Genome-wide association analysis of GAW17 data using an empirical Bayes variable selection

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1 PROCEEDINGS Open Access Genome-wide ssocition nlysis of GAW7 dt using n empiricl Byes vrible selection Vitr Pungppong, Libo Wng, Ynzhu Lin, Dbo Zhng, Min Zhng * From Genetic Anlysis Workshop 7 Boston, MA, USA. 3-6 October 200 Abstrct Next-genertion sequencing technologies enble us to explore rre functionl vrints. However, most current sttisticl techniques re too underpowered to cpture signls of rre vrints in genome-wide ssocition studies. We propose supervised colescing of single-nucleotide polymorphisms to obtin gene-bsed mrkers tht cn stbly revel possible genetic effects relted to rre lleles. We use newly developed empiricl Byes vrible selection lgorithm to identify ssocitions between studied trits nd genetic mrkers. Using our novel method, we nlyzed the three continuous phenotypes in the GAW7 dt set cross 200 replictes, with intriguing results. Bckground With the dvent of next-genertion sequencing, rre vrints such s single-nucleotide polymorphisms (SNPs) with minor llele frequency (MAF) less thn 5% re getting more ttention in genome-wide ssocition studies (GWAS). Becuse of the smll vrince t locus with single rre llele, it is difficult to detect the llele s ssocition with the phenotype of interest. One pproch to tckling this problem is to collpse multiple rre SNPs within defined region nd tret them s single predictor in the model. Known genetic regions re used in the collpsing process to get gene-bsed mrkers. Penlized orthogonl-components regression (POCRE) [] is used to perform this tsk. Genome-wide ssocition studies re chllenged by the curse of dimensionlity ; tht is, lrge number of SNPs re genotyped (lrge p) fromsmllnumberof biologicl smples (smll n). As result, n incresing effort hs been devoted to selecting vribles in highdimensionl dt. One strtegy for deling with vrible selection is through the thresholding concept. Empiricl Byes thresholding [2,3] ws proposed to estimte sprse sequences observed in Gussin white noise. Here, we use the empiricl Byes thresholding method to select vribles in liner regressions with efficient * Correspondence: minzhng@purdue.edu Deprtment of Sttistics, Purdue University, West Lfyette, IN 47907, USA implementtion. Finl models re obtined by entering gene-bsed mrkers nd environmentl fctors possibly ssocited with the phenotype of interest. All nlyses re bsed on three continuous phenotypes in the GAW7 dt set cross 200 replictes. Methods Dt set The genome-wide ssocition of the three continuous phenotypes (Q, Q2, nd Q4) in the GAW7 dt set [4] ws investigted. All nlyses presented here re bsed on the genotype of 697 unrelted individuls. The genotype dt were recoded into counts of minor lleles using PLINK [5]. The other three trits (Age, Sex, nd Smoke) were used in the model to consider the environmentl effects. The nlyses were performed for ll 200 replictes. Supervised colescing of SNPs in genetic region The GAW7 dt consist of 3,205 utosoml genes with 24,487 SNPs, where only 3,32 SNPs (2.79%) hve MAF A lrge proportion of these rre vrints present chllenges for sttisticl nlyses to detect their ssocitions to phenotype of interest when these rre vrints re considered individully. Thus we use gene-bsed colescing method to collpse SNPs tht reside within the sme gene. Considering cusl gene, it is nturl to ssume tht not ll SNPs in the genetic 20 Pungppong et l; licensee BioMed Centrl Ltd. This is n open ccess rticle distributed under the terms of the Cretive Commons Attribution License ( which permits unrestricted use, distribution, nd reproduction in ny medium, provided the originl work is properly cited.

2 Pge 2 of 5 region re necessry to be cusl. Hence we used POCRE in the colescing process. Becuse POCRE cn chieve both vrible selection nd dimension reduction simultneously, it hs dvntges in grouping highly correlted predictors nd in giving dptive sprse liner combintions of the originl predictors. For the kth genetic region, consider regression model: l k k k, j k, j, j= Y = t + q X + x = k where l k is the number of SNPs residing in the kth gene, Y is n n-vector of phenotype, nd Xk X T T = ( k,,..., Xkl, ) k is design mtrix consisting of SNPs residing in the kth gene. Assume tht both Y nd X k re centrlized (τ k =0in Eq. ()). Strting with X X, POCRE sequentilly constructs components X m w m such tht X m is orthogonl to { X,..., w Xm wm }. The loding ω m, m, is obtined s g/ g, with g minimizing g 2 X YYX + ( g), subject to =, (2) m m g l where g l (g) is penlty function with tuning prmeter l. Zhng nd collegues [] used the empiricl Byes thresholding method proposed by Johnstone nd Silvermn [2,3] to introduce proper penlty function, which provides dptive sprse lodings of orthogonl components. POCRE is supervised lerning method tht needs the informtion of both genotype nd phenotype to build model. In the GAW7 dt set, the genotype is held fixed but the phenotype vries cross 200 replictes. To overcome potentil overfitting in the model-building process, we selected one replicte s trining set to obtin the sprse coefficients of SNPs in ech genetic region, nd we then pplied the results from POCRE to dt in nother replicte. In prctice, when only one dt set is vilble, cross-vlidtion cn be performed to select tuning prmeter to llevite overfitting. Empiricl Byes vrible selection In the vrible selection process, 3,205 gene-level mrkers cquired from the colescing process nd the other three trits (Age, Sex, nd Smoke) were put into the model. The reson for putting Age, Sex, nd Smoke in the model is the lck of knowledge bout whether these three trits re ssocited with the studied trit. If some vribles re known to be ssocited with the studied trit, then regression model cn be fitted with these known fctors, with the residuls tken s new responses in the vrible selection process. Empiricl () Byes vrible selection (EBVS) ws proposed to obtin finl model. The EBVS lgorithm works well in fitting lrge-p, smll-n regression model: p Y = m + b X + e, e N( 0, s I ), (3) j= j j 2 p where p is the number of predictors, Y is n n-vector of phenotype, nd X = ( X T,..., X T p ) is design mtrix. By further ssuming tht Y is centrlized nd X is stndrdized (μ = 0 in Eq. (3)), the EBVS puts the following mixture prior distribution to model the sprsity of b j : 2 / ( n ) b b w d b wg b j = j ( ) ( j) + ( j), (4) 0 s where d0( b j ) = if b j = 0 nd d0( b j ) = 0 otherwise; nd g ( b j) = exp( b j ), following Johnston 2 nd Silvermn [2,3]. Dt-driven optiml vlues for ω nd were obtined to chieve dptivity to sprseness nd shpe of prior distribution of b j, respectively. With current vlues of b nd s, the optiml vlues for ω nd re obtined s the vlues tht mximize their full conditionl distribution functions, P(ω b,s) ndp( b, s), respectively. b s the posterior medin is then updted. The itertive procedure for updting b nd hyperprmeters is crried out until convergence. With this mixture prior distribution, EBVS gives sprse solution for b. Results The results of nlyzing Q re shown in Tble, which lists both genetic nd environmentl components identified to hve nonzero effects in t lest 5 out of 200 replictes. Among 200 replictes, four genes were identified s hving nonzero effects: FLT in 200 replictes, KDR in 53 replictes, ARNT in 2 replictes, nd RIPK3 in 6 replictes. The first three genes re true cusl Tble Identified genes nd covrites in t lest 5 out of 200 replictes for Q Gene/covrite Averge of ˆb SD Frequency Age Smoke b FLT KDR ARNT RIPK The verge of ˆb nd its stndrd devition re clculted on the bsis of replictes whose component hs nonzero coefficient. b Smoke is coded s for smokers nd 0 for nonsmokers.

3 Pge 3 of 5 genes, but RIPK3 is not. Another two environmentl fctors, Age nd Smoke, re included in the finl model cross ll 200 replictes. Becuse ll the phenotypes in the GAW7 dt set re simulted to be influenced by SNP-bsed mrkers, the gene-bsed results re trnsformed into SNP-bsed results, nd we find tht 23 out of 39 cusl SNPs detected hve nonzero effects. Eleven of these SNPs ffilite with FLT. Ten of them re within the KDR region, nd two of them re in the ARNT region. In ddition, nother 98 noncusl genes were identified. All of these genes were identified in only one or two out of 200 replictes, which might be due to noise. Another cusl gene, VEGFC, ws lso found nd included in the finl model in two replictes. However, fter trnsforming gene-bsed results into SNP-bsed results, none of the true cusl SNPs ffiliting to VEGFC were identified. For the SNPs identified in t lest 5 out of 200 replictes, we plotted the frequencies of identified SNPs cross 200 replictes ginst chromosoml position (Figure ). In Figure, mny of the identified SNPs re flse positives, even though they ffilite to the cusl genes. Figure 2 provides the plots of frequencies within three cusl genetic regions: FLT, KDR, ndarnt. Considering only genetic components, flse-positive nd flse-negtive rtes were clculted for both gene-bsed nd SNP-bsed results. Using the gene-bsed results obtined from EBVS, we clculted the verge flsepositive nd flse-negtive rtes cross 200 replictes s (± ) nd (± ), respectively. For the SNP-bsed results cross 200 replictes, the verge flse-positive rte ws (± 0.708) nd the verge flse-negtive rte ws (± ). The number of flse-positive selections is not negligible nd it is higher in SNP-bsed results. This is becuse Figure Identified SNPs in t lest 5 out of 200 replictes for Q. The x-xis indictes the chromosoml position of ech SNP. The y-xis represents the frequency t which SNPs were identified s hving nonzero effects cross 200 replictes. Red dots represent true positives, nd blue dots represent flse positives. Figure 2 Identified SNPs for Q within ARNT, KDR, ndflt genetic regions. The frequencies of identified SNPs within three genetic regions, ARNT, KDR, nd FLT, re shown. The x-xes indicte the chromosoml position of ech SNP. The y-xes represent the frequency t which SNPs were identified s hving nonzero effects cross 200 replictes. Red dots represent true positives, nd blue dots represent flse positives.

4 Pge 4 of 5 Tble 2 Identified genes nd covrites in t lest 5 out of 200 replictes for Q2 Gene/covrite Averge of ˆb SD Frequency VNN VNN The verge of ˆb nd its stndrd devition re clculted on the bsis of replictes whose component hs nonzero coefficient. identified gene-bsed mrkers include noncusl SNPs during the colescing process to obtin gene-level mrkers. Tble 2 lists genes ssocited with Q2 tht were found to hve nonzero effect in t lest 5 of the 200 replictes. Note tht there re only two genes in this list nd tht their corresponding frequencies re low mong the 200 replictes: VNN (2 replictes) nd VNN3 (7 replictes). The low frequencies result from the low residul heritbility of Q2 (0.29), which mkes it difficult to detect ny genetic signl. Moreover, Q2 ws found to not be influenced by ny environmentl fctors. For the true discoveries of SNP-level mrkers, 32 out of 72 true cusl SNPs hve been detected to hve nonzero effects. However, the frequency of mny true cusl SNPs is. Only five of identified SNPs hve frequencies greter thn 5 (Figure 3): four of them ffilite to VNN3 nd one ffilites to VNN. BothVNN nd VNN3 re within the 6q23.2 region displyed in Figure 3. The verge flse-positive nd flse-negtive rtes for genebsed results cross 200 replictes re (± ) nd (± 0.000), respectively. For SNP-bsed results, the verge flse-positive rte is (± ) nd the flse-negtive rte is (± 0.000). The difficulty of detecting effects in trit with low residul heritbility results in low flse-positive rte, nd mny flse negtives were found here. For Q4, ll environmentl fctors, Age, Sex, nd Smoke, hve influences on this trit. Among 200 replictes, Age nd Smoke were included in the finl model in ll 200 replictes, wheres Sex ws included in the finl model in 99 replictes (Tble 3). Our results show tht Q4 decreses with ge, is higher in mles, nd is lower in smokers. In the GAW7 simultion, there is no genetic component influencing Q4. However, the nlyses found 5 genes identified to hve nonzero effect, but ll of them were detected in only one mong 200 replictes. The verge flse-positive rtes mong 200 replictes re (± 0.842) nd (± 0.70) bsed on gene-bsed nd SNP-bsed results, respectively. Discussion With the next-genertion sequencing technology, mny rre vrints or low-frequency SNPs cn be detected. The customry criteri for MAF in dt preprocessing Figure 3 Identified SNPs in t lest 5 out of 200 replictes for Q2. The x-xis indictes the chromosoml position of ech SNP. The y-xis represents the frequency t which SNPs were identified s hving nonzero effects cross 200 replictes. Red dots represent true positives, nd blue dots represent flse positives.

5 Pge 5 of 5 Tble 3 Identified genes nd covrites in t lest 5 out of 200 replictes for Q4 Gene/covrite Averge of ˆb SD Frequency Age Smoke b Sex c The verge of ˆb nd its stndrd devition re clculted on the bsis of replictes whose component hs nonzero coefficient. b Smoke is coded s for smokers nd 0 for nonsmokers. c Sex is coded s for mles nd 0 for femles. (i.e., MAF 0.05) in GWAS is not pproprite in this sitution.onepossiblesolutionistoreducethecutoff point of MAF. Although this pproch cn be done esily, it is difficult to determine the optiml cutoff point. With too big cutoff point, the mjority of rre vrints re discrded in nlyses nd little is gined from the next-genertion sequencing dt. With too smll cutoff point, most SNPs re included in model, presenting chllenges in sttisticl nlyses for detecting signls of rre vrints. We grouped both common nd rre vrints in the sme genetic region into gene-bsed mrker using POCRE. POCRE hs vrible selection property tht ssumes tht not ll SNPs in genetic region contribute to gene-bsed mrker. Although this ssumption is relistic, the vrible selection property of POCRE might rule out true cusl SNPs in the colescing process. On the other hnd, the colescing process might include noncusl SNPs, resulting in flse positive when the gene is identified to hve nonzero effect by EBVS. Better techniques to combine SNPs into gene-bsed mrkers need to be further studied to overcome the chllenges in the next-genertion sequencing. Another chllenge in nlyzing the GAW7 dt is signl detection for trit with low heritbility. It is well known tht it is difficult to identify nonzero effects in GWAS for trit with low heritbility. However, true cusl rre vrints worsen the sitution nd mke the vrints more difficult to detect. Better strtegies need to be further explored in GWAS to tckle the problem of low heritbility trit with rre vrints. Conclusions In this study, we proposed using POCRE to colesce common nd rre vrints in the sme gene into gene-level mrker nd pplied the newly developed empiricl Byes vrible selection to detect the ssocition between mrkers nd three continuous phenotypes in the GAW7 dt set: Q, Q2, nd Q4. With lrge number of predictors, the newly developed empiricl Byes pproch not only selects importnt vribles into the model but lso estimtes the effect sizes of nonzero predictors simultneously. Our results show tht combining both common nd rre vrints into gene-level mrkers cn increse the power to detect their signls. In fct, mny identified true cusl SNPs hve MAF = or hve vrints tht re found in only one individul. Nevertheless, there re still number of flse negtives. Bsed on GAW7 dt, we notice tht flse negtives occur when only few cusl SNPs re present in the genetic region. WhenthesizeofcuslSNPsinthegeneregionis moderte, it is still chllenging to detect true signls when most of the cusl SNPs re rre vrints. As shown in our nlysis, cusl SNPs with higher MAFs cn be identified more frequently thn cusl SNPs with lower MAFs. Acknowledgments Support from the Ntionl Institutes of Helth (NIH) grnt R0 GM03575, Ntionl Science Foundtion CAREER Grnt IIS , NIH grnt U0CA28535, nd the Cncer Cre Engineering project t the Oncologicl Sciences Center of Purdue University is grtefully cknowledged. This rticle hs been published s prt of BMC Proceedings Volume 5 Supplement 9, 20: Genetic Anlysis Workshop 7. The full contents of the supplement re vilble online t Authors contributions VP nd MZ designed the study, nd VP performed the sttisticl nlysis s well s drfted the mnuscript. LW nd YL crried out the preprocessing of the dt. DZ nd MZ conceived the study, reviewed, nd edited the mnuscript. All uthors red nd pproved the finl mnuscript. Competing interests The uthors declre tht there re no competing interests. Published: 29 November 20 References. Zhng D, Lin Y, Zhng M: Penlized orthogonl-components regression for lrge p smll n dt. Electron J Stt 2009, 3: Johnstone IM, Silvermn BW: Needles nd strw in hystcks: empiricl Byes estimtes of possibly sprse sequence. Ann Stt 2004, 32: Johnstone IM, Silvermn BW: EbyesThresh: R progrms for empiricl Byes thresholding. J Stt Softwre 2005, 2: Almsy LA, Dyer TD, Perlt JM, Kent JW Jr, Chrlesworth JC, Currn JE, Blngero J: Genetic Anlysis Workshop 7 mini-exome simultion. BMC Proc 20, 5(suppl 9):S2. 5. Purcell S, Nele B, Todd-Brown K, Thoms L, Ferreir MAR, Bender D, Mller J, Sklr P, de Bker PIW, Dly MJ, et l: PLINK: tool set for wholegenome ssocition nd popultion-bsed linkge nlysis. Am J Hum Genet 2007, 8: doi:0.86/ s9-s5 Cite this rticle s: Pungppong et l.: Genome-wide ssocition nlysis of GAW7 dt using n empiricl Byes vrible selection. BMC Proceedings 20 5(Suppl 9):S5.