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      GPA: A Statistical Approach to Prioritizing GWAS Results by Integrating Pleiotropy and Annotation

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          Results from Genome-Wide Association Studies (GWAS) have shown that complex diseases are often affected by many genetic variants with small or moderate effects. Identifications of these risk variants remain a very challenging problem. There is a need to develop more powerful statistical methods to leverage available information to improve upon traditional approaches that focus on a single GWAS dataset without incorporating additional data. In this paper, we propose a novel statistical approach, GPA (Genetic analysis incorporating Pleiotropy and Annotation), to increase statistical power to identify risk variants through joint analysis of multiple GWAS data sets and annotation information because: (1) accumulating evidence suggests that different complex diseases share common risk bases, i.e., pleiotropy; and (2) functionally annotated variants have been consistently demonstrated to be enriched among GWAS hits. GPA can integrate multiple GWAS datasets and functional annotations to seek association signals, and it can also perform hypothesis testing to test the presence of pleiotropy and enrichment of functional annotation. Statistical inference of the model parameters and SNP ranking is achieved through an EM algorithm that can handle genome-wide markers efficiently. When we applied GPA to jointly analyze five psychiatric disorders with annotation information, not only did GPA identify many weak signals missed by the traditional single phenotype analysis, but it also revealed relationships in the genetic architecture of these disorders. Using our hypothesis testing framework, statistically significant pleiotropic effects were detected among these psychiatric disorders, and the markers annotated in the central nervous system genes and eQTLs from the Genotype-Tissue Expression (GTEx) database were significantly enriched. We also applied GPA to a bladder cancer GWAS data set with the ENCODE DNase-seq data from 125 cell lines. GPA was able to detect cell lines that are biologically more relevant to bladder cancer. The R implementation of GPA is currently available at

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          In the past 10 years, many genome wide association studies (GWAS) have been conducted to identify the genetic bases of complex human traits. As of January, 2014, more than 12,000 single-nucleotide polymorphisms (SNPs) have been reported to be significantly associated with at least one complex trait/disease. On one hand, about 85% of identified risk variants are located in non-coding regions, which motivates a systematic understanding of the function of non-coding variants in regulatory elements in the human genome. On the other hand, complex diseases are often affected by many genetic variants with small or moderate effects. To address these issues, we propose a statistical approach, GPA, to integrating information from multiple GWAS datasets and functional annotation. Notably, our approach only requires marker-wise p-values as input, making it especially useful when only summary statistics, instead of the full genotype and phenotype data, are available. We applied GPA to analyze GWAS datasets of five psychiatric disorders and bladder cancer, where the central nervous system genes, eQTLs from the Genotype-Tissue Expression (GTEx), and the ENCODE DNase-seq data from 125 cell lines were used as functional annotation. The analysis results suggest that GPA is an effective method for integrative data analysis in the post-GWAS era.

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          Trait-Associated SNPs Are More Likely to Be eQTLs: Annotation to Enhance Discovery from GWAS

          Introduction Results of genome-wide association studies (GWAS) in complex traits published to date have provided us with surprisingly little new information on the nature of the genetic component to these phenotypes, despite the large number of single nucleotide polymorphisms (SNPs) found to be reproducibly associated with such traits. In some cases, this reflects the fact that major aspects of the biological basis for disease were already well understood; results of GWAS in autoimmune disorders, for example, have reinforced the central importance of the immune system and its regulation. For a few disorders, results of GWAS have highlighted biological contributing factors to disease that had not previously been recognized as central, such as the complement system in macular degeneration [1] or autophagy in Crohn's disease [2]–[4]. While it does seem ungrateful to question the utility of GWAS when they have yielded so many more reproducible associations than we have achieved with any other approach, the fact is that our primary goal in conducting GWAS for a complex trait – achieving a comprehensive understanding of the genetic basis for that trait – remains elusive for most of the traits that have been examined. The failure to achieve this goal is made particularly acute by the recognition that the loci that have been successfully identified not only provide us with little insight into the genetic basis for the trait, but also account for little of the overall heritability [5]. Although there are important caveats to these grim statistics – most published studies have conducted discovery research in populations of European descent, and some important disorders have not even been examined using GWAS yet – the collective experience has led to sharp disagreement as to whether there is sufficient value in targeting near-term investments in genomics to GWAS, or whether such investments are better targeted to sequencing [6]–[8]. The key issue in this controversy is whether the genetic risk factors not yet discovered are largely similar in frequency and effect size to those that have been discovered using GWAS (i.e. common alleles with low risk) or are, instead, rarer alleles that would be best identified through sequencing studies. Studies we report here suggest that we have not yet exhausted the signals that can be discovered through GWAS. Annotating SNPs with information on expression can improve our ability to more easily distinguish those associations likely to be replicated, and provide us with a better understanding of the genes and mechanisms driving the associations we discover. Moreover, it appears that for at least a subset of complex disorders, there are many more common variants truly associated with disease and highly likely to be expression quantitative trait loci (eQTLs). These variants can be identified and characterized using existing GWAS and tools such as the SCAN database (SNP and Copy number ANnotation; [9]. Results SNPs Associated with Complex Traits Are More Likely to Be eQTLs than Frequency-Matched SNPs from GWAS Platforms The 1598 SNPs characterized in the GWAS catalog [10] as showing association with complex traits included 625 that would be classified as eQTLs with a p-value threshold of 10−4 using CEPH (Centre d'Etude du Polymorphisme Humain) samples of European descent from Utah (CEU) or 972 using the combined sample of the CEU plus the Yoruban samples from Ibadan Nigeria (YRI) data to define eQTLs, 46 (83 for the combined CEU+YRI) that would be classified as eQTLs with a p-value threshold of 10−6 and 17 (18 for the combined CEU+YRI) that would be classified as eQTLs with a p-value threshold of 10−8. As summarized in Figure 1, we observed significantly more eQTLs among these 1598 trait-associated SNPs than expected given their minor allele frequency (MAF) distribution. Given that many gene transcript levels show substantial correlations, it is, perhaps, not surprising that we also observed that SNPs associated with many transcripts (sometimes called eQTL hot spots or master regulators) were also enriched among trait-associated SNPs. Using a more stringent definition for defining trait-associated SNPs (up to 10−8) reduced their absolute numbers of such SNPs, but increased the significance of the observed enrichment of eQTLs among trait-associated SNPs. 10.1371/journal.pgen.1000888.g001 Figure 1 Trait-associated SNPs are more likely to be eQTLs. The distribution of the number of eQTLs (defined as p 0.3 and for each replicate conducted 100 simulations conditional on MAF as for Figure 1 (see Materials and Methods for simulation details). The eQTL enrichment was preserved in LD-pruned sets of cataloged variants, for eQTL definition thresholds with p 0.05) on high throughput platforms, associated with traits in the GWAS catalog, and associated with phenotypes selected to represent those for which lymphoblastoid cell lines (LCLs) might be expected to be a poor proxy for the human tissues most relevant for disease (neurological/psychiatric phenotypes, cancers) and those for which LCLs might be expected to be a good proxy for the human tissues most relevant to disease (autoimmune disorders). As is apparent from the table, neurological and psychiatric phenotypes as well as cancers (regardless of tumor site) showed levels of enrichment similar to those observed for the overall trait-associated SNP set, although as expected, autoimmune disorders showed somewhat greater levels of enrichment. Division of the GWAS catalog SNPs into those identified through studies on autoimmune disorders and those identified through studies on other complex traits reveals that the apparent enrichment of eQTLs (defined at a threshold of p .05) 1,213,906 595,285 (.490) 29,347 (.024) All Catalog SNPs 1598 972 (0.608) 83 (0.052) Autoimmune Disorders 259 165 (0.637) 21 (0.081) Cancers 93 56 (0.602) 4 (0.043) Neurological/Psychiatric Disorders 63 41 (0.651) 2 (0.032) Using eQTLs from CEU only Platform SNPs (MAF >.05) 1,213,906 345,249 (.284) 12,749 (.011) All Catalog SNPs 1598 625 (0.391) 46 (0.029) Autoimmune Disorders 259 116 (0.448) 17 (0.066) Cancers 93 30 (0.323) 3 (.032) Neurological/Psychiatric Disorders 63 20 (0.317) 1 (0.016) SNPs from the NHGRI catalog were classified according to the type of disease leading to their inclusion as a trait-associated SNP to investigate whether eQTLs identified in LCLs are more enriched in disorders for which LCLs are more likely to be an appropriate tissue match for the disease. Studies were conducted separately using eQTLs identified in the combined CEU+YRI samples (upper lines), and those identified only in the CEU (lower lines). Only SNPs with MAF >0.05 are included in these studies, and eQTL p-value thresholds of 10−4 and 10−6 are shown. Using eQTL Information Improves Ability to Identify Reproducible Signals in GWAS In order to understand the practical utility of our observation that trait-associated SNPs are more likely to be eQTLs, we examined in more detail results summaries from the Wellcome Trust Case Control Consortium (WTCCC) GWAS [11], using the data on Crohn's disease as a primary example application. If SNPs associated with Crohn's disease are no more likely than non-associated SNPs to be eQTLs, we would expect the proportion of SNPs associated with Crohn's disease at p 3. SNPs have been ordered according to their WTCCC Crohn's association p-values from the most to the least significant, and divided in groups of 10,000. For each group bin of 10,000 trait-associated SNPs, the number of SNPs with expression score larger than 3 was calculated and the results are shown in the scatterplot. The horizontal line illustrates the expectation based on the observed eQTL function scores in all SNPs in the WTCCC Crohn's dataset. The dotted lines represent estimated 95% confidence bands obtained using simulations. Analyses on other phenotypes from the WTCCC association studies [11] confirmed that our proposed annotations benefit phenotypes beyond Crohn's disease. Figure 4 illustrates that both type 1 diabetes (T1D) and rheumatoid arthritis (RA) had significantly more SNPs than expected with phenotype associations (p 3. The plots show results of eQTL enrichment analysis for the remaining Wellcome Trust phenotypes beginning with the SNPs most strongly associated with disease (similar to analyses for Crohn's disease summarized in Figure 3). For each disease, SNPs have been ordered according to their association p-values from the most to the least significant, and divided in groups of 10,000. For each group, the number of SNPs with expression score larger than 3 was calculated and the results are shown in the scatterplots. The horizontal lines illustrate the expectation based on the observed scores in all SNPs in the relevant WTCCC dataset. The dotted lines represent estimated 95% confidence bands obtained using simulations. Discussion Our results build on those of previous studies, particularly those of Schadt and colleagues [12]–[15] that focused on using transcriptome information to improve understanding of genetic signals, but the rapid accumulation of trait-associated SNPs through GWAS, coupled with the systematic efforts to catalog these variants [10],[16] has enabled us to generalize the concept that information on eQTLs will have utility for understanding the genetic component to complex traits. Our primary observations – that SNPs reproducibly associated with complex human traits are more likely to be eQTLs – are novel, although perhaps not unexpected given that few of even those SNPs most reproducibly associated with complex traits have been attributed to missense or nonsense variants. Our subsequent observations made in association studies in which we annotated SNPs with eQTL information, imply that at least some complex disorders have substantial numbers of undiscovered susceptibility loci that can be more easily discovered and characterized by annotating SNPs with information on eQTL scores. This is also a novel observation. Moreover, use of information on expression appears to benefit our understanding of not only more tractable disorders, such as Crohn's disease and autoimmune disorders, for which relatively large numbers of loci have already been identified at the cost of genotyping 10,000 or fewer samples, but also for less tractable disorders such as hypertension and bipolar disease, for which fewer associations have been characterized despite the large numbers of genotyped samples (>29,000 in GWAS and >34,000 for replication in studies of hypertension [17]). Use of expression information should move us closer to that elusive goal of developing a more comprehensive understanding of the genetic basis for complex traits in two ways: (1) by identifying and characterizing a larger number of contributing loci, we should be better able to discern the key biological functions affected by genetic risk factors and (2) SNP signals may be more accurately characterized with respect to target genes and mechanism of effect, further enhancing our ability to discern relevant biological functions. Thus, our results provide a strong additional rationale for the inclusion of eQTL information in the annotation of SNPs from GWAS. Moreover, even the analyses we have completed to characterize trait-associated SNPs as being more likely than allele frequency matched SNPs from the same platform to be eQTLs have revealed information about the potential biological rationale for some of the observed associations. For example, an intronic SNP, rs3129934, on chromosome 6 that is a cis-acting eQTL for multiple HLA transcripts with a high eQTL functional score (24.9) shows the strongest association with T1D in the MHC region in the WTCCC study [11] and is also the SNP most strongly associated with increased risk for multiple sclerosis (MS) in a pooling-based GWAS [18]. A variety of the approaches we used in conducting these studies should be of general utility in enrichment studies. It is clear, for example, that the MAF spectrum of SNPs associated with complex human traits is quite different than that of SNPs on the products used to conduct GWAS, or in the overall HapMap. The much higher minor allele frequencies observed for SNPs reproducibly associated with complex traits than for SNPs on high throughput platforms is a natural consequence of the increased power to detect associations for SNPs with higher minor allele frequencies. It is clearly critical to condition on the MAF in enrichment studies in which simulations are conducted using SNPs from high throughput platforms or from the HapMap, and to date, this has not been widely appreciated. The correlation among SNPs due to LD is a further complicating factor in conducting enrichment studies. We are confident that failure to adequately account for LD will not affect our estimate of the proportion of SNPs that are eQTLs, but rather the variance of this estimate. There are, however, more subtle biases related to LD that might have affected our studies. For example, true associations may be more easily detected in regions of the genome with high LD because these regions are more likely to have good coverage on high throughput platforms for GWAS. Although it is unclear that this would bias results of our studies, it is important to note that these types of subtle biases can affect results of enrichment studies in unpredictable ways. The challenges of conducting eQTL studies are also widely appreciated. The eQTLs identified in array-based transcriptome studies in LCLs are likely to be a limited subset of the eQTLs that will ultimately be identified using more sensitive techniques in comprehensive collections of human tissues. Moreover, a variety of studies have highlighted the potential sensitivity of eQTL studies to cell and tissue subtypes [15],[19],[20]. Although several studies have suggested that eQTLs will be largely tissue specific [21],[22], others note that substantial numbers of eQTLs are shared across tissues [15],[23]. Similarly, some have found that LCLs are prone to such high levels of non-genetic variability (growth parameters, EBV levels, ATP levels, etc.) that they might be considered unreliable for genomic studies [24], while others highlight the reproducibility of results of transcriptome studies [25],[26] and find that LCLs show little variability as a consequence of non-genetic factors [27]. To the degree that the transcriptome is a reflection of the local and temporal environment, it could be argued that eQTLs identified in generic studies will have little value for enhancing understanding of complex trait studies unless eQTLs are identified in relevant tissues of the individuals participating in the complex trait studies. Our results provide little support for such arguments, and instead highlight the utility of LCLs as a reasonable model for the study of expression. And while LCLs are clearly not the ideal tissue for expression studies in many complex disorders, we note that we plan to serve results of eQTL studies in a variety of tissues in SCAN, and consider the studies summarized in this manuscript to be an initial effort that will be enriched by subsequent studies in additional tissues. It is possible that diseases without evidence for eQTL enrichment using data from LCLs will ultimately yield such evidence when data from more relevant tissues is used; alternatively, at least a subset of those disorders without evidence for enrichment for eQTLs may turn out to derive substantial heritability from rare variants. In any case, results of our studies clearly support additional investment in eQTL identification in other tissues, as well as in the development of public access databases and software tools, such as those in SCAN (, that allows results of such studies to be productively used by the scientific community. Materials and Methods SNPs Reproducibly Associated with Complex Human Traits The National Human Genome Research Institute (NHGRI) has collected the results of published GWA studies in a publicly available online database ( [16]. This catalog is continually updated; the version we utilize for the present study was downloaded on June 29, 2009. We used the NHGRI default set of SNPs reported to be associated to complex traits with a p-value of at least 10−5 for all figures and tables in the manuscript, but we note that results show more significant enrichment for more stringent definitions for trait-associated SNPs (we tested 10−5 through 10−8). The SCAN Database We have created an online database to serve the results of our gene-expression studies in LCLs. SCAN (SNP and Copy number ANnotation database; can be queried through either the SNP or gene to retrieve information on the relationship between SNPs and transcript levels at user-specified p-value thresholds [9]. SCAN enables batch queries of genes to retrieve a list of SNPs that predict the expression of the genes at a user-specified threshold. SCAN also holds multi-locus disequilibrium measures [28] to summarize reported LD information among SNPs and to characterize coverage of genes by the high-throughput genotyping platforms. The expression data served in SCAN had been assayed in HapMap LCLs (87 CEU and 89 YRI) with the Affymetrix GeneChip Human Exon 1.0 ST Array [29]. The exon array measures both exon-level and gene-level expression, includes approximately 1.4 million probesets, and profiles over 17,000 gene transcripts. Genome-wide association analyses of 13,080 transcript clusters (gene-level) with reliable expression and more than 2 million SNPs in the CEU or YRI populations were conducted using the Quantitative Trait Disequilibrium Test (QTDT) [30]. A transcript cluster or probeset in the exon array is defined as reliably expressed in LCLs if the log2-transformed expression signal is greater than 6 in at least 80% of the 176 HapMap samples included analyses. Each transcript cluster includes a set of probesets (exon-level) containing all known exons and 5′- and 3′- untranslated regions (UTRs) in the genome. In contrast to other arrays (e.g., U95 and U133 series arrays), the probes on the exon array cover entire gene regions and not just 3′-UTRs. Since SNPs in probes can generate spurious eQTL signals by affecting hybridization, we downloaded SNP data from dbSNP (build 129, human genome assembly build 36) to identify probes in probesets that hybridize to regions containing SNPs. The genomic coordinates of the probes were downloaded from the Affymetrix website ( We filtered these probes before conducting the expression analyses generating the results served in SCAN. Analysis of eQTL Enrichment All analyses have been conducted using all available information (eQTLs for both CEU and YRI samples) and also using only information from the CEU samples. Results are substantially similar, but because most GWAS reported to date have been conducted in samples of recent European descent, and to be conservative, summary figures use only the eQTL information from the CEU samples. We also provide details for some of the key eQTL studies in tabular form (Table 1), where we provide summary information for enrichment studies using CEU+YRI eQTL data and for enrichment studies using only the CEU eQTL data. The MAF distribution for SNPs showing reproducible associations with complex human traits is markedly different from the MAF distribution for all SNPs on the high density SNP genotyping platforms, or the minor allele frequency distribution of SNPs included on high throughput platforms used for GWAS (Figure S1). Thus, any study focused on enrichments among SNPs reproducibly associated with complex human phenotypes must be conditioned on MAF. To enable us to conduct simulations conditional on MAF, we constructed MAF bins as follows: allele frequencies were calculated from HapMap genotype data on the CEU. Only the parents' genotypes were included in the frequency calculations since the children's alleles are not independent. We used the toolkit PLINK [31] to calculate frequencies. We classified SNPs on Affymetrix Genome-Wide Human SNP Array 6.0 and Illumina's High Density Human 1M-Duo into non-overlapping minor allele frequency (MAF) bins, each of width .05, using the MAFs of the SNPs in the CEU samples, as most of the published reports summarized in the NHGRI catalog are from GWAS on individuals of recent European descent. We conducted simulations to test for an enrichment of eQTLs among the NHGRI variants associated with complex traits by generating 1000 randomized SNP sets Si each of the same size as the original NHGRI list (1598) containing variants matched on MAF distribution, sampled without replacement from the set of typed SNPs on each high-throughput platform, which had been grouped into discrete MAF bins. For each set, we determined the number of eQTLs, Qi , at a p-value threshold. We tested the robustness of the eQTL enrichment across a range of p-value thresholds (10−8 to 10−4), as shown in Figure 1. These simulations (N = 1000) yield an empirical p-value, calculated as the proportion of simulations in which the number of eQTLs exceeds the observed number, Q, in the NHGRI list. Because some GWAS report associations for SNPs that were interrogated through imputation rather than direct genotyping, we repeated the analysis described above except that we used the entire set of HapMap SNPs to generate the 1000 randomized SNP sets with MAF matched to catalog SNPs, rather than only the SNPs included on high throughput GWAS platforms. Results of these studies show an even more significant enrichment of eQTLs among catalog SNPs (Figure S2). Thus, we focus in this paper on the more conservative results obtained using the simulations generated from SNPs on high-throughput GWAS platforms. To investigate whether the eQTL enrichment we observe in the NHGRI variants is driven by linkage disequilibrium (LD), an LD-pruned SNP set was generated from the NHGRI list using r2 4 MB from (or on another chromosome than) any gene with which the SNP shows transcript level association. In order to devise a one-dimensional score that summarizes as much of the eQTL signal information as possible for prioritizing GWAS signals according to their “functionality”, we first note that neither the scale of the score nor the distribution of the score for non-functional SNPs are relevant – just the appropriate ranking of SNPs with a function in regulating transcript levels. The building blocks for the SNP score are: po which is the overall smallest eQTL p-value (it can be either cis or trans), pc which is the smallest cis p-value, No which is the overall number of transcripts used in the analysis, and Nc which is the number of cis transcripts (i.e. the number of transcripts annotated to genes in the vicinity of the SNP under investigation). The score we propose: builds on Bonferroni corrections applied separately for trans and cis signals (there are 13,080 transcripts used in the analysis). Note that the scores are truncated at zero. Utilizing Expression Information in GWAS In order to determine whether our newly derived functional score can aid in identifying associations likely to be replicated, we first examined the summary data for Crohn's disease from the WTCCC association study [11] (downloaded when results data were publicly available). After QC (less than 5% missing data, good clustering), we filtered SNPs at a 1% MAF threshold, and removed markers with no rs ID, leaving 391,878 SNPs. We matched these SNPs using the rs IDs within the SCAN database, leaving us with 386,306 SNPs. We then ordered the SNPs according to their score S from largest to smallest score. The top SNPs based on the eQTL score show an excess of small association p-values with Crohn's disease (for example, in the top ten SNPs, six have p-values smaller than 0.01). We divided the SNPs into groups of 10,000 (in the order of their eQTL scores) and counted the number of SNPs in each group with p 3, >2, and >1 among the top 1000 SNPs for Crohn's disease (Figure 3). We repeated the Crohn's disease enrichment studies in the other WTCCC phenotypes. As with Crohn's disease, we first conducted analyses checking for an excess of small association p-values in the SNPs that have high expression annotation scores (Figure 4). Finally, we ranked the SNPs according to their association p-values and looked for an enrichment of high expression scores (Figure 5). To insure that results of enrichment studies were not unduly influenced by large numbers of correlated SNPs in the MHC region with high eQTL scores, we repeated the analyses summarized in Figure 2 and Figure 4 after removing all SNPs on chromosome 6 (see Figure S5). Results were relatively unchanged. Supporting Information Figure S1 Minor allele frequency (MAF) distributions for Affymetrix 6.0 SNPs (A), Illumina 1M SNPs (B), and NHGRI Associated SNPs (C). (1.57 MB TIF) Click here for additional data file. Figure S2 (A) The distribution of the number of eQTLs (at p<10−4 observed for each of 1,000 draws of 1,598 SNPs from bins matched for minor allele frequency to the 1,598 SNPs downloaded from the NHGRI catalog (bins include all HapMap SNPs) is shown in the bar graphs, with the actual number of eQTLs observed in the 1,598 SNPs from the NHGRI catalog shown as a solid circle. (B) Identical to Figure 1, leftmost panel, with analysis as above, except that SNPs for the simulation were drawn from SNPs on high-throughput GWAS panels. (2.69 MB TIF) Click here for additional data file. Figure S3 Observed numbers of eQTLs among all trait-associated SNPs trimmed for LD are shown as solid black circles with the bar graph showing the distribution of eQTLs among SNPs chosen at random from the same allele frequency bins from among all SNPs included on high-throughput GWAS products. Enrichment of eQTLs among trait-associated SNPs is preserved even in the absence of LD among trait-associated SNPs. (2.09 MB TIF) Click here for additional data file. Figure S4 Observed numbers of master regulators among all trait-associated SNPs are indicated by the solid black circles and the distribution of the number of master regulators (defined as SNPs predicting 10 transcripts and SNPs predicting 100 transcripts, both for p<10−4) observed in 1,000 draws of 1,598 SNPs from minor-allele-frequency-matched bins (including all SNPs on Illumina 1M and Affymetrix 6.0 products) is plotted in the bar graphs. (2.14 MB TIF) Click here for additional data file. Figure S5 This is similar to Figure 2, except that all SNPs on chromosome 6 have been removed from calculations, demonstrating that the Crohn's enrichment for eQTLs is not dependent on SNPs in the HLA region. Results were similar for T1D and RA. (0.88 MB TIF) Click here for additional data file.
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            Detecting differential gene expression with a semiparametric hierarchical mixture method.

            Mixture modeling provides an effective approach to the differential expression problem in microarray data analysis. Methods based on fully parametric mixture models are available, but lack of fit in some examples indicates that more flexible models may be beneficial. Existing, more flexible, mixture models work at the level of one-dimensional gene-specific summary statistics, and so when there are relatively few measurements per gene these methods may not provide sensitive detectors of differential expression. We propose a hierarchical mixture model to provide methodology that is both sensitive in detecting differential expression and sufficiently flexible to account for the complex variability of normalized microarray data. EM-based algorithms are used to fit both parametric and semiparametric versions of the model. We restrict attention to the two-sample comparison problem; an experiment involving Affymetrix microarrays and yeast translation provides the motivating case study. Gene-specific posterior probabilities of differential expression form the basis of statistical inference; they define short gene lists and false discovery rates. Compared to several competing methodologies, the proposed methodology exhibits good operating characteristics in a simulation study, on the analysis of spike-in data, and in a cross-validation calculation.
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              Sizing up human height variation.


                Author and article information

                Role: Editor
                PLoS Genet
                PLoS Genet
                PLoS Genetics
                Public Library of Science (San Francisco, USA )
                November 2014
                13 November 2014
                : 10
                : 11
                [1 ]Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut, United States of America
                [2 ]Department of Public Health Sciences, Medical University of South Carolina, Charleston, South Carolina, United States of America
                [3 ]Department of Psychiatry, Yale School of Medicine, New Haven, Connecticut, United States of America
                [4 ]Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
                [5 ]Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut, United States of America
                [6 ]VA CT Healthcare Center, West Haven, Connecticut, United States of America
                [7 ]Department of Genetics, Yale School of Medicine, West Haven, Connecticut, United States of America
                [8 ]Department of Neurobiology, Yale School of Medicine, New Haven, Connecticut, United States of America
                [9 ]VA Cooperative Studies Program Coordinating Center, West Haven, Connecticut, United States of America
                Stanford University, United States of America
                Author notes

                The authors have declared that no competing interests exist.

                Conceived and designed the experiments: DC CY CL JG HZ. Performed the experiments: DC CY CL JG HZ. Analyzed the data: DC CY CL JG HZ. Contributed reagents/materials/analysis tools: DC CY CL JG HZ. Wrote the paper: DC CY CL JG HZ. Jointly developed the GPA method: DC CY. Performed simulation studies: CL. Directed this study: JG HZ.


                This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.

                Page count
                Pages: 14
                This study was supported by National Institutes of Health grants RC2 DA028909, R01 DA12690, R01 DA12849, R01 DA18432, R01 AA11330, R01 AA017535, P50 AA12870, R01 GM59507, R01 DA030976, UL1 RR024139, and the VA Cooperative Studies Program of the Department of Veterans Affairs, Office of Research and Development. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Research Article
                Biology and Life Sciences
                Computational Biology
                Genome Analysis
                Genome-Wide Association Studies
                Human Genetics
                Physical Sciences
                Statistics (Mathematics)



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