficulty and challenge of probability density function estimation. In this paper, we propose a new method, Cdf and Local fdr Assisted multiple Testing method (CLAT), which is optimal for cases when the p value based methods are optimal and for some other cases when p value based methods are not. Additionally, CLAT only relies on the empirical distribution function which quickly converges to the oracle one. Both the simulations and real data analysis demonstrate the superior performance of the CLAT method. Furthermore, the computation is instantaneous based on a novel algorithm and is scalable to large data sets.

MixTwice: large-scale hypothesis testing for peptide arrays by variance mixing.

SummaryPeptide microarrays have emerged as a powerful technology in immunoproteomics as they provide a tool to measure the abundance of different antibodies in patient serum samples. The high dimensionality and small sample size of many experiments challenge conventional statistical approaches, including those aiming to control the false discovery rate (FDR). Motivated by limitations in reproducibility and power of current methods, we advance an empirical Bayesian tool that computes local FDR statistics and local false sign rate statistics when provided with data on estimated effects and estimated standard errors from all the measured peptides. As the name suggests, the MixTwice tool involves the estimation of two mixing distributions, one on underlying effects and one on underlying variance parameters. Constrained optimization techniques provide for model fitting of mixing distributions under weak shape constraints (unimodality of the effect distribution). Numerical experiments show that MixTwice can accurately estimate generative parameters and powerfully identify non-null peptides. In a peptide array study of rheumatoid arthritis, MixTwice recovers meaningful peptide markers in one case where the signal is weak, and has strong reproducibility properties in one case where the signal is strong.Availabilityand implementationMixTwice is available as an R software package https://cran.r-project.org/web/packages/MixTwice/.Supplementary informationSupplementary data are available at Bioinformatics online.

Dimension constraints improve hypothesis testing for large-scale, graph-associated, brain-image data.

SummaryFor large-scale testing with graph-associated data, we present an empirical Bayes mixture technique to score local false-discovery rates (FDRs). Compared to procedures that ignore the graph, the proposed Graph-based Mixture Model (GraphMM) method gains power in settings where non-null cases form connected subgraphs, and it does so by regularizing parameter contrasts between testing units. Simulations show that GraphMM controls the FDR in a variety of settings, though it may lose control with excessive regularization. On magnetic resonance imaging data from a study of brain changes associated with the onset of Alzheimer’s disease, GraphMM produces greater yield than conventional large-scale testing procedures.

Comprehensive Comparative Analysis of Local False Discovery Rate Control Methods.

Due to the advance in technology, the type of data is getting more complicated and large-scale. To analyze such complex data, more advanced technique is required. In case of omics data from two different groups, it is interesting to find significant biomarkers between two groups while controlling error rate such as false discovery rate (FDR). Over the last few decades, a lot of methods that control local false discovery rate have been developed, ranging from one-dimensional to k-dimensional FDR procedure. For comparison study, we select three of them, which have unique and significant properties: Efron’s approach, Ploner’s approach, and Kim’s approach in chronological order. The first approach is one-dimensional approach while the other two are two-dimensional ones. Furthermore, we consider two more variants of Ploner’s approach. We compare the performance of those methods on both simulated and real data.

Optimal Control of False Discovery Criteria in the Two-Group Model

AbstractThe highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal control of the marginal false discovery rate (mFDR), in the sense that it provides maximal power (expected true discoveries) subject to mFDR control, is known to be achieved by thresholding the local false discovery rate (locFDR), the probability of the hypothesis being null given the set of test statistics, with a fixed threshold. We address the challenge of controlling optimally the popular false discovery rate (FDR) or positive FDR (pFDR) in the general two-group model, which also allows for dependence between the test statistics. These criteria are less conservative than the mFDR criterion, so they make more rejections in expectation. We derive their optimal multiple testing (OMT) policies, which turn out to be thresholding the locFDR with a threshold that is a function of the entire set of statistics. We develop an efficient algorithm for finding these policies, and use it for problems with thousands of hypotheses. We illustrate these procedures on gene expression studies.

IMIX: a multivariate mixture model approach to association analysis through multi-omics data integration.

Integrative genomic analysis is a powerful tool used to study the biological mechanisms underlying a complex disease or trait across multiplatform high-dimensional data, such as DNA methylation, copy number variation and gene expression. It is common to perform large-scale genome-wide association analysis of an outcome for each data type separately and combine the results ad hoc, leading to loss of statistical power and uncontrolled overall false discovery rate (FDR). We propose a multivariate mixture model (IMIX) framework that integrates multiple types of genomic data and allows modeling of inter-data-type correlations. We investigated the across-data-type FDR control in IMIX and demonstrated lower misclassification rates at controlled overall FDR than established individual data type analysis strategies, such as the Benjamini-Hochberg FDR control, the q-value and the local FDR control by extensive simulations. IMIX features statistically principled model selection, FDR control and computational efficiency. Applications to The Cancer Genome Atlas data provided novel multi-omics insights into the genes and mechanisms associated with the luminal and basal subtypes of bladder cancer and the prognosis of pancreatic cancer. We have implemented our method in R package 'IMIX' available at https://github.com/ziqiaow/IMIX, as well as CRAN soon. Supplementary data are available at Bioinformatics online.

GWA-based pleiotropic analysis identified potential SNPs and genes related to type 2 diabetes and obesity.

Metabolic syndrome is a cluster of symptoms including excessive body fat and insulin resistance which may lead to obesity and type 2 diabetes (T2D). The physiological and pathological cross-talk between T2D and obesity is crucial and complex, meanwhile, the genetic connection between T2D and obesity is largely unknown. The purpose of this study is to identify pleiotropic SNPs and genes between these two associated conditions by applying genetic analysis incorporating pleiotropy and annotation (GPA) on two large genome-wide association studies (GWAS) data sets: a body mass index (BMI) data set containing 339,224 subjects and a T2D data set containing 110,452 subjects. In all, 5182 SNPs showed pleiotropy in both T2D and obesity. After further prioritization based on suggested local false discovery rates (FDR) by the GPA model, 2146 SNPs corresponding to 217 unique genes are significantly associated with both traits (FDR < 0.2), among which 187 are newly identified pleiotropic genes compare with original GWAS in individual traits. Subsequently, gene enrichment and pathway analyses highlighted several pleiotropic SNPs including rs849135 (FDR = 0.0002), rs2119812 (FDR = 0.0018), rs4506565 (FDR = 1.23E-08), rs1558902 (7.23E-10) and corresponding genes JAZF1, SYN2, TCF7L2, FTO which may play crucial rol5es in the etiology of both T2D and obesity. Additional evidences from expression data analysis of pleiotropic genes strongly supports that the pleiotropic genes including JAZF1 (p = 1.39E-05 and p = 2.13E-05), SYN2 (p = 5.49E-03 and p = 5.27E-04), CDKN2C (p = 1.99E-12 and p = 6.27E-11), RABGAP1 (p = 3.08E-03 and p = 7.46E-03), and UBE2E2 (p = 1.83E-04 and p = 8.22E-03) play crucial roles in both obesity and T2D pathogenesis. Pleiotropic analysis integrated with functional network identified several novel and causal SNPs and genes involved in both BMI and T2D which may be ignored in single GWAS.

A semiparametric mixture method for local false discovery rate estimation from multiple studies

Antineutrophil cytoplasmic antibody associated vasculitis (AAV) is extremely heterogeneous in clinical presentation and involves multiple organ systems. While the clinical presentation of AAV is diverse, we hypothesized that all AAV share common pathways and tested the hypothesis based on three different microarray studies of peripheral leukocytes, sinus and orbital inflammation disease. For the hypothesis testing we developed a two-component semiparametric mixture model to estimate the local false discovery rates from the $p$-values of three studies. The two pillars of the proposed approach are Efron’s empirical null principle and log-concave density estimation for the alternative distribution. Our method outperforms other existing methods, in particular when the proportion of null is not that high. It is robust against the misspecification of alternative distribution. A unique feature of our method is that it can be extended to compute the local false discovery rates by combining multiple lists of $p$-values.

Transfer posterior error probability estimation for peptide identification

BackgroundIn shotgun proteomics, database searching of tandem mass spectra results in a great number of peptide-spectrum matches (PSMs), many of which are false positives. Quality control of PSMs is a multiple hypothesis testing problem, and the false discovery rate (FDR) or the posterior error probability (PEP) is the commonly used statistical confidence measure. PEP, also called local FDR, can evaluate the confidence of individual PSMs and thus is more desirable than FDR, which evaluates the global confidence of a collection of PSMs. Estimation of PEP can be achieved by decomposing the null and alternative distributions of PSM scores as long as the given data is sufficient. However, in many proteomic studies, only a group (subset) of PSMs, e.g. those with specific post-translational modifications, are of interest. The group can be very small, making the direct PEP estimation by the group data inaccurate, especially for the high-score area where the score threshold is taken. Using the whole set of PSMs to estimate the group PEP is inappropriate either, because the null and/or alternative distributions of the group can be very different from those of combined scores.ResultsThe transfer PEP algorithm is proposed to more accurately estimate the PEPs of peptide identifications in small groups. Transfer PEP derives the group null distribution through its empirical relationship with the combined null distribution, and estimates the group alternative distribution, as well as the null proportion, using an iterative semi-parametric method. Validated on both simulated data and real proteomic data, transfer PEP showed remarkably higher accuracy than the direct combined and separate PEP estimation methods.ConclusionsWe presented a novel approach to group PEP estimation for small groups and implemented it for the peptide identification problem in proteomics. The methodology of the approach is in principle applicable to the small-group PEP estimation problems in other fields.

Omega-3 Fatty Acids Responsive Proteins and Reduction in Breast Density in Obese Postmenopausal Women.

We reported that breast density (BD) was inversely correlated with the plasma level of DHA in postmenopausal obese, but not in nonobese, women given Lovaza (n-3FA). To identify protein biomarkers for the possible differential effect of n-3FA on BD between obese and nonobese women, an iTRAQ method was performed to analyze plasma from obese and lean women at each time point (baseline, 12 and 24-months, n = 10 per group); 173 proteins with >95% confidence (Unuses Score >1.3 and local false discovery rate estimation <5%) wereidentified. Comparative analysis between various groups identified several differentially expressed proteins (hemopexin precursor, vitamin D binding protein isoform 1 precursor [VDBP], fibronectin isoform 10 precursor [FN], and α-2 macroglobulin precursor [A2M]). Western blot analysis was performed to verify the differential expression of proteins in the iTRAQ study, and those found to be altered in a tumor protective fashion by an n-3FA rich diet in our previous preclinical study; gelsolin, VDBP, and FN were altered by n-3FA in a manner consistent with reduction in inflammation in obese women. To test the impact of our findings on breast cancer risk reduction by n-3FA, a posthoc analysis revealed that n-3FA administration reduced BD selectively in obese postmenopausal women.

Correcting false discovery rates for their bias toward false positives

The way false discovery rates (FDRs) are used in the analysis of genomics data leads to excessive false positive rates. In this sense, FDRs overcorrect for the excessive conservatism (bias toward false negatives) of methods of adjusting p values that control a family-wise error rate. Estimators of the local FDR (LFDR) are much less biased but have not been widely adopted due to their high variance and lack of availability in software. To address both issues, we propose estimating the LFDR by correcting an estimated FDR or the level at which an FDR is controlled.

Cell-level somatic mutation detection from single-cell RNA sequencing.

MotivationBoth single-cell RNA sequencing (scRNA-seq) and DNA sequencing (scDNA-seq) have been applied for cell-level genomic profiling. For mutation profiling, the latter seems more natural. However, the task is highly challenging due to the limited input materials from only two copies of DNA molecules, while whole-genome amplification generates biases and other technical noises. ScRNA-seq starts with a higher input amount, so generally has better data quality. There exists various methods for mutation detection from DNA sequencing, it is not clear whether these methods work for scRNA-seq data.ResultsMutation detection methods developed for either bulk-cell sequencing data or scDNA-seq data do not work well for the scRNA-seq data, as they produce substantial numbers of false positives. We develop a novel and robust statistical method—called SCmut—to identify specific cells that harbor mutations discovered in bulk-cell data. Statistically SCmut controls the false positives using the 2D local false discovery rate method. We apply SCmut to several scRNA-seq datasets. In scRNA-seq breast cancer datasets SCmut identifies a number of highly confident cell-level mutations that are recurrent in many cells and consistent in different samples. In a scRNA-seq glioblastoma dataset, we discover a recurrent cell-level mutation in the PDGFRA gene that is highly correlated with a well-known in-frame deletion in the gene. To conclude, this study contributes a novel method to discover cell-level mutation information from scRNA-seq that can facilitate investigation of cell-to-cell heterogeneity.Availability and implementationThe source codes and bioinformatics pipeline of are available at https://github.com/nghiavtr/SCmut.Supplementary information Supplementary data are available at Bioinformatics online.

Gene Expression Pathways across Multiple Tissues in Antineutrophil Cytoplasmic Antibody-associated Vasculitis Reveal Core Pathways of Disease Pathology.

To identify commonalities in gene expression data across all antineutrophil cytoplasmic antibody (ANCA)-associated vasculitis (AAV) tissues thus far characterized. Gene expression data were collected from the 3 AAV tissues thus far characterized (orbit, peripheral leukocytes, and sinus brushings). These data were analyzed to identify commonly expressed genes and disease pathways. The pathways data were adjusted for multiple comparisons using a combined local false discovery rate, which estimates the probability of a false discovery of a given pathway in all 3 tissues analyzed. Only 4 genes were upregulated in all 3 tissues - IL1RN, TLR2, SLC11A1, and MMP9. After multiple comparison adjustments, the network pathway analysis revealed 28 pathways associated with all 3 tissues. The most strongly associated pathway for all 3 tissues was the neutrophil degranulation pathway [multidimensional local false discovery (md-locfdr) = 1.05 × 10-12], followed by the osteoclast differentiation (md-locfdr = 3.8 × 10-05), cell surface interactions at the vascular wall (md-locfdr = 4.2 × 10-04), signaling by interleukins (md-locfdr = 6.1 × 10-04), and phagosome (md-locfdr = 0.003) pathways. There were no downregulated genes or pathways common to all 3 tissues. This analysis identified individual genes and pathways of disease common to all AAV tissues thus far characterized. The use of a network pathway analysis allowed us to identify pathologic mechanisms that were not readily apparent in the commonly expressed genes alone. Many of these pathways are consistent with current theories about infectious drivers and the crossroads of innate and adaptive immune mechanisms. In addition, this analysis highlights novel pathways, such as vessel wall interactions and platelet activation, which require further investigation.

SU18 - INVESTIGATING SHRINKAGE METHODS TO IMPROVE ACCURACY OF GWAS AND PRS EFFECT SIZE ESTIMATES

Background As the scale and power of GWAS have increased to detect the small genetic effect sizes involved in complex polygenic traits, the results of GWAS, especially SNP effect size estimates, are increasingly utilised for prediction. A popular approach is the application of Polygenic Risk Scores (PRS). However, the effect size estimates are inherently prone to overfit the specific samples on which the GWAS were performed (e.g. “the Winner's Curse”). The inflation of effect size estimation reduces the out-of-sample accuracy of prediction based on GWAS results. Many shrinkage methods have been developed to correct for such inflation. As GWAS results and large individual genotype data sets become widely available, there is greater opportunity to accurately evaluate effect size inflation and compare the performance of different shrinkage methods. Methods We develop a novel permutation-based shrinkage method and compare its performance with previously developed methods based on local false discovery rate and the LASSO. We evaluate the performance of the methods across a wide range of phenotypes and investigate different factors (e.g. phenotype heritability) that influence their impact on the predictive power of polygenic risk scores. Results Using large-scale real genotype data, we show that SNP effect sizes are markedly overfit even in relatively large samples, but that our permutation-based shrinkage approach can improve PRS prediction dramatically. Discussion Our results suggest that GWAS results can be adjusted using an efficient empirical approach to provide more accurate effect size estimates and thus greater downstream predictive power. This approach could be applied to a wide variety of big data settings.

Estimating the local false discovery rate via a bootstrap solution to the reference class problem.

Methods of estimating the local false discovery rate (LFDR) have been applied to different types of datasets such as high-throughput biological data, diffusion tensor imaging (DTI), and genome-wide association (GWA) studies. We present a model for LFDR estimation that incorporates a covariate into each test. Incorporating the covariates may improve the performance of testing procedures, because it contains additional information based on the biological context of the corresponding test. This method provides different estimates depending on a tuning parameter. We estimate the optimal value of that parameter by choosing the one that minimizes the estimated LFDR resulting from the bias and variance in a bootstrap approach. This estimation method is called an adaptive reference class (ARC) method. In this study, we consider the performance of ARC method under certain assumptions on the prior probability of each hypothesis test as a function of the covariate. We prove that, under these assumptions, the ARC method has a mean squared error asymptotically no greater than that of the other method where the entire set of hypotheses is used and assuming a large covariate effect. In addition, we conduct a simulation study to evaluate the performance of estimator associated with the ARC method for a finite number of hypotheses. Here, we apply the proposed method to coronary artery disease (CAD) data taken from a GWA study and diffusion tensor imaging (DTI) data.

Precision global health and comorbidity: a population-based study of 16 357 people in rural Uganda.

In low-income countries, complex comorbidities and weak health systems confound disease diagnosis and treatment. Yet, data-driven approaches have not been applied to develop better diagnostic strategies or to tailor treatment delivery for individuals within rural poor communities. We observed symptoms/diseases reported within three months by 16 357 individuals aged 1+ years in 17 villages of Mayuge District, Uganda. Symptoms were mapped to the Human Phenotype Ontology. Comorbidity networks were constructed. An edge between two symptoms/diseases was generated if the relative risk greater than 1, ϕ correlation greater than 0, and local false discovery rate less than 0.05. We studied how network structure and flagship symptom profiles varied against biosocial factors. 88.05% of individuals (14 402/16 357) reported at least one symptom/disease. Young children and individuals in worse-off households—low socioeconomic status, poor water, sanitation, and hygiene, and poor medical care—had dense network structures with the highest comorbidity burden and/or were conducive to the onset of new comorbidities from existing flagship symptoms, such as fever. Flagship symptom profiles for fever revealed self-misdiagnoses of fever as malaria and sexually transmitted infections as a potentially missed cause of fever in individuals of reproductive age. Network analysis may inform the development of new diagnostic and treatment strategies for flagship symptoms used to characterize syndromes/diseases of global concern.

Controlling two-dimensional false discovery rates by combining two univariate multiple testing results with an application to mass spectral data

Mass spectral data exhibit a small number of signals (true peaks) among many noisy observations (signals or true peaks) in a high-dimensional space. This unique aspect of mass spectral data necessitates solving the problem of testing for many composite null hypotheses simultaneously. In this study, we develop a new procedure to control the false discovery rate of simultaneous multiple hypothesis tests, consisting of many “bivariate” composite null hypotheses. Two types of composite null hypothesis, the intersection-type and the union-type null, are considered separately. The proposed procedure comprises two stages. In the first stage, we simultaneously test each “univariate” simple hypothesis of “bivariate” composite hypotheses at the pre-decided false discovery rate. In the second stage, we combine the marginal univariate test results so that the two-dimensional false discovery rate for the “bivariate” composite null hypotheses is less than the desired significance level α. The new procedure provides a closed-form decision rule on the bivariate test statistics, unlike existing methods for controlling the two-dimensional local false discovery rate (2d-fdr). We numerically compare the performance of our procedure to existing 2d-fdr control methods in different settings. We then apply the procedure to the problem of differentiating the origins of herbal medicine using gas chromatography-mass spectrometry.

Incorporating Prior Knowledge about Genetic Variants into the Analysis of Genetic Association Data: An Empirical Bayes Approach.

In a genome-wide association study (GWAS), the probability that a single nucleotide polymorphism (SNP) is not associated with a disease is its local false discovery rate (LFDR). The LFDR for each SNP is relative to a reference class of SNPs. For example, the LFDR of an exonic SNP can vary widely depending on whether it is considered relative to the separate reference class of other exonic SNPs or relative to the combined reference class of all SNPs in the data set. As a result, the analysis of the data based on the combined reference class might indicate that a specific exonic SNP is associated with the disease, while using the separate reference class indicates that it is not associated, or vice versa. To address that, we introduce empirical Bayes methods that simultaneously consider a combined reference class and a separate reference class. Our simulation studies indicate that the proposed methods lead to improved performance. The new maximum entropy method achieves that by depending on the separate class when it has enough SNPs for reliable LFDR estimation and depending solely on the combined class otherwise. We used the new methods to analyze data from a GWAS of 2,000 cases and 3,000 controls. R functions implementing the proposed methods are available on CRAN <https://cran.r-project.org/web/packages/LFDREmpiricalBayes> and Shiny <https://empiricalbayes.shinyapps.io/lfdrempiricalbayesapp>.