With the availability of high-throughput microarray technologies, investigators can simultaneously measure the expression levels of many thousands of genes in a short period. Although there are rich statistical methods for analyzing microarray data in the literature, limited work has been done in mapping expression quantitative trait loci (eQTL) that influence the variation in levels of gene expression. Most existing eQTL mapping methods assume that the expression phenotypes follow a normal distribution and violation of the normality assumption may lead to inflated type I error and reduced power. QTL analysis of expression data involves the mapping of many expression phenotypes at thousands or hundreds of thousands of marker loci across the whole genome. An appropriate procedure to adjust for multiple testing is essential for guarding against an abundance of false positive results. In this study, we applied a semiparametric quantitative trait loci (SQTL) mapping method to human gene expression data. The SQTL mapping method is rank-based and therefore robust to non-normality and outliers. Furthermore, we apply an efficient Monte Carlo procedure to account for multiple testing and assess the genome-wide significance level. Particularly, we apply the SQTL mapping method and the Monte-Carlo approach to the gene expression data provided by Genetic Analysis Workshop 15

Diao, Guoqing

Lin, DY

English

PubMed

Abstract With the availability of high-throughput microarray technologies, investigators can simultaneously measure the expression levels of many thousands of genes in a short period. Although there are rich statistical methods for analyzing microarray data in the literature, limited work has been done in mapping expression quantitative trait loci (eQTL) that influence the variation in levels of gene expression. Most existing eQTL mapping methods assume that the expression phenotypes follow a normal distribution and violation of the normality assumption may lead to inflated type I error and reduced power. QTL analysis of expression data involves the mapping of many expression phenotypes at thousands or hundreds of thousands of marker loci across the whole genome. An appropriate procedure to adjust for multiple testing is essential for guarding against an abundance of false positive results. In this study, we applied a semiparametric quantitative trait loci (SQTL) mapping method to human gene expression data. The SQTL mapping method is rank-based and therefore robust to non-normality and outliers. Furthermore, we apply an efficient Monte Carlo procedure to account for multiple testing and assess the genome-wide significance level. Particularly, we apply the SQTL mapping method and the Monte-Carlo approach to the gene expression data provided by Genetic Analysis Workshop 15

Lin, Danyu

Carolina Digital Repository

BioMed CentralBMC ProceedingsssOpen AcceProceedingsSemiparametric methods for genome-wide linkage analysis of human gene expression dataGuoqing Diao*1 and DY Lin2Address: 1Department of Statistics, George Mason University, 4400 University Drive, MS 4A7, Fairfax, Virginia 22030, USA and 2Department of Biostatistics, University of North Carolina, McGavran-Greenberg Hall, CB #7420, Chapel Hill, North Carolina 27599, USAEmail: Guoqing Diao* - gdiao@gmu.edu; DY Lin - lin@bios.unc.edu* Corresponding author    AbstractWith the availability of high-throughput microarray technologies, investigators can simultaneouslymeasure the expression levels of many thousands of genes in a short period. Although there arerich statistical methods for analyzing microarray data in the literature, limited work has been donein mapping expression quantitative trait loci (eQTL) that influence the variation in levels of geneexpression. Most existing eQTL mapping methods assume that the expression phenotypes followa normal distribution and violation of the normality assumption may lead to inflated type I errorand reduced power. QTL analysis of expression data involves the mapping of many expressionphenotypes at thousands or hundreds of thousands of marker loci across the whole genome. Anappropriate procedure to adjust for multiple testing is essential for guarding against an abundanceof false positive results. In this study, we applied a semiparametric quantitative trait loci (SQTL)mapping method to human gene expression data. The SQTL mapping method is rank-based andtherefore robust to non-normality and outliers. Furthermore, we apply an efficient Monte Carloprocedure to account for multiple testing and assess the genome-wide significance level.Particularly, we apply the SQTL mapping method and the Monte-Carlo approach to the geneexpression data provided by Genetic Analysis Workshop 15.from Genetic Analysis Workshop 15St. Pete Beach, Florida, USA. 11–15 November 2006Published: 18 December 2007BMC Proceedings 2007, 1(Suppl 1):S83<supplement> <title> <p>Genetic Analysis Workshop 15: Gene Expression Analysis and Approaches to Detecting Multiple Functional Loci</p> </title> <editor>Heather J Cordell, Mariza de Andrade, Marie-Claude Babron, Christopher W Bartlett, Joseph Beyene, Heike Bickeböller, Robert Culverhouse, Adrienne Cupples, E Warwick Daw, Josée Dupuis, Catherine T Falk, Saurabh Ghosh, Katrina A Goddard, Ellen L Goode, Elizabeth R Hauser, Lisa J Martin, Maria Martinez, Kari E North, Nancy L Saccone, Silke Schmidt, William Tapper, Duncan Thomas, David Tritchler, Veronica J Vieland, Ellen M Wijsman, Marsha A Wilcox, John S Witte, Qio g Yang, Andreas Ziegler, Laura Almasy a d Jean W MacCluer</editor> <note>Proce dings</note> <url>http://www.biomedc ntral.com/content/pdf/1753-6561-1-S1-info.pdf</url> </supplement>This article is available from: http://www.biomedcentral.com/1753-6561/1/S1/S83© 2007 Diao and Lin; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Page 1 of 6(page number not for citation purposes)BMC Proceedings 2007, 1(Suppl 1):S83 http://www.biomedcentral.com/1753-6561/1/S1/S83BackgroundWith the availability of high-throughput microarray tech-nologies to measure the expression levels of many thou-sands of genes simultaneously, investigators havedeveloped a vast amount of statistical and computationalmethods for analyzing microarray data in the last decade.On the other hand, because of the abundance of single-nucleotide polymorphisms (SNPs) as well as the moderngenotyping technologies, tremendous efforts have beenfocused on the genetic mapping of complex human dis-eases, many of which are associated with quantitativetraits. However, limited work has been done in combin-ing gene expression data and marker genotype data anddetecting expression quantitative trait loci that influencethe variation in levels of gene expression.There are important challenges in mapping of eQTL. First,it is well known that microarray data are noisy due to sys-tematic biases and appropriate normalization proceduresare needed to adjust for such biases. Many expression phe-notypes may be non-normally distributed even afterproper normalization procedures, as is evident by thegene expression data provided by Genetic Analysis Work-shop 15 (GAW15). Commonly used eQTL mappingmethods such as the standard variance-component (VC)approach implemented in programs SOLAR [1] and Mer-lin [2] assume that the expression phenotypes follow anormal distribution. However, violation of the normalityassumption may lead to inflated type I error and reducedpower. The other challenge is the multiple testing intro-duced in the mapping of many expression phenotypes atthousands or hundreds of thousands of marker loci acrossthe whole genome. A proper procedure to adjust for mul-tiple testing is essential for guarding against an abundanceof false-positive results.To overcome the aforementioned challenges, we firstapplied the semiparametric quantitative trait loci map-ping method of Diao and Lin [3] to gene expression data.The SQTL mapping method is rank-based and thereforeless sensitive to non-normality and outliers. Next, we usedan efficient Monte Carlo procedure to assess the genome-wide significance level. The usefulness of the SQTLmethod and the Monte-Carlo approach is demonstratedthrough an application to the gene expression data pro-vided by GAW15, which were previously analyzed byMorley et al. [4].MethodsSemiparametric QTL mappingVery recently, Diao and Lin [3] proposed the so-calledSQTL mapping method for human pedigrees by allowinga completely unspecified transformation on trait values.Specifically, the phenotypic variation after the unspecifiedtransformation is partitioned into fixed effects due toenvironmental variables and random effects due to majorgene, polygene, and residual errors. In the context of VCanalysis, the SQTL tends to be more powerful than theregression-based methods, including the one used in Mor-ley et al. [4], as is shown in the simulation studies in Diaoand Lin [3]. Moreover, the SQTL approach is rank-basedand less sensitive to non-normality and outliers. Simula-tion studies in Diao and Lin [3] demonstrate that theSQTL is as powerful as the standard VC method assumingnormality and tends to be more powerful than the stand-ard VC method when the phenotype data are non-nor-mally distributed or there exist outliers.For the gene expression data, we repeatedly applied theSQTL and perform a genome-wide linkage scan for eachexpression phenotype. The resultant likelihood ratio teststatistics or LOD scores for testing H0 :  = 0 vs. HA : > 0 can be stored in a matrix with the (i, j)th componentcorresponding to the result for mapping the ith expressionphenotype at the jth marker on the genome, where  isthe variance component attributable to the major genelocus. Under the null hypothesis of no linkage at a markerlocus, the likelihood-ratio test statistic has an approxi-mate distribution of .Adjustment for multiple testingIn eQTL mapping, one performs testing on thousands ofmarker loci for each expression trait and one thus needs toadjust for multiple testing to guard against an abundanceof false-positive results. Carlborg et al. [5] suggested thatsignificance testing should be based on empiricalgenome-wide significance thresholds that are derived foreach trait separately. Lin and Zou [6] and Lin [7] proposedan efficient Monte Carlo approach to adjusting for multi-ple comparisons in a genomic study. The Monte Carloapproach involves repeatedly generating standard normalrandom variables to approximate the joint distribution ofthe test statistics under the null distribution. Unlike thepermutation resampling approach, the Monte Carloapproach does not involve repeated analyses of simulateddata sets and is thus computationally less demanding.Computing is a critical issue in practice because one mayperform millions of tests for each gene expression trait.For example, to perform genome-wide linkage scans forall expression phenotypes in the GAW15 (Problem 1)data set, one needs to perform approximately 10.2 mil-lion tests. Even if we only perform 1000 permutation testsfor each phenotype, the total number of tests increases to10.2 billion, which makes it almost impossible with cur-rent computing power. To obtain results at more stringentgenome-wide significance levels, even more permutationsσ g2 σ g2σ g212120212χ χ:Page 2 of 6(page number not for citation purposes)BMC Proceedings 2007, 1(Suppl 1):S83 http://www.biomedcentral.com/1753-6561/1/S1/S83are required. Furthermore, the Monte Carlo approach iswidely applicable in practical situations, whereas permu-tation tests may not always be applicable in the presenceof covariates and nuisance parameters, especially whenthe covariates are related to the pedigree structure such asage and gender. For sibship data, one can simply decouplethe marker data from the phenotype data, with any covari-ates following the phenotype data in permutation tests.This strategy, however, may not always work for pedigreedata. For example, if covariates include age and gender,the permutation of the covariates together with pheno-type data may not be consistent with the pedigree struc-ture because age and gender are not interchangeablebetween parents and offspring.To apply the Monte Carlo approach to the gene expressiondata, we assess the genome-wide significance level foreach expression trait and obtain the trait-specific adjustedp-values as described in Lin [7]. Note that the test in SQTLis one-sided and corresponding adjustment is required[6].ResultsThe gene expression data provided to GAW15 include 14three-generation CEPH (Centre d'Etude du Polymor-phisme Humain) Utah families, each of which consists of13 or 14 individuals. We performed genome-wide linkagescans for expression levels of 3554 genes at 2882 SNPsusing SQTL. We utilized SOLAR to estimate the identity-by-descent (IBD) allele-sharing probabilities at each SNPlocus after eliminating Mendelian inconsistencies. Genderis included in the model as a covariate. The genome-widesignificance levels and the adjusted p-values for each traitwere based on 100,000 Monte Carlo samples. The averagethresholds (on a LOD scale) at the genome-wide signifi-cance levels of 0.05, 0.01, 1.0 × 10-3, 1.0 × 10-4, and 1.0 ×10-5 are 1.34, 1.70, 2.50, 3.59, and 4.68 corresponding topoint-wise p-values of 6.5 × 10-3, 2.6 × 10-3, 3.5 × 10-4, 2.4× 10-5, and 1.7 × 10-6, respectively. The relatively lowthresholds compared to those used in Morley et al. [4]may reflect the strong correlations among the test statisticsacross the genome.At the genome-wide significance level of 0.05, for 954expression phenotypes, there was evidence of linkage tospecific chromosomal regions. We found 356, 200, 185,and 179 expression phenotypes with evidence of linkageat the genome-wide significance levels of 0.01, 1.0 × 10-3,1.0 × 10-4 and 1.0 × 10-5, respectively. We detected 58more expression traits at the genome-wide significancelevel of 1.0 × 10-3 than Morley et al. [4].As in Morley et al. [4], we divided the autosomal chromo-somes into 491 windows of 5 Mb and determined thenumber of regulators mapping to each window. Table 1presents the results for the five windows that have themost mapped phenotypes at a genome-wide significancelevel of 1.0 × 10-5. At the genome-wide significance levelof 1.0 × 10-3, we found 68 hotspots with six or more hits,including the only 2 hotspots on chromosomes 14 and20, with six and seven hits each detected by Morley et al.[4]. Even at the very stringent genome-wide significancelevel of 1.0 × 10-5, regulators for 51 phenotypes werefound to map to the window on chromosome 10(10p12).Among the total 3554 expression phenotypes, almost halfof them appear to be non-normally distributed by usingthe Shapiro test at a significance level of 0.05. At a signifi-cance level of 0.0001, the Shapiro tests for normality arestill significant for more than 19% of phenotypes. Table 2presents the summary statistics for four extremely non-normally distributed expression traits with p-values ofShapiro test less than 1.0 × 10-12: 211518_s_at,204695_at, 202982_s_at, and 202950_at. The histogramsof these four traits are shown in Figure 1. Phenotype211518_s_at appears to be right-skewed and the otherthree appear to be left-skewed. There exist two and oneoutliers in the left for 202982_s_at and 202950_at, respec-tively, each with difference from the mean greater thanseven times the corresponding standard deviation.We further performed multipoint genome-wide linkageanalysis for the four non-normally distributed pheno-types and compared the performance of SQTL with that ofTable 1: Number of mapped phenotypes at the genome-wide significance levels of 0.01, 0.05, 1.0 × 10-3, 1.0 × 10-4, and 1.0 × 10-5Count of mapped phenotypesaChromosome Region *α = 0.05 α = 0.01 α = 1.0 × 10-3 α = 1.0 × 10-4 α = 1.0 × 10-510 26.35817Mb-29.46754Mb 244 117 61 56 5119 60.12027Mb-63.63787Mb 52 25 17 17 1721 46.14523Mb-46.84680Mb 91 34 18 15 1522 21.40594Mb-24.67240Mb 79 34 25 23 2322 42.36342Mb-43.48228Mb 54 19 15 15 15aα, is the genome-wide significance levelPage 3 of 6(page number not for citation purposes)BMC Proceedings 2007, 1(Suppl 1):S83 http://www.biomedcentral.com/1753-6561/1/S1/S83the standard VC approach assuming normality. Themultipoint IBD probabilities were estimated by usingSOLAR. The whole genome linkage scan results are shownin Figure 2. For 211518_s_at, neither the SQTL nor thestandard VC approaches detected any linkage signals.Linkage scans of 204695_at and 202982_s_at demon-strate that the standard VC approach is sensitive to non-normality and outliers and may obtain false-positiveresults. The standard VC approach fails to detect the eQTLon chromosome 1 identified by SQTL for 202950_at. ThisHistograms showing distributions of four non-normally distributed expression phenotypesFigure 1Histograms showing distributions of four non-normally distributed expression phenotypes.211518_s_atFrequency0204060801002 4 6 8 10204695_atFrequency01030504 5 6 7 8 9 10202982_s_atFrequency0204060803 4 5 6 7 8 9202950_atFrequency02040606 7 8 9 10 11 12Table 2: Summary statistics of four non-normally distributed expression phenotypesGene Mininum Mean SD Maximum Skewness Kurtosis p-Value of Shapiro test211518_s_at 2.10 3.50 1.06 9.13 2.59 8.47 3.3 × 10-17204695_at 4.21 8.44 0.94 9.79 -1.82 3.95 1.7 × 10-13202982_s_at 3.20 7.98 0.68 9.19 -3.25 18.89 2.7 × 10-16202950_at 5.99 10.62 0.59 11.80 -2.67 19.16 3.3 × 10-13Page 4 of 6(page number not for citation purposes)BMC Proceedings 2007, 1(Suppl 1):S83 http://www.biomedcentral.com/1753-6561/1/S1/S83finding may reflect the fact that SQTL tends to be morepowerful than the standard VC QTL mapping method inthe presence of non-normally distributed data or outliers.DiscussionIn this work, we applied the robust and powerful SQTLmethod to gene expression data and applied an efficientMonte Carlo procedure to account for multiple testingand to assess the genome-wide significance level. With theapplication to the GAW15 data, we detected many moreeQTLs and hotspots at stringent genome-wide signifi-cance levels than Morley et al. [4]. Our new findings maybe attributable to four factors. First, Morley et al. utilizedonly the data of siblings and much information from theparents and grandparents were missing, whereas the SQTLis applicable to arbitrary pedigrees. Second, in the contextof VC analysis, SQTL tends to be more powerful than theregression-based methods including the one used in Mor-ley et al.; see Diao and Lin [3]. Third, the SQTL approachis rank-based and tends to be more powerful than its par-ametric counterpart in the presence of nonnormal traits oroutliers. Finally, the procedure used in Morley et al. toadjust for multiple testing is overly conservative.The Monte-Carlo approach described in this work adjustsfor multiple testing across the genome. It would be desir-able to develop an efficient procedure to account for mul-tiplicities across the genome and multiplicities across geneLOD score plots for four non-normally distributed expression phenotypes: SQTL (red solid) and standard VC approach (black solid)Figure 2LOD score plots for four non-normally distributed expression phenotypes: SQTL (red solid) and standard VC approach (black solid).0.00.20.40.60.8211518_s_atChromosomesLOD Score0.01.02.03.0204695_atChromosomesLOD Score0.01.02.03.00.00.20.40.60.80.01.02.03.0202982_s_atChromosomesLOD Score0.01.02.0202950_atChromosomesLOD Score0.01.02.03.00.01.02.0Page 5 of 6(page number not for citation purposes)BMC Proceedings 2007, 1(Suppl 1):S83 http://www.biomedcentral.com/1753-6561/1/S1/S83expressions simultaneously. Furthermore, the Monte-Carlo approach requires a large sample size in order toaccurately approximate the joint distribution of the teststatistics. Previous simulation studies demonstrated thatthe Monte-Carlo approach performed well for sample sizeas small as 50 pedigrees (results not shown). Futureresearch is needed in evaluating the performance of theMonte-Carlo approach in small sample size situations.With the availability of the abundance of SNPs, it is desir-able to perform genome-wide association analysis ofexpression quantitative traits following genome-widelinkage analysis. We are currently extending the semipar-ametric quantitative transmission-disequilibrium test [8]to the genome-wide association analysis of expressiondata.Competing interestsThe author(s) declare that they have no competing inter-ests.AcknowledgementsThis research was supported by the National Institutes of Health grant R01 CA082659.This article has been published as part of BMC Proceedings Volume 1 Sup-plement 1, 2007: Genetic Analysis Workshop 15: Gene Expression Analysis and Approaches to Detecting Multiple Functional Loci. The full contents of the supplement are available online at http://www.biomedcentral.com/1753-6561/1?issue=S1.References1. Almasy L, Blangero J: Multipoint quantitative-trait linkage anal-ysis in general pedigrees.  Am J Hum Genet 1998, 62:1198-1211.2. Abecasis GR, Cherny SS, Cookson WO, Cardon LR: Merlin-rapidanalysis of dense genetic maps using sparse gene flow trees.Nat Genet 2002, 30:97-101.3. Diao G, Lin DY: A powerful and robust method for mappingquantitative trait loci in general pedigrees.  Am J Hum Genet2005, 77:97-111.4. Morley M, Molony CM, Weber TM, Devlin JL, Ewens KG, SpielmanRS, Cheung VG: Genetic analysis of genome-wide variation inhuman gene expression.  Nature 2004, 430:743-747.5. Carlborg O, De Koning DJ, Manly KF, Chesler E, Williams RW, HaleyCS: Methodological aspects of the genetic dissection of geneexpression.  Bioinformatics 2005, 21:2383-2393.6. Lin DY, Zou F: Assessing genomewide statistical significance inlinkage studies.  Genet Epidemiol 2004, 27:202-214.7. Lin DY: An efficient Monte Carlo approaches to assessing sta-tistical significance in genomic studies.  Bioinformatics 2005,21:781-787.8. Diao G, Lin DY: Improving the power of association tests forquantitative traits in family studies.  Genet Epidemiol 2006,30:301-313.Page 6 of 6(page number not for citation purposes)

Semiparametric methods for genome-wide linkage analysis of human gene expression data

A powerful and robust method for mapping quantitative trait loci in general pedigrees.

An efficient Monte Carlo approaches to assessing statistical significance in genomic studies. Bioinformatics

Assessing genomewide statistical significance in linkage studies. Genet Epidemiol

Cheung VG: Genetic analysis of genome-wide variation in human gene expression. Nature

CS: Methodological aspects of the genetic dissection of gene expression. Bioinformatics

Improving the power of association tests for quantitative traits in family studies. Genet Epidemiol

LR: Merlin-rapid analysis of dense genetic maps using sparse gene flow trees. Nat Genet

Multipoint quantitative-trait linkage analysis in general pedigrees.

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Semiparametric methods for genome-wide linkage analysis of human gene expression data

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