We examine a Bayesian Markov-chain Monte Carlo framework for simultaneous segregation and linkage analysis in the simulated single-nucleotide polymorphism data provided for Genetic Analysis Workshop 16. We conducted linkage only, linkage and association, and association only tests under this framework. We also compared these results with variance-component linkage analysis and regression analyses. The results indicate that the method shows some promise, but finding genes that have very small (<0.1%) contributions to trait variance may require additional sources of information. All methods examined fared poorly for the smallest in the simulated "polygene" range (h(2 )of 0.0015 to 0.0002)

Borecki, Ingrid

Czajkowski, Jacek

Daw, E Warwick

Feitosa, Mary

Gao, Xiaoyi

Ma, Duanduan

Plunkett, Jevon

Province, Michael A

Van Brunt, Andrew

PubMed

Digital Commons@Becker

Washington University School of MedicineDigital Commons@BeckerOpen Access Publications2009A framework for analyzing both linkage andassociation: An analysis of Genetic AnalysisWorkshop 16 simulated dataE Warwick DawWashington University School of Medicine in St. LouisJevon PlunkettWashington University School of Medicine in St. LouisMary FeitosaWashington University School of Medicine in St. LouisXiaoyi GaoWashington University School of Medicine in St. LouisAndrew Van BruntWashington University School of Medicine in St. LouisSee next page for additional authorsFollow this and additional works at: http://digitalcommons.wustl.edu/open_access_pubsPart of the Medicine and Health Sciences CommonsThis Open Access Publication is brought to you for free and open access by Digital Commons@Becker. It has been accepted for inclusion in OpenAccess Publications by an authorized administrator of Digital Commons@Becker. For more information, please contact engeszer@wustl.edu.Recommended CitationDaw, E Warwick; Plunkett, Jevon; Feitosa, Mary; Gao, Xiaoyi; Van Brunt, Andrew; Ma, Duanduan; Czajkowski, Jacek; Province,Michael A.; and Borecki, Ingrid, ,"A framework for analyzing both linkage and association: An analysis of Genetic Analysis Workshop16 simulated data." BMC Proceedings.3,Suppl 7. S98. (2009).http://digitalcommons.wustl.edu/open_access_pubs/283AuthorsE Warwick Daw, Jevon Plunkett, Mary Feitosa, Xiaoyi Gao, Andrew Van Brunt, Duanduan Ma, JacekCzajkowski, Michael A. Province, and Ingrid BoreckiThis open access publication is available at Digital Commons@Becker: http://digitalcommons.wustl.edu/open_access_pubs/283BMC ProceedingsProceedingsA framework for analyzing both linkage and association: an analysisof Genetic Analysis Workshop 16 simulated dataE Warwick Daw*, Jevon Plunkett, Mary Feitosa, Xiaoyi Gao,Andrew Van Brunt, Duanduan Ma, Jacek Czajkowski, Michael A Provinceand Ingrid BoreckiAddress: Division of Statistical Genomics, Washington University School of Medicine, 4444 Forest Park Boulevard, Campus Box 8506, St. Louis,Missouri 63108 USAE-mail: E Warwick Daw* - warwick@wustl.edu; Jevon Plunkett - jevon.plunkett@gmail.com; Mary Feitosa - mfeitosa@wustl.edu;Xiaoyi Gao - xgao23@wustl.edu; Andrew Van Brunt - andrew@dsgmail.wustl.edu; Duanduan Ma - duan@dsgmail.wustl.edu;Jacek Czajkowski - jake@dsgmail.wustl.edu; Michael A Province - mprovince@wustl.edu; Ingrid Borecki - ingrid@dsgmail.wustl.edu*Corresponding authorfrom Genetic Analysis Workshop 16St Louis, MO, USA 17-20 September 2009Published: 15 December 2009BMC Proceedings 2009, 3(Suppl 7):S98 doi: 10.1186/1753-6561-3-S7-S98This article is available from: http://www.biomedcentral.com/1753-6561/3/S7/S98© 2009 Daw et al; 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.AbstractWe examine a Bayesian Markov-chain Monte Carlo framework for simultaneous segregation andlinkage analysis in the simulated single-nucleotide polymorphism data provided for Genetic AnalysisWorkshop 16. We conducted linkage only, linkage and association, and association only tests underthis framework. We also compared these results with variance-component linkage analysis andregression analyses. The results indicate that the method shows some promise, but finding genesthat have very small (<0.1%) contributions to trait variance may require additional sources ofinformation. All methods examined fared poorly for the smallest in the simulated “polygene” range(h2 of 0.0015 to 0.0002).BackgroundBoth linkage analysis and association analysis provideuseful, but slightly different, forms of information inidentifying genetic contributions to complex traits.Frequently, either one or the other type of analysis isemployed, which can result in information being over-looked: linkage does not account for the associationfrequently seen between disease alleles and nearbymarkers, while association (on family data) may accountfor family structure, but does not make use of thelocation information that the meiotic events provide.When both are used, the analyses are typically doneunder different frameworks. Here, we consider anintegrated analysis of both linkage and associationunder an oligogenic model [1] and compare it with alinkage method and an association method.DataFor Genetic Analysis Workshop (GAW) 16, a simulateddata set was provided based on the Framingham HeartPage 1 of 6(page number not for citation purposes)BioMed CentralOpen AccessStudy. Multiple replicates of the simulation were pro-vided to help assess methods and we used several of thesereplicates for this purpose. This simulation used~550,000 single-nucleotide polymorphisms (SNPs)(GeneChip® Human Mapping 500 k Array Set and the50 k Human Gene Focused Panel) from actual Framing-ham data, also provided to GAW16. Traits were simulatedon to these SNPs by selecting several SNPs as oligogenes(h2 of 0.01 to 0.001) and 1000 SNPs as polygenes (h2 of0.0015 to 0.0002) for each trait. Some of the “polygenes”have effects as large as those of the “oligogenes.” As in realdata, the boundary between the two is fuzzy. Thepolygenes were selected more randomly, although somewere selected as clusters. We focused our analysis onchromosome 11 and simulated low-density lipoprotein(LDL) and high-density lipoprotein (HDL) at the firstvisit. For linkage, we selected two subsets of 1-cM spacedmarkers with a simple algorithm that traversed thechromosome at 1-cM distances given two starting points.Linkage information is captured almost completely bymarkers at this density. Thus, adding additional markersonly provides a marginal increase in information, whileincreasing the computational burden [2]. We selected twosubsets to control for both potential tight associationsbetween markers and trait genes and for the potentialeffects of undetected typing error. We examined ourability to identify both oligogenes and polygenes,including clusters of polygenes, and in particular, ifthere is any benefit to conducting linkage and associationanalysis in a common framework.MethodsWe used Markov-chain Monte Carlo (MCMC) methodsto produce Bayesian statistics for segregation, linkage,and association. These methods are implemented in thecomputer program Loki [1]. Covariate effects are alsoestimated, and the trait model is given by:y X Q S ei i j jjlik= + + + +==∑∑μ β α γ11, (1)where μ is the “reference” trait value, X is the incidencematrix for covariate effects, b is the vector of covariateeffects, Qi is the incidence matrix for the effects ofquantitative trait locus (QTL) i, ai is the vector of effectsfor QTL i, e is the normally distributed residual effect, k isthe number of QTLs currently estimated (k ≥ 0), Sj is theincidence matrix for the effects of SNP j, gj is the vector ofeffects for SNP j, and l is the number of SNPs beingtested for association in the analysis run. The MCMCprocess samples μ, b, ai, gj, i, and e as well as parameterssuch as unobserved marker genotypes and QTL geneticposition. All of these parameters are sampled from thespace of model values consistent with the data observed.Values are sampled proportional to their posteriorprobability. After the number of sampling iterations issufficiently large, the sampled values provide an estimateof the posterior probability distribution over the para-meter space. The difference between this and previousapplications of the method is in the number of SNPs wetest. Previously, we have included select candidate genesas genetic covariates. Here we will test all the SNPsavailable on chromosome 11 for association with thismethod to examine how the method scales up togenome-wide association testing.Initially, LDL was analyzed with the two 1-cM SNPsubsets for linkage only (l = 0). Subsequently, singleSNPs and sets of SNPs were added to test forassociation. When testing SNPs for association, weconsidered 1) z-scores for each of the elements of gjbeing non-zero, which assessed the strength of theassociation, and 2) whether adding SNP j reduced anylinkage signal found in the region, which indicated thatSNP j was associated with the mutation causing thelinkage signal. If a single SNP in a region producedthe linkage signal, including it for association testingshould eliminate the linkage peak, by moving the effectfrom the segregation term ( Qi iik α=∑1) to the associationterm ( S j jjl γ=∑1). Genetic effects in the segregation termwere tested for linage to the included markers. Geneticeffects in the association term were those of typed genesand thus not reflected in the linkage signal. Even whennot testing for linkage, including the segregation termcould improve association testing as a result of allowingexplicit modeling of the effects of loci other than theone tested. To examine this hypothesis, we conductedanalysis runs with only one SNP for all ~26,000 SNPson chromosome 11.To evaluate evidence for linkage, we used Bayesian“L-scores” estimated over 1-cM bins along the chromo-somes. An L-score is simply the posterior probabilitydivided by the prior probability. In the absence of anydata, the posterior probability should be equal to theprior probability. Thus, a L-score of 1 indicated that thedata contained no information for or against linkage,while a L-score >1 indicated evidence for linkage.For comparison, we also conducted linkage analysis withthe computer program SOLAR, and association analysiswith a family-based test implemented with PROCMIXEDin the computer program SAS [3]. In addition, wecomputed r2 for age- and sex-adjusted HDL in 2-cMintervals, sliding 1 cM at a time across chromosome 11.BMC Proceedings 2009, 3(Suppl 7):S98 http://www.biomedcentral.com/1753-6561/3/S7/S98Page 2 of 6(page number not for citation purposes)For this regression analysis, we used PROC REG in SASwith forward selection and an inclusion threshold of 0.1for including a SNP in the regression. These r2 values givean indication of the strength of association in eachreplicate, whether due to causative loci or random chance.In particular, they provide an indicator of the predictiveinformation present for association present in the data.ResultsFirst, we compared the MCMC linkage L-scores with andwithout simultaneous association testing at most causa-tive SNPs (Figure 1). Some SNPs could not be placed onthe linkage map and so were excluded. The linkage scoreswere reduced, as expected, and 19 out of the 62 SNPshad association |z-scores| > 2. All of these SNPs were partof the simulation model, so ideally, we would like to seemore |z-scores| > 2. However, the small effects of someof these SNPs (with h2 < 0.001) led to insufficient power.These results indicate that this method can be useful incandidate gene studies.In comparison of the variance-component linkage resultsand MCMC oligogenic linkage, we found that within asimulated replicate for this data set, the two methodsproduce similar results (Figure 2). However, betweenreplicates, the locations in which the signals were founddiffered, sometimes markedly (Figure 3). This differenceholds for both linkage methods, so we included only theLOD plots, which are more familiar to most. We notethat the two different subsets of 1-cM distant SNPsproduced concordant linkage signals within the samereplicate (see yellow and gold lines in Figure 3). Thediscordance between replicates likely reflects thatalthough there were many signals on each chromosome,the power to map these signals, most with h2 < 0.001,was marginal and so different replicates may have haddifferent signal strength at different locations.To further explore between-replicate variation, we com-puted r2 explained within 2-cM intervals. In Figure 4, weshow these values (red), the LOD scores (black), and thelocations of the causative SNPs (green bars) for tworeplicates. There is variation in both the LOD and r2between replicates and neither seems to reflect theconcentration of SNPs around 110 cM. These resultssuggest that both linkage and association tests alonemight fare poorly within gene clusters with a multitude ofmutations with each h2 < 0.001.Finally, in single-SNP association tests under the MCMColigogenic model, ~1,700 out of ~26,000 SNPs had|z-scores| > 2. This is slightly greater than the 5% expectedunder the null hypothesis. With many simulated “causa-tive” SNPs, nearly all z-scores could be argued to be “near”a causative SNP, and thus there was no empirical null inthis data. These single-SNP tests were computationallyintensive, and probably not practical on a genome-widescale with current technology. There were some positivesignals here, so an alternate methodology may facilitatethese tests with dense SNPs. As currently implemented,these methods are best suited to combined linkage andcandidate gene association studies.DiscussionOligogenic analysis of combined linkage and candidategene association appears to work for genes with an h2 onFigure 1Associated SNPs account for linkage peaks. L-scoresfor MCMC oligogenic linkage analysis of LDL with (green)and without (red) simultaneous association testing at mostcausative SNPs. Including the causative SNPs reduces thelinkage signal in most regions.Figure 2Agreement between methods within replicate.Comparison of linkage results for simulated LDL at Visit 1,adjusted for age and sex, for L-scores from oligogenicsimultaneous segregation and linkage analysis (withoutassociation testing) and for LOD from variance-componentsmethods. Vertical scales are not comparable, but noteagreement of peak locations.BMC Proceedings 2009, 3(Suppl 7):S98 http://www.biomedcentral.com/1753-6561/3/S7/S98Page 3 of 6(page number not for citation purposes)the order of 0.01. We had issues detecting some of the“polygenes” in this simulation (h2 of 0.0015 to 0.0002),but all methods appear to lack power to detect thesmallest of these “polygene” effects. At the margin ofsuch effects, it is important to extract as much informa-tion from the data as possible and our motivation herewas to examine the benefits of combining both linkageand association.Here, we saw that there was some benefit to examiningboth types of information simultaneously. However, thelack of power to detect the very smallest “polygenes” iscause for concern. If the genes in this simulation are notunrealistically smaller than those that exist in real traits,these results suggest that many true positives could bedue to random reinforcing of true signals, and replica-tion will be difficult. It could be that the very smallesteffects in the simulation may be undetectable. Theresults of computed r2 explained in regression computedover 2-cM intervals are discouraging because of the poorcorrespondence between gene locations and r2 peaks.However, there does appear to be room for improve-ment.The methods used here, in their current state, are veryuseful for testing of candidate gene associations. Fullyincorporating genome-wide association study data willrequire algorithmic improvements. In particular, whilethere were many z-scores with an absolute value >2, theydo not survive multiple testing corrections at thegenome-wide association study level. Incorporatingadditional sources of information, such as that on genenetworks, might help with this issue. While our successhere was more limited than we hoped, incorporatinginformation from multiple sources in a single frameworkmay help detect marginal genetic signals.Figure 3Different signals in different replicates. LDL SOLAR linkage results. While several regions exhibited LOD > 1 in multiplereplicates, no region did so in all replicates.BMC Proceedings 2009, 3(Suppl 7):S98 http://www.biomedcentral.com/1753-6561/3/S7/S98Page 4 of 6(page number not for citation purposes)List of abbreviations usedGAW: Genetic Analysis Workshop; HDL: High-densitylipoprotein; LDL: Low-density lipoprotein; MCMC:Markov-chain Monte Carlo; QTL: Quantitative traitlocus; SNP: Single-nucleotide polymorphismCompeting interestsThe authors declare that they have no competinginterests.Authors’ contributionsEWD conceived and coordinated the study, participatedin its design, carried out the MCMC analyses, and draftedthe manuscript. JP performed the variance-componentlinkage analysis and plotted the results. MF participatedin the design and helped with the variance-componentlinkage. XG participated in the design. DM carried outthe association analysis. JC helped prepare the data anddesign algorithms for marker selection. MAP participatedin the design. IB participated in the design.AcknowledgementsThe Genetic Analysis Workshops are supported by NIH grant R01GM031575 from the National Institute of General Medical Sciences.This article has been published as part of BMC Proceedings Volume 3Supplement 7, 2009: Genetic Analysis Workshop 16. The full contents ofthe supplement are available online at http://www.biomedcentral.com/1753-6561/3?issue=S7.Figure 4Linkage and Association vs. gene locations. HDL Visit 1 adjusted for age and sex analyzed SOLAR and regressionanalyses in 2-cM wide windows (moving in 1-cM increments). In Replicate 1, no evidence for linkage was found. In Replicate 2,a LOD score > 2 at ~80 cM was found.BMC Proceedings 2009, 3(Suppl 7):S98 http://www.biomedcentral.com/1753-6561/3/S7/S98Page 5 of 6(page number not for citation purposes)References1. Heath SC:Markov chain Monte Carlo segregation and linkageanalysis for oligogenic models. Am J Hum Genet 1997,61:748–760.2. Daw EW, Heath SC and Lu Y: Single-nucleotide polymorphismversus microsatellite markers in a combined linkage andsegregation analysis of a quantitative trait. BMC Genet 2005,6(suppl 1):S32.3. Borecki IB and Province MA: Genetic and genomic discoveryusing family studies. Circulation 2008, 118:1057–1063.Publish with BioMed Central   and  every scientist can read your work free of charge"BioMed Central will be the most significant development for disseminating the results of biomedical research in our lifetime."Sir Paul Nurse, Cancer Research UKYour research papers will be:available free of charge to the entire biomedical communitypeer reviewed and published immediately upon acceptancecited in PubMed and archived on PubMed Central yours — you keep the copyrightSubmit your manuscript here:http://www.biomedcentral.com/info/publishing_adv.aspBioMedcentralBMC Proceedings 2009, 3(Suppl 7):S98 http://www.biomedcentral.com/1753-6561/3/S7/S98Page 6 of 6(page number not for citation purposes)

A framework for analyzing both linkage and association: An analysis of Genetic Analysis Workshop 16 simulated data

Genetic and genomic discovery using family studies. Circulation

SC: Markov chain Monte Carlo segregation and linkage analysis for oligogenic models.

Single-nucleotide polymorphism versus microsatellite markers in a combined linkage and segregation analysis of a quantitative trait.

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A framework for analyzing both linkage and association: An analysis of Genetic Analysis Workshop 16 simulated data

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