Group 6: Pleiotropy and Multivariate Analysis

Peter Kraft1n and Mariza de Andrade2

1Department of Biostatistics, University of California at Los Angeles, Los Angeles, California2Department of Health Sciences Research, Mayo Clinic, Rochester, Minnesota

Analysis techniques using data on several traits simultaneously allow researchers to dissect the genetic architectureaffecting correlated traits, and can increase the power to detect pleiotropic genes, i.e., genes that influence two or moretraits. Several of the papers in this group from Genetic Analysis Workshop 13 presented promising univariate summaries ofmultiple traits that detected linkage signals that standard single-trait univariate methods did not. Other papers foundlinkage signals using multivariate techniques that univariate techniques missed, although this was not uniformly the case.Some papers also considered the correlation among measurements of a single trait taken at different ages to assess whetherthe genetic architecture of the trait changed over age. Applications of the Framingham Heart Study data identified majorloci jointly influencing body mass index and high-density lipoprotein cholesterol, high-density lipoprotein cholesterol andtriglycerides, total cholesterol and triglycerides, and various combinations of four traits involved in metabolic syndrome.Genet Epidemiol 25 (Suppl. 1):S50–S56, 2003. & 2003 Wiley-Liss, Inc.

Key words: variance components; principal components; longitudinal data

nCorrespondence to: Peter Kraft, Ph.D., UCLA School of Public Health, Box 951772, Los Angeles, CA 90095-1772. E-mail: pkraft@ucla.eduPublished online in Wiley InterScience (www.interscience.wiley.com)DOI: 10.1002/gepi.10284

INTRODUCTION

There are several advantages to using multiplecorrelated traits simultaneously in genetic ana-lyses. First, if the correlation among traits is dueat least in part to a shared gene or suite of genes,analyses that use all of the available traits may bemore powerful than several analyses using eachtrait separately [Allison et al., 1998; Amos et al.,2001; Boomsma and Dolan, 1998]. Second, re-searchers may be intrinsically interested in thegenetic correlation among traits: how large is it? Isit due to pleitropy (i.e., shared genes) or coin-cident linkage?Of the 11 papers summarized here, all but one

addressed the first issue (does consideration ofseveral correlated traits increase power?), andseveral addressed the second (dissecting thegenetics of correlated traits). Depending on theirprincipal focus, they adopted various analyticstrategies.One strategy involved calculating a new,

derived phenotype, which was then analyzedusing univariate techniques. For example, Liuet al. [2003] separately analyzed principalcomponents derived from six traits, including

triglycerides (TG) and high-density lipoprotein(HDL) cholesterol. They compared this approachwith analyzing the individual component traits ora priori combinations (such as the ratio of TG toHDL cholesterol). Other derived traits includedthe area under the curve for longitudinal mea-surements [Pankratz et al., 2003] and estimatedbreeding values [Zabaneh and Mackay, 2003].A second strategy involved modeling the joint

density for several traits. Unlike the previousapproach, this allowed researchers to estimate theproportion of genetic correlation due to commongenes and test the hypothesis of pleitropy vs.coincident linkage [Almasy et al., 1997]. However,joint analysis required stronger modeling assump-tions. The power of this approach relative tounivariate analyses or simple derived phenotypeanalyses (e.g., the sum of several traits) dependson the magnitude and direction of the sharedgenetic and environmental correlations amongtraits [Allison et al., 1998; Amos et al., 2001;Evans, 2002]. The papers by Arya et al. [2003],Havill and Mahaney [2003], Kraft et al. [2003],Olswold and de Andrade [2003], and Zhang andWang [2003] took this approach; the latter applieda novel score test.

Genetic Epidemiology 25 (Supplement 1): S50–S56 (2003)

& 2003 Wiley-Liss, Inc.

Most of the papers used the variance-compo-nents (VC) approach to estimate the proportion oftrait variance due to shared genes or to conductquantitative trait linkage analysis. The VCapproach is described elsewhere in detail fortwo-point [Amos, 1994; de Andrade et al., 1999]and multipoint [Almasy and Blangero, 1998]analysis and for multivariate traits [Almasyet al., 1997; de Andrade et al., 1997; Iturria andBlangero, 2000; Lange and Boehnke, 1983].Aside from providing researchers with data on

a wide variety of traits (e.g., systolic bloodpressure, body mass index (BMI), TG, or HDLcholesterol), the Framingham Heart Study (FHS)also provided the opportunity to study long-itudinal trends, because many of these traits weremeasured at different time points on the sameindividuals. Considering the repeated measure-ments as multiple traits leads to similar questionsas with distinct traits. Are analyses that takemeasurements at several time points into accountmore powerful than those that use only one? Doesthe same set of genes influence a trait at differenttimes, e.g., at younger or older ages?

Our papers again took several differentapproaches to longitudinal data, as shown inFigure 1. Some considered cross-sectional data onmultiple traits taken at one point in calendar timeor biological age [Arya et al., 2003; Havill andMahaney, 2003; Liu et al., 2003]. Others con-structed aggregate measurements for each of theseveral traits they considered, e.g., by taking theaverage over repeated measurements for anindividual [Olswold and de Andrade, 2003;Pankratz et al., 2003; Ulgen et al., 2003; Zabanehand Mackay, 2003; Zhang and Wang, 2003].Two papers considered treating the repeated

measures on a single biological trait as multipletraits, e.g., systolic blood pressure at age 30 andsystolic blood pressure at age 60 [Havill andMahaney, 2003; Kraft et al., 2003]. This approachcan answer the question of whether similar genesinfluence a trait at different ages. This is a relevantconcern, as illustrated by a segregation study byPerusse et al. [1991], which suggested that bloodpressure is influenced by a major gene with age-dependent effects. Animal studies also found thatdifferent genes can influence a trait at different

Fig. 1. Schematic representing four approaches to longitudinal data described in text. Approach I is cross-sectional analysis. Approach

II uses repeated measures on each trait to form a single, aggregate statistic for each. Approach III treats each measurement of a single

biological trait separately, yielding multiple ‘‘traits,’’ one for each measurement time point. Approach IV considers multiple traitsmeasured at multiple time points.

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ages [Cheverud et al., 1996]. Taking lifetimeaverages may mask such effects.The last approach considered several traits

simultaneously at different time points. Havilland Mahaney [2003], for example, comparedseparate bivariate analyses using measurementsfrom two cross-sectional samples taken at differ-ent ages. They found evidence that the geneticrelationship between systolic blood pressure andtotal cholesterol differs between the fourth andsixth decades of life. The correlation betweenmultiple traits and multiple measurements canalso be jointly modeled, as discussed in Blangero[1993]. However, none of the papers took thisapproach.We summarize the 11 papers contributed by

Group 6 in Table I. All papers except one includedsome form of linkage analysis. The methodologiesused were diverse. Eight papers analyzed FHSdata, and four papers analyzed the simulateddata. We discuss the methods and results for eachpaper below, grouped according to how theyhandled longitudinal data. The first group, Sum-mary Across Time, consists of five papers thatanalyzed multiple traits across time. The secondgroup, Cross-Sectional, consists of four papersthat analyzed multiple traits at a particular timepoint. The third group, Longitudinal, consists oftwo papers that analyzed one trait at several timepoints.

SUMMARY ACROSS TIME

The first paper, by Olswold and de Andrade[2003], sought to localize pleiotropic genes in-volved in metabolic syndrome. This syndrome is

identified clinically by the presence of three ormore of these five characteristics: larger waistcircumference, higher TG levels, lower HDL-cholesterol concentrations, hypertension, and im-paired fasting glucose. Since waist circumferencewas not available on the FHS, all four sets of threeof the available variables were used in theanalysis. Since most of these variables, except forTG, were measured at several time points, theresiduals from the regression-adjustment ap-proach described in Levy et al. [2000] for thesevariables were used as quantitative traits in themultivariate genome-wide linkage analysis forquantitative traits. This approach averages traitsand covariates over a fixed age interval (25–75years in the case of Levy et al. [2000]), and thenregresses the averaged trait on the averagedcovariates. The expectation maximization (EM)-VC method was applied to fit a multivariatevariance-components model [Iturria and Blan-gero, 2000]. Olswold and Andrade [2003] foundstrong evidence for linkage on chromosomes 2, 5,and 6 for several trivariate combinations of traits,with P o 0.0001, and concluded that multivariatelinkage analysis increases the power to detect aquantitative trait locus when there is small tomoderate genetic correlation.The second paper, by Pankratz et al. [2003], used

the complete genotypic and phenotypic data fromReplicate 1 of the simulated data without knowl-edge of the underlying model (i.e., neither thenumber of genes nor their locations were knownbeforehand). To maximize the information forlinkage, they utilized the repeated longitudinalmeasurements to compute the average area underthe curve for seven traits (BMI, total cholesterol,fasting glucose levels, HDL cholesterol, height,

TABLE I. Summary of data sets and analytic approaches used by Group 6

Data set Lead author Cohorts Replicate Traita Markers Analysis approachb Softwarec

Framingham Olswold 1, 2 N/A Several All Multivariate VC linkage EMVCUlgen 1, 2 N/A Several All VC linkage MERLINArya 1, 2 N/A BMI, HDL All VC linkage SOLARHavill 1, 2 N/A Several All VC linkage SOLARKraft 1, 2 N/A SBP, HBP All Multivariate VC linkage SIMWALK, FISHERLiu 1, 2 N/A Several All VC linkage SOLARZhang 1, 2 N/A TG, TC All VC linkage OwnStassen 1, 2 N/A HBP All Adaptive clustering procedure Own

Simulated Zabaneh 1, 2 1 TRIG All Estimated breeding values, PC GENSTAT, VCE, MERLINPankratz 1, 2 1 AUC All VC linkage SOLARBensen 1, 2 57 Several All PC, VC linkage SAS, SOLAR

aPrimary trait(s) analyzed. AUC, area under curve. See individual papers for further descriptions of additional traits.bVC, variance components; HE, Haseman-Elston; PC, principal components.cSee individual papers for further descriptions of software programs and references.

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systolic blood pressure, and TG). They then usedthese derived traits as the quantitative traits inseparate univariate VC linkage analyses. Theyidentified 10 genes with major to moderateeffects, and identified no false-positive results.The third paper, by Ulgen et al. [2003], analyzed

the FHS data to address the question of whetherstatistical correlation among quantitative traitsleads to correlation of linkage analysis results ofthese traits. Three quantitative traits (total choles-terol, HDL cholesterol, and TG), and one derivedquantitative trait (total cholesterol divided byHDL cholesterol), were used for linkage analysis.They concluded that even though two traits mightbe correlated, their LOD scores need not be.A LOD peak at a given location for one trait doesnot imply that the other trait has a LOD peak atthat location.The fourth paper, by Zabaneh and Mackay

[2003], explored the merit of using estimatedbreeding values (EBVs) as the quantitative traitin a genome-wide scan. EBVs were developed foruse in animal breeding and are equivalent to‘‘sigma squared A random effects,’’ i.e., estimatesof individual-level random effects from a VCmodel (multivariate, in this case) reflecting theadditive effects of genes not included in the fixedcomponents of the model [Palmer et al., 2001]. Themotivation was to improve the precision ofmeasurement of the primary trait by removingany environmental correlation with the othertraits, while including the effect of any geneticcorrelation. They used fasting TG levels fromReplicate 1 of the simulated data as the primarytrait. Breeding values were estimated using thebest linear unbiased prediction as implemented inVCE [Neumaier and Groeneveld, 1998], andmultipoint linkage analysis was performed usingMERLIN [Abecasis et al., 2002]. Their genome-wide scan results from the EBV traits were thencompared with a second set of TG-derived traitsdetermined by principal-components analysis.They found a precise correspondence betweengene location and high LOD score when usingEBV traits, and concluded that estimating breed-ing values could provide a suitable method ofderiving traits. However, the consequence ofusing EBV traits on type I and type II error ratesremains to be investigated. Only one slope gene(of four in the model) was found, suggesting thatthe method may miss some real effects.The fifth paper, by Zhang and Wang [2003],

performed a bivariate linkage analysis on choles-terol and TG levels in the FHS using sib-pair

analysis. A new score statistic was used instead ofthe usual likelihood-ratio statistic. With this newtest, they found significant evidence for linkageon chromosome 7, suggesting a pleiotropic geneticeffect; however, this significant evidence oflinkage was due primarily to TG levels.Stassen et al. [2003] screened for gene� gene

interactions underlying hypertension, using af-fected sib pairs (defined on the basis of anydiagnosis of hypertension or hypertension treat-ment) and parent-offspring pairs. They calculatedsimilarity scores for pairs of subjects based on allpairwise combinations of 40 10-marker segmentscovering the genome, and tested for differencesbetween sib-sib similarities and parent-offspringsimilarities. They reported several signals whichwere consistent across subpopulations identifiedby clustering subjects on the basis of 20 highlyvariable markers [Stassen et al., 2003]. Althoughthey did not investigate pleiotropy or multipletraits, their approach can be extended to accountfor multiple traits by correlating multivariatephenotypes and genotypes (H. Stassen, personalcommunication).

CROSS-SECTIONAL ANALYSES

The three cross-sectional analyses focused ondissecting the shared genetics of highly correlatedrisk factors for cardiovascular disease. Two [Aryaet al., 2003; Liu et al., 2003] used data collected(mostly) at exams 10–12 in the original FHS cohort(corresponding to the years 1969–1971) and atexam 1 (1971–1973) in the offspring cohort. Thiswas done to match the observations on calendartime, and because TG levels were only measuredonce (at exams 10–12) in the original cohort. Thethird [Bensen et al., 2003] used data from exams 11and 1 for the first and second simulated cohorts,respectively.Arya et al. [2003] examined obesity and HDL

cholesterol levels, which are inversely correlatedand thought to be at least partly under the controlof a common set of genes. They conducted abivariate linkage analysis and identified a locuson chromosome 6 near marker DS6S1009 influen-cing both traits. Univariate analyses found sug-gestive evidence for linkage in the same region,but the bivariate analysis provided strongerevidence (maximum LOD¼6.2 for the bivariateanalysis, vs. 3.9 and 2.7 for univariate analyses).Furthermore, the bivariate model allowed them totest whether these results were due to pleiotropy

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or coincident linkage. They found significantevidence for a QTL with pleiotropic effects, whichappears to influence both BMI and HDL-Cphenotypes.Liu et al. [2003] used principal-component

factor analysis to construct factors capturing thecorrelation among six traits in the FHS data: BMI,systolic blood pressure, TG, total cholesterol, HDLcholesterol, and glucose levels. They analyzed thefirst three principal components separately ascontinuous traits, using standard VC linkagemodels. They compared these results to analysesof the component traits (e.g., BMI, glucose levels)and various lipid ratios (e.g., TG:HDL).They found no suggestive linkage results

(LOD 42) for the first principal component (acombination of BMI, glucose, and blood pressuremeasurements). However, they found two sug-gestive LOD scores for the second principalcomponent (made up of TG and HDL cholesterol),and three suggestive LODs for the third principalcomponent (TG and total cholesterol). The lociwith suggestive evidence of linkage for the secondfactor also had suggestive evidence of linkage forat least one of the component traits.Use of the TG-total cholesterol factor identified

two loci with suggestive evidence of linkage thatthe component traits did not. This suggests thatprincipal-component factor analysis can helpdissect the genetic basis of tightly correlated traits.As Liu at al. [2003] noted, there are concerns withthis approach, e.g., the choice of component traits.Traits should be chosen on the basis of known orhypothesized genetic relationships; a ‘‘fishingexpedition’’ should be avoided.Bensen et al. [2003] applied principal-compo-

nent analysis to six quantitative traits from thesimulated data: total cholesterol, TG, HDLcholesterol, low-density lipoprotein cholesterol,systolic blood pressure, and BMI. In contrast toLiu et al. [2003], they found no suggestive linkagesignals using the principal components. Theyhypothesized that this was likely due to theiromission of a key component of the simulatedpleiotropic trait (glucose) from the principal-component analysis.

LONGITUDINAL ANALYSES

The two longitudinal analyses considered traitsmeasured at two roughly equivalent time pointson the scale of biological age: the fourth and sixthdecades of life. Havill and Mahaney [2003] created

two cross-sectional samples. The first consisted ofall subjects between ages 30–39 years at a givenexamination; the second consisted of all subjectsbetween ages 50–59 years at an examinationroughly 20 years after the first. They formed alongitudinal sample by intersecting these twocross-sectional samples. Thus the data at eachtime point consisted of a single measurement(exam) for each subject; the longitudinal sampleconsisted of subjects who were measured (aliveand on study) at both exams. Kraft et al. [2003]constructed age-specific systolic blood pressuretraits by averaging over set time intervals (e.g.,35–50 years, 50–65 years). Subjects contributed tothe analysis even if they were only measuredfor one of the time periods. Both papers conductedlongitudinal analyses using multivariate VCanalysis.Havill and Mahaney [2003] analyzed three

traits: total cholesterol, systolic blood pressure,and weight. Using each of the cross-sectionalsamples, they estimated the proportion of additivegenetic variance due to shared genes for each traitpair, as well as the proportion of environmentalvariance due to shared environment. Interestingly,they showed that the patterns of shared geneticeffects differed between the two age classes. Forexample, the shared additive genetic effects forsystolic blood pressure and total cholesterolincreased greatly from the younger to the oldersample.Using the longitudinal sample, Havill and

Mahaney [2003] estimated the genetic and envir-onmental correlations between the younger andolder measurements for each trait. They did notfind evidence that the genes that influencedweight or total cholesterol differed between thetwo age ranges, but they did find such evidencefor systolic blood pressure. They estimated that atleast 96% of the additive genetic variance inweight was due to shared genes; the correspond-ing proportion for total cholesterol was at least57%, and that for systolic blood pressure was 20%.Kraft et al. [2003] only analyzed systolic blood

pressure, but they analyzed as many as fourseparate age classes simultaneously. They alsofound evidence that different genes influenceblood pressure at different ages. They estimatedthat 82% of the additive genetic variance forsystolic blood pressure in the two age ranges35–50 and 50–65 years was due to shared genes;that figure dropped to 22% for the age ranges 0–35and 50–65 years. Kraft et al. [2003] also carried outunivariate and bivariate linkage analyses. They

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found linkage signals on chromosome 17, consis-tent with an earlier report [Levy et al., 2000]. Thebivariate analysis did not noticeably increasepower over univariate analyses. This likely reflectsthe fact that when traits are strongly positivelycorrelated, univariate analyses are more powerful[Amos et al., 2001]. This may also explain why theapproach of averaging systolic blood pressuremeasures taken in Levy et al. [2000] performedbetter than multivariate analysis in this case.In contrast to this approach, which defined

traits based on the Framingham subjects’ biologi-cal age, de Andrade and Olswold [2003] definedtraits based on calendar time (exam number).They failed to replicate the linkage signal onchromosome 17. This is consistent with the resultsof Mathias et al. [2003], who found that age-matched analyses of systolic blood pressure fromthe FHS produced higher estimates of heritabilitythan calendar-year-matched analyses. This sug-gests that care should be taken when definingtraits in a longitudinal analysis, depending onwhether a gene� age interaction or gene� calendar time (environment) interaction is morerelevant.

DISCUSSION

The papers in this group took various ap-proaches to dissecting the genetics underlyingmultiple correlated traits. Several presented pro-mising measures summarizing several traits thatproduced linkage signals where standard univari-ate methods did not. These included novelmeasures such as the area under the curve forlongitudinal traits [Pankratz et al., 2003] andestimated breeding values [Zabaneh and Mackay,2003], as well as principal-components analysis[Liu et al., 2003]. The success of the latter approachvaried according to the choice of traits included inthe principal-components analysis [Bensen et al.,2003]. Other papers found linkage signals usingmultivariate techniques that univariate techniquesmissed [Arya et al., 2003; Olswold and deAndrade, 2003], although this was not uniformlythe case [Kraft et al., 2003; Zhang and Wang, 2003].This is consistent with previous results showingthat multivariate linkage techniques can be morepowerful than univariate techniques in somesituations, but not in others [Amos et al., 2001].Applications to the Framingham Heart Study

identified major loci jointly influencing BMI andHDL cholesterol [Arya et al., 2003], HDL choles-

terol and TG [Liu et al., 2003; Zhang and Wang,2003], total cholesterol and TG [Liu et al., 2003],and various combinations of the four traitsinvolved in metabolic syndrome [Olswold andde Andrade, 2003]. Independent bivariate andunivariate analyses of BMI and HDL cholesterolimplicated a region on chromosome 6 near markerD6S1009 as harboring a gene influencing thesetraits [Arya et al., 2003; Liu et al., 2003]. This isconsistent with previous reports [Atwood et al.,2002]. Bivariate analysis of HDL cholesterol andTG provided evidence for a gene influencing bothtraits near marker GATA112F07 on chromosome 7.This is also consistent with a previous analysis ofthese traits in the FHS [Shearman et al., 2000].

ACKNOWLEDGMENTS

The authors thank all the authors of Group 6who contributed papers, and the reviewers fortheir helpful comments.

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