All SNPs Are Not Created Equal: Genome-Wide Association Studies Reveal a Consistent Pattern of Enrichment among Functionally Annotated SNPs

Recent results indicate that genome-wide association studies (GWAS) have the potential to explain much of the heritability of common complex phenotypes, but methods are lacking to reliably identify the remaining associated single nucleotide polymorphisms (SNPs). We applied stratified False Discovery Rate (sFDR) methods to leverage genic enrichment in GWAS summary statistics data to uncover new loci likely to replicate in independent samples. Specifically, we use linkage disequilibrium-weighted annotations for each SNP in combination with nominal p-values to estimate the True Discovery Rate (TDR = 1−FDR) for strata determined by different genic categories. We show a consistent pattern of enrichment of polygenic effects in specific annotation categories across diverse phenotypes, with the greatest enrichment for SNPs tagging regulatory and coding genic elements, little enrichment in introns, and negative enrichment for intergenic SNPs. Stratified enrichment directly leads to increased TDR for a given p-value, mirrored by increased replication rates in independent samples. We show this in independent Crohn''s disease GWAS, where we find a hundredfold variation in replication rate across genic categories. Applying a well-established sFDR methodology we demonstrate the utility of stratification for improving power of GWAS in complex phenotypes, with increased rejection rates from 20% in height to 300% in schizophrenia with traditional FDR and sFDR both fixed at 0.05. Our analyses demonstrate an inherent stratification among GWAS SNPs with important conceptual implications that can be leveraged by statistical methods to improve the discovery of loci.     

Unifying candidate gene and GWAS Approaches in Asthma

The first genome wide association study (GWAS) for childhood asthma identified a novel major susceptibility locus on chromosome 17q21 harboring the ORMDL3 gene, but the role of previous asthma candidate genes was not specifically analyzed in this GWAS. We systematically identified 89 SNPs in 14 candidate genes previously associated with asthma in >3 independent study populations. We re-genotyped 39 SNPs in these genes not covered by GWAS performed in 703 asthmatics and 658 reference children. Genotyping data were compared to imputation data derived from Illumina HumanHap300 chip genotyping. Results were combined to analyze 566 SNPs covering all 14 candidate gene loci. Genotyped polymorphisms in ADAM33, GSTP1 and VDR showed effects with p-values <0.0035 (corrected for multiple testing). Combining genotyping and imputation, polymorphisms in DPP10, EDN1, IL12B, IL13, IL4, IL4R and TNF showed associations at a significance level between p = 0.05 and p = 0.0035. These data indicate that (a) GWAS coverage is insufficient for many asthma candidate genes, (b) imputation based on these data is reliable but incomplete, and (c) SNPs in three previously identified asthma candidate genes replicate in our GWAS population with significance after correction for multiple testing in 14 genes.     

A Multi-Trait,Meta-analysis for Detecting Pleiotropic Polymorphisms for Stature,Fatness and Reproduction in Beef Cattle

Polymorphisms that affect complex traits or quantitative trait loci (QTL) often affect multiple traits. We describe two novel methods (1) for finding single nucleotide polymorphisms (SNPs) significantly associated with one or more traits using a multi-trait, meta-analysis, and (2) for distinguishing between a single pleiotropic QTL and multiple linked QTL. The meta-analysis uses the effect of each SNP on each of n traits, estimated in single trait genome wide association studies (GWAS). These effects are expressed as a vector of signed t-values (t) and the error covariance matrix of these t values is approximated by the correlation matrix of t-values among the traits calculated across the SNP (V). Consequently, t''V⁻¹t is approximately distributed as a chi-squared with n degrees of freedom. An attractive feature of the meta-analysis is that it uses estimated effects of SNPs from single trait GWAS, so it can be applied to published data where individual records are not available. We demonstrate that the multi-trait method can be used to increase the power (numbers of SNPs validated in an independent population) of GWAS in a beef cattle data set including 10,191 animals genotyped for 729,068 SNPs with 32 traits recorded, including growth and reproduction traits. We can distinguish between a single pleiotropic QTL and multiple linked QTL because multiple SNPs tagging the same QTL show the same pattern of effects across traits. We confirm this finding by demonstrating that when one SNP is included in the statistical model the other SNPs have a non-significant effect. In the beef cattle data set, cluster analysis yielded four groups of QTL with similar patterns of effects across traits within a group. A linear index was used to validate SNPs having effects on multiple traits and to identify additional SNPs belonging to these four groups.     

A new approach to account for the correlations among single nucleotide polymorphisms in genome: wide association studies

In genetic association studies, such as genome-wide association studies (GWAS), the number of single nucleotide polymorphisms (SNPs) can be as large as hundreds of thousands. Due to linkage disequilibrium, many SNPs are highly correlated; assuming they are independent is not valid. The commonly used multiple comparison methods, such as Bonferroni correction, are not appropriate and are too conservative when applied to GWAS. To overcome these limitations, many approaches have been proposed to estimate the so-called effective number of independent tests to account for the correlations among SNPs. However, many current effective number estimation methods are based on eigenvalues of the correlation matrix. When the dimension of the matrix is large, the numeric results may be unreliable or even unobtainable. To circumvent this obstacle and provide better estimates, we propose a new effective number estimation approach which is not based on the eigenvalues. We compare the new method with others through simulated and real data. The comparison results show that the proposed method has very good performance.     

Pathways of distinction analysis: a new technique for multi-SNP analysis of GWAS data

Genome-wide association studies (GWAS) have become increasingly common due to advances in technology and have permitted the identification of differences in single nucleotide polymorphism (SNP) alleles that are associated with diseases. However, while typical GWAS analysis techniques treat markers individually, complex diseases (cancers, diabetes, and Alzheimers, amongst others) are unlikely to have a single causative gene. Thus, there is a pressing need for multi-SNP analysis methods that can reveal system-level differences in cases and controls. Here, we present a novel multi-SNP GWAS analysis method called Pathways of Distinction Analysis (PoDA). The method uses GWAS data and known pathway-gene and gene-SNP associations to identify pathways that permit, ideally, the distinction of cases from controls. The technique is based upon the hypothesis that, if a pathway is related to disease risk, cases will appear more similar to other cases than to controls (or vice versa) for the SNPs associated with that pathway. By systematically applying the method to all pathways of potential interest, we can identify those for which the hypothesis holds true, i.e., pathways containing SNPs for which the samples exhibit greater within-class similarity than across classes. Importantly, PoDA improves on existing single-SNP and SNP-set enrichment analyses, in that it does not require the SNPs in a pathway to exhibit independent main effects. This permits PoDA to reveal pathways in which epistatic interactions drive risk. In this paper, we detail the PoDA method and apply it to two GWAS: one of breast cancer and the other of liver cancer. The results obtained strongly suggest that there exist pathway-wide genomic differences that contribute to disease susceptibility. PoDA thus provides an analytical tool that is complementary to existing techniques and has the power to enrich our understanding of disease genomics at the systems-level.     

Prioritizing GWAS Results: A Review of Statistical Methods and Recommendations for Their Application

Genome-wide association studies (GWAS) have rapidly become a standard method for disease gene discovery. A substantial number of recent GWAS indicate that for most disorders, only a few common variants are implicated and the associated SNPs explain only a small fraction of the genetic risk. This review is written from the viewpoint that findings from the GWAS provide preliminary genetic information that is available for additional analysis by statistical procedures that accumulate evidence, and that these secondary analyses are very likely to provide valuable information that will help prioritize the strongest constellations of results. We review and discuss three analytic methods to combine preliminary GWAS statistics to identify genes, alleles, and pathways for deeper investigations. Meta-analysis seeks to pool information from multiple GWAS to increase the chances of finding true positives among the false positives and provides a way to combine associations across GWAS, even when the original data are unavailable. Testing for epistasis within a single GWAS study can identify the stronger results that are revealed when genes interact. Pathway analysis of GWAS results is used to prioritize genes and pathways within a biological context. Following a GWAS, association results can be assigned to pathways and tested in aggregate with computational tools and pathway databases. Reviews of published methods with recommendations for their application are provided within the framework for each approach.     

Pathways-Driven Sparse Regression Identifies Pathways and Genes Associated with High-Density Lipoprotein Cholesterol in Two Asian Cohorts

Standard approaches to data analysis in genome-wide association studies (GWAS) ignore any potential functional relationships between gene variants. In contrast gene pathways analysis uses prior information on functional structure within the genome to identify pathways associated with a trait of interest. In a second step, important single nucleotide polymorphisms (SNPs) or genes may be identified within associated pathways. The pathways approach is motivated by the fact that genes do not act alone, but instead have effects that are likely to be mediated through their interaction in gene pathways. Where this is the case, pathways approaches may reveal aspects of a trait''s genetic architecture that would otherwise be missed when considering SNPs in isolation. Most pathways methods begin by testing SNPs one at a time, and so fail to capitalise on the potential advantages inherent in a multi-SNP, joint modelling approach. Here, we describe a dual-level, sparse regression model for the simultaneous identification of pathways and genes associated with a quantitative trait. Our method takes account of various factors specific to the joint modelling of pathways with genome-wide data, including widespread correlation between genetic predictors, and the fact that variants may overlap multiple pathways. We use a resampling strategy that exploits finite sample variability to provide robust rankings for pathways and genes. We test our method through simulation, and use it to perform pathways-driven gene selection in a search for pathways and genes associated with variation in serum high-density lipoprotein cholesterol levels in two separate GWAS cohorts of Asian adults. By comparing results from both cohorts we identify a number of candidate pathways including those associated with cardiomyopathy, and T cell receptor and PPAR signalling. Highlighted genes include those associated with the L-type calcium channel, adenylate cyclase, integrin, laminin, MAPK signalling and immune function.     

Linkage disequilibrium clustering‐based approach for association mapping with tightly linked genomewide data

Genomewide association studies (GWAS) aim to identify genetic markers strongly associated with quantitative traits by utilizing linkage disequilibrium (LD) between candidate genes and markers. However, because of LD between nearby genetic markers, the standard GWAS approaches typically detect a number of correlated SNPs covering long genomic regions, making corrections for multiple testing overly conservative. Additionally, the high dimensionality of modern GWAS data poses considerable challenges for GWAS procedures such as permutation tests, which are computationally intensive. We propose a cluster‐based GWAS approach that first divides the genome into many large nonoverlapping windows and uses linkage disequilibrium network analysis in combination with principal component (PC) analysis as dimensional reduction tools to summarize the SNP data to independent PCs within clusters of loci connected by high LD. We then introduce single‐ and multilocus models that can efficiently conduct the association tests on such high‐dimensional data. The methods can be adapted to different model structures and used to analyse samples collected from the wild or from biparental F₂ populations, which are commonly used in ecological genetics mapping studies. We demonstrate the performance of our approaches with two publicly available data sets from a plant (Arabidopsis thaliana) and a fish (Pungitius pungitius), as well as with simulated data.     

Placental Genome and Maternal-Placental Genetic Interactions: A Genome-Wide and Candidate Gene Association Study of Placental Abruption

While available evidence supports the role of genetics in the pathogenesis of placental abruption (PA), PA-related placental genome variations and maternal-placental genetic interactions have not been investigated. Maternal blood and placental samples collected from participants in the Peruvian Abruptio Placentae Epidemiology study were genotyped using Illumina’s Cardio-Metabochip platform. We examined 118,782 genome-wide SNPs and 333 SNPs in 32 candidate genes from mitochondrial biogenesis and oxidative phosphorylation pathways in placental DNA from 280 PA cases and 244 controls. We assessed maternal-placental interactions in the candidate gene SNPS and two imprinted regions (IGF2/H19 and C19MC). Univariate and penalized logistic regression models were fit to estimate odds ratios. We examined the combined effect of multiple SNPs on PA risk using weighted genetic risk scores (WGRS) with repeated ten-fold cross-validations. A multinomial model was used to investigate maternal-placental genetic interactions. In placental genome-wide and candidate gene analyses, no SNP was significant after false discovery rate correction. The top genome-wide association study (GWAS) hits were rs544201, rs1484464 (CTNNA2), rs4149570 (TNFRSF1A) and rs13055470 (ZNRF3) (p-values: 1.11e-05 to 3.54e-05). The top 200 SNPs of the GWAS overrepresented genes involved in cell cycle, growth and proliferation. The top candidate gene hits were rs16949118 (COX10) and rs7609948 (THRB) (p-values: 6.00e-03 and 8.19e-03). Participants in the highest quartile of WGRS based on cross-validations using SNPs selected from the GWAS and candidate gene analyses had a 8.40-fold (95% CI: 5.8–12.56) and a 4.46-fold (95% CI: 2.94–6.72) higher odds of PA compared to participants in the lowest quartile. We found maternal-placental genetic interactions on PA risk for two SNPs in PPARG (chr3∶12313450 and chr3∶12412978) and maternal imprinting effects for multiple SNPs in the C19MC and IGF2/H19 regions. Variations in the placental genome and interactions between maternal-placental genetic variations may contribute to PA risk. Larger studies may help advance our understanding of PA pathogenesis.     

SNP-based pathway enrichment analysis for genome-wide association studies

Background  

Recently we have witnessed a surge of interest in using genome-wide association studies (GWAS) to discover the genetic basis of complex diseases. Many genetic variations, mostly in the form of single nucleotide polymorphisms (SNPs), have been identified in a wide spectrum of diseases, including diabetes, cancer, and psychiatric diseases. A common theme arising from these studies is that the genetic variations discovered by GWAS can only explain a small fraction of the genetic risks associated with the complex diseases. New strategies and statistical approaches are needed to address this lack of explanation. One such approach is the pathway analysis, which considers the genetic variations underlying a biological pathway, rather than separately as in the traditional GWAS studies. A critical challenge in the pathway analysis is how to combine evidences of association over multiple SNPs within a gene and multiple genes within a pathway. Most current methods choose the most significant SNP from each gene as a representative, ignoring the joint action of multiple SNPs within a gene. This approach leads to preferential identification of genes with a greater number of SNPs.     

ABC Transporters and the Proteasome Complex Are Implicated in Susceptibility to Stevens–Johnson Syndrome and Toxic Epidermal Necrolysis across Multiple Drugs

Stevens–Johnson syndrome (SJS) and Toxic Epidermal Necrolysis (TEN) represent rare but serious adverse drug reactions (ADRs). Both are characterized by distinctive blistering lesions and significant mortality rates. While there is evidence for strong drug-specific genetic predisposition related to HLA alleles, recent genome wide association studies (GWAS) on European and Asian populations have failed to identify genetic susceptibility alleles that are common across multiple drugs. We hypothesize that this is a consequence of the low to moderate effect size of individual genetic risk factors. To test this hypothesis we developed Pointer, a new algorithm that assesses the aggregate effect of multiple low risk variants on a pathway using a gene set enrichment approach. A key advantage of our method is the capability to associate SNPs with genes by exploiting physical proximity as well as by using expression quantitative trait loci (eQTLs) that capture information about both cis- and trans-acting regulatory effects. We control for known bias-inducing aspects of enrichment based analyses, such as: 1) gene length, 2) gene set size, 3) presence of biologically related genes within the same linkage disequilibrium (LD) region, and, 4) genes shared among multiple gene sets. We applied this approach to publicly available SJS/TEN genome-wide genotype data and identified the ABC transporter and Proteasome pathways as potentially implicated in the genetic susceptibility of non-drug-specific SJS/TEN. We demonstrated that the innovative SNP-to-gene mapping phase of the method was essential in detecting the significant enrichment for those pathways. Analysis of an independent gene expression dataset provides supportive functional evidence for the involvement of Proteasome pathways in SJS/TEN cutaneous lesions. These results suggest that Pointer provides a useful framework for the integrative analysis of pharmacogenetic GWAS data, by increasing the power to detect aggregate effects of multiple low risk variants. The software is available for download at https://sourceforge.net/projects/pointergsa/.     

MultiPhen: joint model of multiple phenotypes can increase discovery in GWAS

The genome-wide association study (GWAS) approach has discovered hundreds of genetic variants associated with diseases and quantitative traits. However, despite clinical overlap and statistical correlation between many phenotypes, GWAS are generally performed one-phenotype-at-a-time. Here we compare the performance of modelling multiple phenotypes jointly with that of the standard univariate approach. We introduce a new method and software, MultiPhen, that models multiple phenotypes simultaneously in a fast and interpretable way. By performing ordinal regression, MultiPhen tests the linear combination of phenotypes most associated with the genotypes at each SNP, and thus potentially captures effects hidden to single phenotype GWAS. We demonstrate via simulation that this approach provides a dramatic increase in power in many scenarios. There is a boost in power for variants that affect multiple phenotypes and for those that affect only one phenotype. While other multivariate methods have similar power gains, we describe several benefits of MultiPhen over these. In particular, we demonstrate that other multivariate methods that assume the genotypes are normally distributed, such as canonical correlation analysis (CCA) and MANOVA, can have highly inflated type-1 error rates when testing case-control or non-normal continuous phenotypes, while MultiPhen produces no such inflation. To test the performance of MultiPhen on real data we applied it to lipid traits in the Northern Finland Birth Cohort 1966 (NFBC1966). In these data MultiPhen discovers 21% more independent SNPs with known associations than the standard univariate GWAS approach, while applying MultiPhen in addition to the standard approach provides 37% increased discovery. The most associated linear combinations of the lipids estimated by MultiPhen at the leading SNPs accurately reflect the Friedewald Formula, suggesting that MultiPhen could be used to refine the definition of existing phenotypes or uncover novel heritable phenotypes.     

Identifying disease related sub-pathways for analysis of genome-wide association studies

Most methods for genome-wide association studies (GWAS) focus on discovering a single genetic variant, but the pathogenesis of complex diseases is thought to arise from the joint effect of multiple genetic variants. Information about pathway structure, such as the interactions and distances between gene products within pathways, can help us learn more about the functions and joint effect of genes associated with disease risk. We developed a novel sub-pathway based approach to study the joint effect of multiple genetic variants that are modestly associated with disease. The approach prioritized sub-pathways based on the significance values of single nucleotide polymorphisms (SNPs) and the interactions and distances between gene products within pathways. We applied the method to seven complex diseases. The result showed that our method can efficiently identify statistically significant sub-pathways associated with the pathogenesis of complex diseases. The approach identified sub-pathways that may inform the interpretation of GWAS data.     

Multi-locus test conditional on confirmed effects leads to increased power in genome-wide association studies

Complex diseases or phenotypes may involve multiple genetic variants and interactions between genetic, environmental and other factors. Current genome-wide association studies (GWAS) mostly used single-locus analysis and had identified genetic effects with multiple confirmations. Such confirmed single-nucleotide polymorphism (SNP) effects were likely to be true genetic effects and ignoring this information in testing new effects of the same phenotype results in decreased statistical power due to increased residual variance that has a component of the omitted effects. In this study, a multi-locus association test (MLT) was proposed for GWAS analysis conditional on SNPs with confirmed effects to improve statistical power. Analytical formulae for statistical power were derived and were verified by simulation for MLT accounting for confirmed SNPs and for single-locus test (SLT) without accounting for confirmed SNPs. Statistical power of the two methods was compared by case studies with simulated and the Framingham Heart Study (FHS) GWAS data. Results showed that the MLT method had increased statistical power over SLT. In the GWAS case study on four cholesterol phenotypes and serum metabolites, the MLT method improved statistical power by 5% to 38% depending on the number and effect sizes of the conditional SNPs. For the analysis of HDL cholesterol (HDL-C) and total cholesterol (TC) of the FHS data, the MLT method conditional on confirmed SNPs from GWAS catalog and NCBI had considerably more significant results than SLT.     

Functional analysis of HapMap SNPs

Genome-wide association studies (GWAS) have successfully identified many genetic variants associated with complex diseases and traits. However, functional consequence of genetic variants studied in GWAS is not yet fully investigated, which would hinder the application of GWAS. We therefore performed a systematic functional analysis of HapMap SNPs, which have been most commonly used as the reference panel for GWAS. Our study highlights several characteristics of HapMap SNPs and identifies subsets of genetic variants with interesting functional implication. The results show that HapMap SNPs have good coverage within RefSeq genes, especially within known disease-related genes. On the other hand, only a small percentage of SNPs are non-synonymous SNPs while many SNPs are actually located at gene deserts. Moreover, many functionally important variants are not yet still interrogated. A redesigned SNP reference panel with additional functionally important variants would be useful to identify disease-causal variants in the future genome-wide studies.     

Post-GWAS functional characterization of susceptibility variants for chronic lymphocytic leukemia

Recent genome-wide association studies (GWAS) have identified several gene variants associated with sporadic chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL). Many of these CLL/SLL susceptibility loci are located in non-coding or intergenic regions, posing a significant challenge to determine their potential functional relevance. Here, we review the literature of all CLL/SLL GWAS and validation studies, and apply eQTL analysis to identify putatively functional SNPs that affect gene expression that may be causal in the pathogenesis of CLL/SLL. We tested 12 independent risk loci for their potential to alter gene expression through cis-acting mechanisms, using publicly available gene expression profiles with matching genotype information. Sixteen SNPs were identified that are linked to differential expression of SP140, a putative tumor suppressor gene previously associated with CLL/SLL. Three additional SNPs were associated with differential expression of DACT3 and GNG8, which are involved in the WNT/β-catenin- and G protein-coupled receptor signaling pathways, respectively, that have been previously implicated in CLL/SLL pathogenesis. Using in silico functional prediction tools, we found that 14 of the 19 significant eQTL SNPs lie in multiple putative regulatory elements, several of which have prior implications in CLL/SLL or other hematological malignancies. Although experimental validation is needed, our study shows that the use of existing GWAS data in combination with eQTL analysis and in silico methods represents a useful starting point to screen for putatively causal SNPs that may be involved in the etiology of CLL/SLL.     

Genetics of sputum gene expression in chronic obstructive pulmonary disease

Previous expression quantitative trait loci (eQTL) studies have performed genetic association studies for gene expression, but most of these studies examined lymphoblastoid cell lines from non-diseased individuals. We examined the genetics of gene expression in a relevant disease tissue from chronic obstructive pulmonary disease (COPD) patients to identify functional effects of known susceptibility genes and to find novel disease genes. By combining gene expression profiling on induced sputum samples from 131 COPD cases from the ECLIPSE Study with genomewide single nucleotide polymorphism (SNP) data, we found 4315 significant cis-eQTL SNP-probe set associations (3309 unique SNPs). The 3309 SNPs were tested for association with COPD in a genomewide association study (GWAS) dataset, which included 2940 COPD cases and 1380 controls. Adjusting for 3309 tests (p<1.5e-5), the two SNPs which were significantly associated with COPD were located in two separate genes in a known COPD locus on chromosome 15: CHRNA5 and IREB2. Detailed analysis of chromosome 15 demonstrated additional eQTLs for IREB2 mapping to that gene. eQTL SNPs for CHRNA5 mapped to multiple linkage disequilibrium (LD) bins. The eQTLs for IREB2 and CHRNA5 were not in LD. Seventy-four additional eQTL SNPs were associated with COPD at p<0.01. These were genotyped in two COPD populations, finding replicated associations with a SNP in PSORS1C1, in the HLA-C region on chromosome 6. Integrative analysis of GWAS and gene expression data from relevant tissue from diseased subjects has located potential functional variants in two known COPD genes and has identified a novel COPD susceptibility locus.     

Genome wide association studies for milk production traits in Chinese Holstein population

Genome-wide association studies (GWAS) based on high throughput SNP genotyping technologies open a broad avenue for exploring genes associated with milk production traits in dairy cattle. Motivated by pinpointing novel quantitative trait nucleotide (QTN) across Bos Taurus genome, the present study is to perform GWAS to identify genes affecting milk production traits using current state-of-the-art SNP genotyping technology, i.e., the Illumina BovineSNP50 BeadChip. In the analyses, the five most commonly evaluated milk production traits are involved, including milk yield (MY), milk fat yield (FY), milk protein yield (PY), milk fat percentage (FP) and milk protein percentage (PP). Estimated breeding values (EBVs) of 2,093 daughters from 14 paternal half-sib families are considered as phenotypes within the framework of a daughter design. Association tests between each trait and the 54K SNPs are achieved via two different analysis approaches, a paternal transmission disequilibrium test (TDT)-based approach (L1-TDT) and a mixed model based regression analysis (MMRA). In total, 105 SNPs were detected to be significantly associated genome-wise with one or multiple milk production traits. Of the 105 SNPs, 38 were commonly detected by both methods, while four and 63 were solely detected by L1-TDT and MMRA, respectively. The majority (86 out of 105) of the significant SNPs is located within the reported QTL regions and some are within or close to the reported candidate genes. In particular, two SNPs, ARS-BFGL-NGS-4939 and BFGL-NGS-118998, are located close to the DGAT1 gene (160bp apart) and within the GHR gene, respectively. Our findings herein not only provide confirmatory evidences for previously findings, but also explore a suite of novel SNPs associated with milk production traits, and thus form a solid basis for eventually unraveling the causal mutations for milk production traits in dairy cattle.     

Empirical Bayes screening of many p-values with applications to microarray studies

MOTIVATION: Statistical tests for the detection of differentially expressed genes lead to a large collection of p-values one for each gene comparison. Without any further adjustment, these p-values may lead to a large number of false positives, simply because the number of genes to be tested is huge, which might mean wastage of laboratory resources. To account for multiple hypotheses, these p-values are typically adjusted using a single step method or a step-down method in order to achieve an overall control of the error rate (the so-called familywise error rate). In many applications, this may lead to an overly conservative strategy leading to too few genes being flagged. RESULTS: In this paper we introduce a novel empirical Bayes screening (EBS) technique to inspect a large number of p-values in an effort to detect additional positive cases. In effect, each case borrows strength from an overall picture of the alternative hypotheses computed from all the p-values, while the entire procedure is calibrated by a step-down method so that the familywise error rate at the complete null hypothesis is still controlled. It is shown that the EBS has substantially higher sensitivity than the standard step-down approach for multiple comparison at the cost of a modest increase in the false discovery rate (FDR). The EBS procedure also compares favorably when compared with existing FDR control procedures for multiple testing. The EBS procedure is particularly useful in situations where it is important to identify all possible potentially positive cases which can be subjected to further confirmatory testing in order to eliminate the false positives. We illustrated this screening procedure using a data set on human colorectal cancer where we show that the EBS method detected additional genes related to colon cancer that were missed by other methods.This novel empirical Bayes procedure is advantageous over our earlier proposed empirical Bayes adjustments due to the following reasons: (i) it offers an automatic screening of the p-values the user may obtain from a univariate (i.e., gene by gene) analysis package making it extremely easy to use for a non-statistician, (ii) since it applies to the p-values, the tests do not have to be t-tests; in particular they could be F-tests which might arise in certain ANOVA formulations with expression data or even nonparametric tests, (iii) the empirical Bayes adjustment uses nonparametric function estimation techniques to estimate the marginal density of the transformed p-values rather than using a parametric model for the prior distribution and is therefore robust against model mis-specification. AVAILABILITY: R code for EBS is available from the authors upon request. SUPPLEMENTARY INFORMATION: http://www.stat.uga.edu/~datta/EBS/supp.htm