Assessing multivariate gene-metabolome associations with rare variants using Bayesian reduced rank regression

Vol. 30 no. 14 2014, pages 2026–2034 BIOINFORMATICS ORIGINAL PAPER doi:10.1093/bioin o ma ics/b u140 Gene ics and popula ion analysis Ad ance Access publica ion Ma ch 24, 2014 Assessing mul i a ia e gene-me abolome associa ions wi h a e a ian s using Bayesian educed ank eg ession Pekka Ma inen 1,2 , Ma i Pi inen 3 , An i-Pekka Sa in 3,4 , Jussi Gillbe g 1 , Johannes Ke unen 3,4 , Ida Su akka 3,4 , An i J. Kangas 5 , Pasi Soininen 5,6 , Paul O’Reilly 7 , Ma ika Kaakinen 8,9 ,MikaKa ¨ho ¨nen 10 , Te ho Leh ima ¨ki 11 , Mika Ala-Ko pela 5,6,12 ,Olli T. Rai aka i 13,14 ,VeikkoSalomaa 15 , Ma jo-Rii a Ja ¨ elin 7,8,9,16,17 , Samuli Ripa i 3,4,18,19, *and Samuel Kaski 1,20, * 1 Depa men o In o ma ion and Compu e Science, Helsinki Ins i u e o In o ma ion Technology HIIT, Aal o Uni e si y, Esbo, Finland, 2 Cen e o Communicable Disease Dynamics, Ha a d School o Public Heal h, Bos on, MA, USA 3 Ins i u e o Molecula Medicine Finland (FIMM), Uni e si y o Helsinki, 4 Uni o Public Heal h Genomics, Na ional Ins i u e o Heal h and Wel a e, Helsinki, 5 Compu a ional Medicine, Ins i u e o Heal h Sciences, Uni e si y o Oulu and Oulu Uni e si y Hospi al, Oulu, 6 NMR Me abolomics Labo a o y, School o Pha macy, Uni e si y o Eas e n Finland, Kuopio, Finland, 7 Depa men o Epidemiology and Bios a is ics, MRC Heal h P o ec ion, Agency (HPA) Cen e o En i onmen and Heal h, School o Public Heal h, Impe ial College, London, UK, 8 Ins i u e o Heal h Sciences, 9 Biocen e Oulu, Uni e si y o Oulu, Oulu, 10 Depa men o Clinical Physiology, Tampe e Uni e si y Hospi al and Uni e si y o Tampe e, 11 Depa men o Clinical Chemis y, Fimlab Labo a o ies, Uni e si y o Tampe e School o Medicine, Tampe e, Finland, 12 Compu a ional Medicine, School o Social and Communi y Medicine and he Medical Resea ch Council In eg a i e Epidemiology Uni , Uni e si y o B is ol, B is ol, UK, 13 Depa men o Clinical Physiology and Nuclea Medicine, 14 Resea ch Cen e o Applied and P e en i e Ca dio ascula Medicine, Uni e si y o Tu ku and Tu ku Uni e si y Hospi al, Tu ku, 15 Depa men o Ch onic Disease P e en ion, Na ional Ins i u e o Heal h and Wel a e, Helsinki, 16 Uni o P ima y Ca e, Oulu Uni e si y Hospi al, 17 Depa men o Child en and Young People and Families, Na ional Ins i u e o Heal h and Wel a e, Oulu, Finland, 18 Wellcome T us Sange Ins i u e, Hinx on, Camb idge, UK, 19 Hjel Ins i u e and 20 Depa men o Compu e Science, Helsinki Ins i u e o In o ma ion Technology HIIT, Uni e si y o Helsinki, Helsinki, Finland Associa e Edi o : Je ey Ba e ABSTRACT Mo i a ion: A ypical genome-wide associa ion s udy sea ches o associa ions be ween single nucleo ide polymo phisms (SNPs) and a uni a ia e pheno ype. Howe e , he e is a g owing in e es o in es i- ga e associa ions be ween genomics da a and mul i a ia e pheno- ypes, o example, in gene exp ession o me abolomics s udies. A common app oach is o pe o m a uni a ia e es be ween each geno- ype–pheno ype pai , and hen o apply a s ingen signi icance cu o o accoun o he la ge numbe o es s pe o med. Howe e , his app oach has limi ed abili y o unco e dependencies in ol ing mul- iple a iables. Ano he end in he cu en gene ics is he in es iga ion o he impac o a e a ian s on he pheno ype, whe e he s anda d me hods o en ail owing o lack o powe when he mino allele is p esen in only a limi ed numbe o indi iduals. Resul s: We p opose a new s a is ical app oach based on Bayesian educed ank eg ession o assess he impac o mul iple SNPs on a high-dimensional pheno ype. Because o he me hod’s abili y o com- bine in o ma ion o e mul iple SNPs and pheno ypes, i is pa icula ly sui able o de ec ing associa ions in ol ing a e a ian s. We demon- s a e he po en ial o ou me hod and compa e i wi h al e na i es using he No he n Finland Bi h Coho wi h 4702 indi iduals, o whom genome-wide SNP da a along wi h lipop o ein p o iles comp is- ing 74 ai s a e a ailable. We disco e ed wo genes (XRCC4 and MTHFD2L) wi hou p e iously epo ed associa ions, which eplica ed in a combined analysis o wo addi ional coho s: 2390 indi iduals om he Ca dio ascula Risk in Young Finns s udy and 3659 indi iduals om he FINRISK s udy. A ailabili y and implemen a ion: R-code eely a ailable o down- load a h p://use s.ics.aal o. i/pema i/gene_me abolome/. Con ac : samuli. ipa i@helsinki. i; samuel.kaski@aal o. i Supplemen a y in o ma ion: Supplemen a y da a a e a ailable a Bioin o ma ics online. Recei ed on No embe 7, 2013; e ised on Feb ua y 27, 2014; accep ed on Ma ch 4, 2014 1 INTRODUCTION Concen a ions o human me aboli es a e associa ed wi h isk o many common diseases; o example, low- and high-densi y lipo- p o ein choles e ol (LDL and HDL) le els a e associa ed wi h co ona y a e y disease. Fo his eason, human me abolism has been unde in ensi e in es iga ion and o e he pas ew yea s se e al genome-wide associa ion s udies ha e success ully un- co e ed a pa o i s gene ic basis (Ke unen e al., 2012; *To whom co espondence should be add essed. ßThe Au ho 2014. Published by Ox o d Uni e si y P ess. This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion Non-Comme cial License (h p://c ea i ecommons.o g/licenses/ by-nc/3.0/), which pe mi s non-comme cial e-use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. Fo comme cial e-use, please con ac jou nals.pe [email protected] Saba i e al., 2008; Suh e e al., 2011; Teslo ich e al., 2010). Fo example, a la ge me a-analysis (Teslo ich e al., 2010) iden i ied 95 loci in luencing he le els o o al choles e ol, LDL, HDL and iglyce ides. Mo e ecen s udies used ine subclassi ica ions o me aboli es and disco e ed dozens o no el loci (Ke unen e al., 2012; Suh e e al., 2011). Despi e hese ad ances, he a iance explained by all epo ed single nucleo ide polymo phisms (SNPs) alls a below he sugges ed he i abili y o he common me aboli es, as es ima ed ei he om win s udies (Ke unen e al., 2012) o om mo e dis an ly ela ed indi iduals (Va iku i e al., 2012). This mo i a es us o de elop new app oaches o associa ion es ing ha could be e use all in o - ma ion a ailable o us. The p esen -day coho s udies o en come wi h a ich se o pheno ypic ea u es. Examples in addi ion o me abolomics (Ke unen e al., 2012; Soininen e al., 2009; Suh e e al., 2011) include s udies o gene exp ession (Acke mann e al., 2013) and 3D- acial imaging (Hammond and Su ie, 2012). As a conse- quence, we need s a is ical me hods ha inc ease he powe o unco e geno ype–pheno ype dependencies by combining in o - ma ion o e se e al ela ed pheno ypes (Fe ei a and Pu cell, 2009; Inouye e al., 2012; O’Reilly e al., 2012). The unde lying idea is ha i a gene ic a ian a ec s a ai , hen i is likely o a ec o he ai s ha a e ela ed o he i s one and, by es ing o associa ion wi h he wo ai s join ly, powe may be inc eased. This easoning can be aken a s ep u he by es ing all ai s in high-dimensional omics da a simul aneously, o ex- ample, all me aboli es in comp ehensi e me abolomic p o iles. A compa ison o di e en s a is ical me hods a ailable o join es ing o comple e me abolomics p o iles was ecen ly con- duc ed (Ma inen e al., 2013). Besides es ing se e al pheno ypes simul aneously, he abili y o de ec ce ain kinds o associa ions may be boos ed by com- bining s a is ical e idence o e se e al SNPs. Usually his is done in a supe ised manne , such ha SNPs ela ed by loca ion o unc ion, o example, a e es ed simul aneously. Combining in o ma ion o e mul iple SNPs is pa icula ly c ucial wi h a e a ian s, i.e. SNPs whe e he mino allele is p esen in a small p opo ion o he popula ion. Tes ing such SNPs indi idually is unlikely o yield signi ican indings because o limi ed powe . Mos app oaches o handling a e a ian s a e based on collap- sing se e al a e SNPs in o a single a iable (Bansal e al., 2010). Fo example, one can simply collapse se e al a e a ian s in o a single indica o , elling whe he any o he a e a ian s is p esen in he indi idual (Mo gen hale and Thilly, 2007) o o coun he numbe o a e a ian s p esen in he indi idual (Mo is and Zeggini, 2010). The p oblem wi h he collapsing me hods is he implici assump ion ha he e ec s a e in he same (o a p ede- ined) di ec ion. A mo e sophis ica ed a iance componen me hod a oiding his assump ion is able o in es iga e he impac o se e al a e a ian s on a uni a ia e ai (Wu e al., 2011). E en i he e exis s a la ge numbe o me hods o analyzing a e a ian s, none o hose has been ailo ed o mul i a ia e pheno ypes. On he o he hand, s anda d me hods o mul i a i- a e pheno ypes (Fe ei a and Pu cell, 2009) ha e no been ho - oughly in es iga ed in he con ex o a e a ian s, and we will see la e in he ex ha se e e o e i ing may occu . In summa y, me hods o dealing wi h a e a ian s in he con- ex o mul i a ia e pheno ypes a e clea ly lacking. In his a icle, we de i e a no el o mula ion o he Bayesian educed ank eg ession model (Geweke, 1996) o de ec mul i- a ia e associa ions be ween p ede ined g oups o SNPs and a high-dimensional pheno ype. In pa icula , ou app oach is sui - able o analyzing bo h common and a e a ian s. Ou o mu- la ion inco po a es p io knowledge abou e ec sizes o inc ease he powe o de ec associa ions. Fu he mo e, i is capable o co ec ing o he numbe o SNPs conside ed, which is impo - an when es ing a la ge numbe o SNP g oups o di e en sizes. We alida e ou me hod by assessing associa ions be ween SNPs in all human genes, one gene a a ime, and me abolic p o iles comp ising ine-scale lipop o ein measu emen s o 4702 indi id- uals om he No he n Finland Bi h Coho 1966 (Ran akallio, 1969; Saba i e al., 2008). Among he op-sco ing genes wi hou known associa ions o he ai s s udied, wo genes (XRCC4 and MTHFD2L) eplica ed in a combined analysis o 2390 indi id- uals om he Ca dio ascula Risk in Young Finns s udy (YFS; Rai aka i e al., 2008) and 3659 indi iduals om he FINRISK s udy (Va iainen e al., 2010). Addi ional analyses o he same da a con i med ha al e na i e me hods disco e ed only one o hese associa ions and did no iden i y any u he associa ions ha we e no known be o e. 2 METHODS 2.1 Model To build ou model, we assume ha he pheno ypes may be a ec ed by h ee kinds o a iables, (i) known ac o s, such as age, sex o popula ion s uc u e, (ii) unknown ac o s, such as expe imen al condi ions and o he ba ch e ec s, and (iii) SNPs unde conside a ion, as schema ically p e- sen ed in Figu e 1. In con as o s anda d eg ession, whe e each SNP– pheno ype pai has a pa ame e ep esen ing he e ec o he SNP on he pheno ype, he e we assume ha a combina ion o se e al SNPs is in lu- encing se e al pheno ypes h ough some unknown ac o s. This assump- ion is compac ly exp essed in e ms o he educed ank eg ession, whe e he SNPs a e i s p ojec ed on o a low-dimensional subspace, and he p ojec ions a e hen used as eg esso s when p edic ing he pheno ypes. The educed ank eg ession o mula ion immedia ely implies some s uc u al assump ions deemed sensible in he cu en se - ing: i s , i a SNP has an e ec on a pheno ype, hen he SNP is likely o ha e an e ec on o he pheno ypes; second, i a pheno ype is a ec ed by a SNP, hen he pheno ype is mo e likely o be a ec ed by o he ela ed SNPs as well. Le Ndeno e he numbe o indi iduals, S he numbe o SNPs, P he numbe o pheno ypes and C he numbe o o he co a ia es. Fo mally, we conside he Bayesian educed ank eg ession model Y¼X þZA þHTþEð1Þ whe e YNPcon ains he pheno ypes, XNScon ains he SNPs, SK1 and K1P ep esen a low- ank app oxima ion o he eg ession coe i- cien ma ix ¼,ZNC ep esen s o he co a ia es wi h he co es- ponding coe icien ma ix ACP,HNK2con ains hidden con ounding ac o s wi h he co esponding coe icien ma ix PK2and ENP¼½e1,...,eNT,wi heiNð0, Þ,whe e¼diagð2 1,...,2 PÞ. No e ha by in eg a ing o e he hidden ac o s H, he model is equi a- len o yiNðTxiþATzi,TþÞ,i¼1, ...,Nð2Þ 2027 Gene-me abolome associa ions whe e i is assumed ha he ac o s ha e independen s anda d no mal p io dis ibu ions. The e o e, we see ha ha ing he la en a iable pa HTin he model co esponds o assuming a low- ank app oxima ion o he ull co a iance ma ix, which is impo an when analyzing high- dimensional da ase s. Fo compu a ional easons, we es ic he ank o he eg ession model, K 1 , o uni y in ou genome-wide analysis (w.l.o.g. in he de ec ion ask, see below) and show esul s wi h K1¼1, 2, 3 o a ew ep esen a- i e examples. Howe e , he e we p esen a gene al in ini e-dimensional amewo k a ailable in ou implemen a ion, which does no necessi a e he selec ion o a ixed ank. In gene al, o use he Bayesian educed ank eg ession model, he ank o he model, K 1 , and he ank o he low- ank app oxima ion o he co a iance ma ix, K 2 , mus be selec ed. A ecen Bayesian in ini e spa se ac o analysis model (Bha acha ya and Dunson, 2011) ci cum en s he selec ion o a ixed ank o K 2 by assum- ing in p inciple an in ini e numbe o columns in he ma ix; howe e , he columns sh ink p og essi ely such ha only he i s anks a e in lu- en ial in p ac ice. We assume his p io o mula ion o ou noise model HTþE. We exploi he idea u he by allowing also he ank K 1 o be in ini e in p inciple, and en o cing he low- ank na u e by sh inking he columns o and he ows o inc easingly as he column/ ow index g ows. In p ac ice, one needs o speci y uppe bounds o K 1 and K 2 .We selec he uppe bound o K 2 using he adap i e p ocedu e o Bha acha ya and Dunson (2011), and we ha e implemen ed an analo- gous me hod o lea ning he uppe bound o K 1 . In p ac ice, we wan ed o minimize he model complexi y o maximize he powe o de ec asso- cia ions and speed up he compu a ions. The e o e, we decided o un he genome-wide analysis (see Sec ion 3.1) using a ixed ank K1¼1. The model wi h K1¼1 is su icien o ou pu poses o de ec ing whe he a gene is un ela ed o he pheno ypes (in which case, ank ze o would al eady be su icien ), al hough o p edic ion a highe ank migh be mo e sui able. We expe imen ed wi h a selec ed se o known genes wi h uppe bounds 2 and 3 (see below) and no iced ha he e ec o inc easing he uppe bound om uni y had only a small impac on he amoun o a ia ion ha is explained by he model. F om he biological pe spec i e, his means ha he in luence o a gene on he pheno ypes can mos ly be desc ibed in e ms o a single la en ac o media ing he e ec . A de ailed model desc ip ion is gi en in Supplemen a y Sec ion 1. The model is ela ed o many published me hods, and a ho ough compa ison can be ound in Supplemen a y Sec ion 2. Co ec ion o unknown ac o s has ecen ly been conside ed wi h he s anda d eg es- sion model, ypically o jus one SNP a a ime (Fusi e al., 2012; S egle e al., 2010). The di e ence o he o iginal Bayesian educed ank eg es- sion o mula ion (Geweke, 1996) is ha ou model uses low- ank ap- p oxima ion o he co a iance ma ix, making i mo e sui able o high-dimensional pheno ypes, and in o ma i e p io dis ibu ions accom- moda ing p oblem-speci ic knowledge. Fu he mo e, we use he model in a new way, as desc ibed in he subsequen sec ions. The Bayesian in ini e spa se ac o analysis model has been used o high-dimensional da a (Bha acha ya and Dunson, 2011); he e, we use i o ep esen he mul i- a ia e noise. Canonical co ela ion analysis (CCA) is a classical ool o modeling mul i a ia e dependencies ha ha e ecen ly been in oduced in he associa ion s udy con ex (Fe ei a and Pu cell, 2009; Ho elling, 1936). Spa se CCA (Pa khomenko e al., 2009; Waaijenbo g e al., 2008; Wi en and Tibshi ani, 2009) is mo e sui able o high-dimensional da ase s; howe e , in oducing p io dis ibu ions o CCA ha would be in ui i e in he associa ion s udy con ex does no seem s aigh o wa d. 2.2 P opo ion o o al a ia ion explained A commonly used measu e o he impac o mul iple SNPs, say x1,...,xS, on a uni a ia e ai yis he p opo ion o a iance explained (PVE) by he SNPs: PVE ¼1Va ðyPS i¼1^ aixiÞ Va ðyÞ ¼Va ðPS i¼1^ aixiÞ Va ðyÞ: He e, PS i¼1^ aixiis a linea p edic ion o he pheno ype y, gi en he SNPs. Analogously, as a measu e o he o e all impac o mul iple SNPs on a high-dimensional pheno ype, we p opose o use he p opo ion o o al a ia ion o he pheno ypes explained (PTVE) by he model, namely PTVE ¼T ðCo ð^ YÞÞ T ðCo ðYÞÞ ð3Þ whe e ^ Yis a p edic ion o a high-dimensional pheno ype Y om he model and T deno es he ace, i.e. he sum o he diagonal elemen s o he ma ix. In (3) and in gene al, he o al a ia ion o a mul i a ia e andom a iable is de ined as he ace o he co a iance ma ix, i.e. he sum o he a iances o he indi idual a iables. The e o e, PTVE meas- u es he join impac o he SNPs on se e al pheno ypes and hence is expec ed o yield high sco es o such dependencies in which many pheno ypes a e a ec ed by he SNPs, e en i none o he e ec s is la ge by i sel . In he Bayesian s a is ical amewo k, he in e ences a e based on pos- e io p obabili y dis ibu ions o he quan i ies o in e es (Gelman e al., 2004). Wi h he Bayesian educed ank eg ession model, samples om he pos e io dis ibu ion o he PTVE can be ob ained om PTVEðiÞ¼T Co XðiÞðiÞ  T Co YðÞðÞ ð4Þ whe e ðiÞand ðiÞa e samples om he pos e io dis ibu ion o he pa ame e s and . I is simila ly s aigh o wa d o es ima e he pos- e io dis ibu ion o he p opo ion o a ia ion explained by he a e Y X ψΓ ZA H T E, Y X Z A H T E A B Fig. 1. G aphical illus a ion o he model. (A) The a iables and depen- dencies be ween hem. The pheno ypes Ya e assumed o be a ec ed by known ac o s, such as age o sex, unknown ac o s, such as ba ch e ec s caused by a ying expe imen al condi ions, and he SNPs. The in luence o he SNPs is media ed by unknown combina ions o he o iginal SNPs, ep esen ed by black squa es. (B) The same model using ma ix no a ion. Ma ices con aining he obse ed a iables, Y( he pheno ypes), X( he SNPs) and Z(known ac o s), a e blue. The eg ession coe icien ma i- ces a e ed. No e ha he coe icien ma ix o he SNP e ec s is w i en as a p oduc o wo ma ices, and , co esponding o a low- ank app oxima ion o an uncons ained coe icien ma ix. The b own ma i- ces comp ise unobse ed a iables, H(unknown ac o s) and E(noise e ms) 2028 P.Ma inen e al. a ian s, by di iding he a ia ion o he p edic ion in o wo componen s, one co esponding o he a e a ian s, he o he o he common a ian s. The sco e ob ained in his way is e e ed o as PTVE- a e in he sequel and i s exac de ini ion is gi en in Supplemen a y Sec ion 3. In p ac ice, we app oxima e he pos e io dis ibu ion by using a mode-based poin es ima e o one o he pa ame e s, , and es ima ing he join dis ibu- ion o he o he pa ame e s using an Ma ko chain Mon e Ca lo (MCMC) algo i hm, as desc ibed ho oughly in Supplemen a y Sec ions 4 and 5. 2.3 In o ma i e p io In he Bayesian analysis, ex e nal backg ound knowledge may be inco - po a ed in he s a is ical analysis h ough p io p obabili y dis ibu ions. As ou analysis is ocused on es ima ing he pos e io dis ibu ion o PTVE, a sensible p io is ob ained by making he p io dis ibu ion o he PTVE ep esen ou ue belie s abou his quan i y. The p io dis i- bu ion o he PTVE appea s no o be a ailable in a closed o m; how- e e , in Supplemen a y Sec ion 6, we de i e esul s ha show how he dis ibu ion o he mean o he PTVE, PTVE, depends on model hype - pa ame e s. Using hese esul s, we se he p io dis ibu ions o sa is y he ollowing p ope ies: MedianðPTVEÞ¼106ð5Þ and PðPTVE40:001Þ¼0:01 ð6Þ Equa ion (5) means ha he p io median o PTVE is close o ze o, as we expec mos o he genes o be un ela ed o he pheno ypes. Equa ion (6) says ha wi h a small p obabili y, he e equal o 0.01, he gene may explain40.1% o he o al a ia ion, a alue deemed esonable based on he backg ound knowledge. The esul ing p io dis ibu ion o he PTVE is ob ained by in eg a ing o e he dis ib ion o PTVE,andweused Mon e Ca lo simula ion o in es iga e he dis ibu ion. Figu e 2 shows PTVE alues sampled om he p io dis ibu ion. The ollowing desi able cha ac e is ics can be seen: i s , a peak close o ze o, sh inking he coe - icien s when no e ec is p esen ; second, a long ail, co esponding o he genes wi h a non-negligible impac on he pheno ypes, wi hou imposing s ong belie s abou he ac ual size o hese non-ze o e ec s. Ano he impo an p ope y ha ollows om using he in o ma i e p io is ha he numbe o SNPs unde conside a ion can be accoun ed o . De ailed examina ion o Co olla y 1 in Supplemen a y Sec ion 6 e eals ha wi h ixed hype pa ame e s, he expec ed PTVE is p opo - ional o PS i¼1Va ðxiÞ, i.e. he o al a ia ion o he SNPs. Roughly, his means ha i he numbe o SNPs doubles, he expec ed PTVE doubles as well, i he hype pa ame e s a e kep ixed. Using he Co olla ies 1 and 2 in Supplemen a y Sec ion 6, i is s aigh o wa d o modi y he hype - pa ame e dis ibu ions o asse he p io condi ions (5) and (6), implying in ou se ing ha all genes a e expec ed o explain he same amoun o he a ia ion o he pheno ypes, ega dless o how many SNPs hey con ain. 2.4 Da a As a da ase o de ec ing associa ions, we conside a sample o 4702 indi iduals om he No he n Finland Bi h Coho 1966 (NFBC1966), a bi h coho s udy o child en bo n in 1966 in he wo no he nmos p o inces o Finland (Ran akallio, 1969). The blood sam- ples o he DNA ex ac ion and pheno ype da a we e collec ed a a ollow-up isi when he pa icipan s we e 31 yea s o age. Fo eplica- ion, we conside wo coho s. The YFS is a popula ion-based p ospec i e coho s udy (Rai aka i e al., 2008) conduc ed in Finland, he pu pose o which was o in es iga e he le els o ca dio ascula isk ac o s in chil- d en and adolescen s in di e en pa s o he coun y. The FINRISK s udy comp ises c oss-sec ional popula ion su eys ha ha e been ca ied ou e e y 5 yea s since 1972, o assess he isk ac o s o ch onic diseases, wi h emphasis on ca dio ascula isk ac o s (Va iainen e al., 2010). The indi iduals analyzed in his s udy belong o he sample om he yea 1997. The blood samples o he wo eplica ion coho s we e collec ed when he pa icipan s we e 30–45 and 25–71 yea s o age, espec i ely. The s udy p o ocols o all da ase s ha e been app o ed by he local e hics commi ees. The samples we e geno yped wi h Illumina a ays (Illumina, Inc. San Diego, CA, USA) and impu ed wi h IMPUTE 2 (Howie e al.,2009, 2011) using a 1000 Genomes P ojec e e ence panel (The 1000 Genomes P ojec Conso ium, 2012). O he esul ing good-quali y au o- somal SNPs (in o 40.4), we ex ac ed SNPs in 24025 human genes by adding 50 kb lanking egions on bo h sides o he endpoin s o he genes gi en in NCBI gene da abase (genome assembly GRCh37.p10, NCBI anno a ion 104, No embe 2012). As a p ep ocessing s ep, we educed he geno ype space wi hin each gene o he mos p omising 200 SNPs (a mos ) ha had he highes canonical co ela ion es sco e (Fe ei a and Pu cell, 2009) wi h he me aboli es; howe e , o p e en o e i ing, he p io s we e speci ied as desc ibed abo e using he unp uned SNP se . In p elimina y expe imen s, dec easing he numbe o SNPs in his way om 800 o 200 had no isible e ec on he esul s. Finally, he SNPs we e scaled o ha e uni a iance. Pheno ype da a came om he se um NMR me abolomics pla o m desc ibed ea lie (Soininen e al., 2009). As a p ep ocessing s ep, he ai s we e quan ile-no malized o ha e s anda d no mal dis ibu ion. Indi iduals wi h 20% missing alues we e emo ed and he emaining missing alues we e impu ed by sampling hem om he mul i a ia e no mal dis ibu ion. In his wo k, we analyzed a subse o 74 lipop o ein subclass measu es (Supplemen a y Table S3). The empi ical co ela ion ma ix o he ai s is shown in Supplemen a y Figu e S1. Linea eg es- sion was used o co ec he pheno ypes o age, sex and popula ion s uc u e using 10 p incipal componen s (P ice e al., 2006). P io dis ibu ion o PTVE PTVE (x10 ) P obabili y 0246810 0 0.3 0.6 0.9 0.000 0.005 0.010 0.015 0 1000 2000 3000 4000 5000 Pos e io PTVE o LIPC gene PTVE Densi y O iginal Pe mu ed Fig. 2. P io and pos e io dis ibu ions o he p opo ion o o al a i- a ion explained (PTVE) by he model. The panel on he le shows he p io dis ibu ion imposed on he p opo ion o o al a ia ion o he pheno ypes explained by he SNPs unde conside a ion (he e, he SNPs om he LIPC gene). The median o he p io dis ibu ion is loca ed a 4e-6. The cha ac e is ic ea u es o he p io dis ibu ion include he peak a alues close o ze o, e ec i ely emo ing noise unless he e is s ong e idence abou a possible associa ion, and he long ail allowing a small pe cen age o genes o explain la ge p opo ions o he pheno ype a ia ion. The igh mos bin on he x-axis con ains he o al p obabili y o alues exceeding he maximum alue on he axis. The panel on he igh shows he pos e io dis ibu ion o he PTVE o he same SNPs. Two pos e io densi ies a e shown, one showing he dis ibu ion o he o iginal da a, he o he showing he dis ibu ion o da a in which he ows o he pheno ype ma ix ha e been pe mu ed. No ice he di e ing scales on he x-axes o he wo panels 2029 Gene-me abolome associa ions 3RESULTS 3.1 Genome-wide analysis o NFBC1966 da a We compu ed he PTVE and PTVE- a e sco es o each o he 24 025 human genes in he NFBC1966 da a, one gene a a ime, using he Bayesian educed ank eg ession. Table 1(a) shows he op i e genes wi h he highes PTVE sco es, all o which a e well-known lipid-associa ed loci. Mo e gene ally, all 43 op-sco - ing genes we e loca ed wi hin 1Mb om p e iously epo ed genome-wide signi ican lipid associa ions (Ke unen e al., 2012; Teslo ich e al., 2010; The Global Lipids Gene ics Conso ium, 2013), and de ailed lis ing o he op genes is gi en in Supplemen a y Table S4. Fu he mo e, o he op 100 genes, which co espond o 0.2 alse disco e y a e (FDR) (see he nex sec ion), 73 genes had known associa ions. Toge he , hese indings se e as a alida ion o he me hod and i s implemen a ion. To illus a e he e ec o he model ank on he esul s, we ca ied ou a de ailed analysis o h ee known lipid genes: LIPC, APOB and PLTP,wi h ankK1¼1, 2, 3. The genes we e se- lec ed such ha hey we e loca ed in di e en ch omosomes and had dissimila associa ion p o iles [APOB associa ed mos s ongly o VLDL, IDL and LDL, PLTP o HDL and LIPC o VLDL, IDL and HDL (Tukiainen e al., 2012)]. In addi ion o conside ing he genes sepa a ely, we epea ed a join analysis o all h ee possible pai wise gene combina ions. The esul s a e shown in Supplemen a y Figu e S2 and a e summa ized as ol- lows: (i) he ank o he model had a mino e ec on he esul s o a single gene, (ii) inc easing he ank om K1¼1 oK1¼2 inc eased he a iance explained in all join pai wise analyses, and he inc ease was signi ican in wo o he h ee cases, (iii) a combina ion o wo genes always had a la ge e ec han ei he gene indi idually; howe e , he sum o he indi idual e ec s was sligh ly la ge han he e ec o he combina ion. We a ibu e his di e ence mainly o he s onge sh inkage in he second han he i s geno ype componen . (i ) The i s componen o a join model was always s ongly co ela ed wi h he single-gene model wi h he la ge e ec , he second componen wi h he single-gene model wi h he smalle e ec . This is as expec ed, as he p io dis ibu ion was designed o iden i y he s onges associa ions using he i s geno ype componen . To check whe he no el associa ions could be de ec ed by any me hod, we ca ied ou a eplica ion expe imen wi h he YFS and FINRISK da ase s o he mos p omising genes, a e excluding genes loca ed wi hin 1 Mb om p e iously epo ed associa ions. We conside ed om each me hod all genes wi h FDR 50.4 as p omising. Fo he PTVE- a e sco e, six genes we e es ed, none o which had p e iously epo ed associa ions o lipids. Fo he PTVE sco e, 305 genes had FDR 50.4; how- e e , only 167 we e no loca ed close o known associa ions, and hese 167 genes we e selec ed o eplica ion. Fo he pu poses o eplica ion, he mul i a ia e dependency be ween he mul iple SNPs and pheno ypes was educed in o a uni a ia e es by using pa ame e s es ima ed in he NFBC1966 da a o cons uc uni a ia e geno ype and pheno ype combin- a ions (see Supplemen a y Sec ion 7 o u he de ails). Then, he s anda d linea model was used o es o posi i e co ela ion be ween he geno ype and pheno ype combina ions. A pooled linea eg ession coe icien combining YFS and FINRISK da ase s was o med using a ixed e ec model o e he wo da ase s (Thompson e al., 2011), and he P- alue was ob ained by ela ing he pooled es ima e o i s SD. A one- ailed es was used,as we we e only in e es ed in indings in which he e ec s we e in he same di ec ion in he eplica ion da ase s as in he NFBC1966 da a. Bon e oni co ec ion was used o accoun o he numbe o genes es ed wi h each me hod, such ha co ec ed Table 1. Summa y o esul s om he genome-wide analysis o he eal da a Ch Locus PTVE (SD) Ra e P- alue Gene ank PTVE Pai wise S-CCA CCA-single (a) 15 LIPC 0.01 (5e-04) 0.015 5e-19 1 1 1 132 19 APOC1 0.0046 (3e-04) 0.017 1.4e-26 2 8 18 275 19 PVRL2 0.0045 (1e-04) 0.0015 7e-35 3 9 14 276 2APOB 0.0044 (3e-04) 0.017 1.1e-17 4 45 41 3244 11 APOA5 0.0043 (2e-04) 0.021 5e-10 5 26 33 2433 (b) 16 SPIRE2 a 0.0015 (9e-05) 0.89 0.00091 b 5 ( a e) 8344 5490 4973 5XRCC4 0.0024 (2e-04) 0.55 0.0016 6 ( a e) 2706 5163 2155 (c) 2DTNB a 0.0015 (2e-04) 0.15 2.6e-04 c 138 4715 338 7652 4MTHFD2L 0.0015 (2e-04) 0.019 7e-06 163 102 1444 1552 No e: (a) Re e ence esul s o genes wi h i e highes PTVE sco es. (b) Replica ed genes om he PTVE- a e sco e (o six genes es ed o eplica ion). (c) Replica ed genes om he PTVE sco e (o 167 genes). Fi e o he eplica ed genes (PPBP, CXCL5, CXCL2, PF4 and CXCL3) a e no shown as hey we e loca ed wi hin 1 Mb om MTHFD2L, which had he s onges e ec . Column PTVE (SD) shows he p opo ion o o al a ia ion explained and i s SD, a e speci ies he p opo ion o he a ia ion explained by he gene a ibu ed o he a e a ian s, P- alue speci ies he P- alue pooled o e YFS and FINRISK eplica ion da ase s (unless s a ed o he wise) and he las ou columns speci y he anking o he gene among all genes wi h di e en me hods. a Deno es genes ha eplica ed signi ican ly in only one o he wo eplica ion da ase s. b/c Replica ion P- alue in FINRISK/YFS. 2030 P.Ma inen e al. P- alue h eshold co esponding o he nominal 0.05 le el o signi icance was equal o P50:0083 o he six pu a i e no el genes om PTVE- a e sco e and P50:00030 o he 167 pu a i e genes om PTVE sco e. We conside ed a eplica ion signi ican i he es was nomin- ally signi ican (P50.05) in bo h eplica ion da ase s, and he P- alue o he pooled es ima e was signi ican a e co ec ing o he mul iple es s. In o ma ion abou genes ha eplica ed signi ican ly is p o ided in Table 1(b) and (c) and in Figu e 3. One gene wi h PTVE- a e and six genes wi h PTVE we e de- ec ed, co esponding o wo independen genes: XRCC4 and MTHFD2L.MTHFD2L is loca ed wi hin 1 Mb om wo SNPs ( s2168889 and s16850360) associa ed wi h ‘me abolic ne wo ks’ con aining some lipop o ein ai s om ou da a (Inouye e al., 2012). Howe e , he op me aboli e in he associ- a ions was Albumin, and when we epea ed he mul i a ia e es wi h he lipop o ein ai s conside ed he e, hese associa ions we e no longe genome-wide signi ican (P¼2.5e-4 and P¼6.4e-7). In addi ion, wo genes, SPIRE2 and DTNB, epli- ca ed signi ican ly (a e he mul iple es ing co ec ion) in one, bu no in he o he eplica ion da ase . Table 1 also p esen s he ankings o hese genes by al e na i e me hods (see below). We see ha XRCC4,SPIRE2 and DTNB we e comple ely missed by he o he me hods. Supplemen a y Table S1 shows he SNPs con ibu ing o he epo ed associa ions. We see ha wi h XRCC4,SPIRE2 and DTNB, many SNPs, some o which a e a e, a e equi ed o ep esen he o e all associa ion. This ex- plains why hese genes did no ecei e any signal om he s and- a d es ing wi h he pai wise linea model. Supplemen a y Figu e S3 shows g aphically how he pheno ypes a e a ec ed by he signi ican genes and he known LIPC gene. We see ha in nei- he o he new genes is he e ec ocused on any single ai , bu a he a small e ec is seen on many lipop o ein measu es. This is no su p ising, as he PTVE sco e is expec ed o gi e high sco es o p ecisely his kind o associa ion. Supplemen a y Figu e S4 shows he es ima ed SNP coe icien s o he genes and demon- s a es he use ulness o analyzing all SNPs in a gene simul an- eously o educe noise esul ing om he co ela ion be ween he SNPs. Fu he backg ound in o ma ion on hese genes is p e- sen ed in Supplemen a y Table S2; howe e , a mo e ho ough biological in e p e a ion o he genes emains o u u e wo k. Finally, we epea ed a simila analysis wi h h ee al e na i e me hods: (i) exhaus i e pai wise sea ch wi h a linea model, whe e he minus loga i hm o he smalles pai wise P- alue o e all SNPs in he gene and me aboli es was aken as he es sco e o he gene, (ii) CCA, applied o a single SNP e sus all me aboli es a a ime as by Fe ei a and Pu cell (2009) and Inouye e al. (2012) and (iii) spa se CCA, which was used o compu e he canonical co ela ion be ween all SNPs in a gene and all pheno ypes (Pa khomenko e al., 2009). The me hods (ii) and (iii) we e ound o be he mos powe ul in a ecen com- pa ison o app oaches o a mul i a ia e me abolomics Fig. 3. Resul s o genes wi h signi ican eplica ion in bo h es se s: XRCC4 and MTHFD2L; o e e ence, he well-known LIPC lipid locus is also shown. Each panel shows he iden i ied pheno ype combina ion plo ed agains he geno ype combina ion. The le column shows esul s in he NFBC1966 da ase , in which he associa ions we e de ec ed. The cen e and igh columns show esul s wi h he YFS and FINRISK da ase s, whe e coe icien ma ices lea ned wi h he NFBC1966 da a we e used o o m he a iable combina ions. The g een and ed backg ound colo ings ma k he indi iduals wi h he highes /lowes geno ype combina ion alues, and he pheno ype alues in hese ex eme g oups a e in es iga ed in mo e de ail in Supplemen a y Figu e S3 2031 Gene-me abolome associa ions pheno ype (Ma inen e al., 2013); howe e , he e he SNPs we e no p uned using he mino allele equency be o e applying he me hods as by Ma inen e al. (2013) because he e he ocus is in he a e a ian se ing. Simila ly o PTVE and PTVE- a e me h- ods, we ied o eplica e he op-sco ing genes up o FDR ¼0.4. The las column in Table 2 shows he numbe s o genes included in he eplica ion wi h de ailed lis ings gi en in Supplemen a y Tables S4–S8. The associa ion in MTHFD2L was con i med o be genome-wide signi ican using he s anda d pai wise linea eg ession (SNP s185567543, ai S.LDL.P, P¼2.5e-15, whe e he P- alue is pooled o e all h ee da ase s). All o he eplica ed associa ions we e loca ed wi hin 1 Mb o his o p e- iously known associa ions, hus yielding no addi ional no el de ec ions. 3.2 Powe compa ison To in es iga e he powe o he in oduced me hod and compa e i wi h al e na i e me hods, we es ima ed FDR co esponding o di e en h esholds d o decla ing a gene as de ec ed. FDR es- ima es we e ob ained by pe mu ing he ows o he pheno ype ma ix and analyzing he pe mu ed da a in exac ly he same way as he o iginal da a (Benjamini and Hochbe g, 1995; S o ey and Tibshi ani, 2003; Xie e al., 2005). In de ail, we compu ed he a e age numbe o genes in he pe mu ed da ase s wi h sco es exceeding a gi en h eshold d( alse-posi i e a es, FPðdÞ), he numbe o genes in he o iginal da a wi h sco es exceeding hesame h esholdd( o al posi i e a es, TPðdÞ)andconside ed he a io o he wo FDRðdÞ¼FPðdÞ TPðdÞ Because o compu a ional bu den, only one pe mu a ion was used wi h he Bayesian educed ank eg ession. Wi h he o he me hods, h ee pe mu a ions we e used. The e o e, he FDR es- ima es a e app oxima e, which we conside o be su icien o ou pu poses, especially because he mos ex eme quan iles a e no conside ed. The numbe s o genes decla ed de ec ed wi h di e en FDR h esholds a e p esen ed in Table 2, and he o e all conco dance o he sco es om di e en me hods is shown in Supplemen a y Figu e S5. In summa y, he esul s show ha he me hod wi h which mos associa ions we e ound was exhaus i e pai wise sea ch and he second-mos powe ul me hod was he Bayesian educed ank eg ession wi h PTVE as he es sco e. These wo me hods also had he highes ag eemen in sco ing genes. CCA applied o es o associa ion be ween indi idual SNPs and he mul i a ia e pheno ype pe o med badly. These esul s a e some- wha di e en om wha has been epo ed be o e by us and o he s (Inouye e al., 2012; Ma inen e al., 2013). In pa icula , he CCA applied o indi idual SNPs pe o med much wo se ha he pai wise es ing, al hough p e iously i has been epo ed o ha e clea ly highe powe . The explana ion is ha he e we applied he me hods o all SNPs, including he a e a ian s. Speci ically, he single-SNP-CCA s a s o o e i when applied o a e a ian s. Fo example, when we in es iga ed he esul s mo e ca e ully, we disco e ed SNPs in which he mino allele was p esen in ew indi iduals, and such indi iduals could be almos pe ec ly iden i ied by a seemingly andom combina ion o pheno ypes, leading o a la ge spu ious canonical co ela ion es sco e (o , equi alen ly, a highly signi ican P- alue). Bayesian educed ank eg ession and spa se CCA we e less a - ec ed by he o e i ing because hey exploi ways o con ol he complexi y o he model, he o me using he in o ma i e p io s, he la e using he c oss- alida ion. Combining in o ma ion o e se e al SNPs using CCA o ela ed me hods has ecen ly been demons a ed o imp o e powe o de ec associa ions unde ce ain condi ions (Ma inen e al., 2013; Tang and Fe ei a, 2012; Zhang e al., 2011). He e we see ha he spa se CCA and also he Bayesian educed ank eg ession, which use mul i-SNP in o ma ion, ha e lowe powe in he genome-wide analysis han he simple pai - wise es ing. The di e ence om he ea lie expe imen s is ha he e he me hods a e applied o geno ype da a wi h a much highe SNP densi y, as ob ained h ough ca e ul impu a ion. The conclusion is ha i he mul i-SNP in o ma ion has al eady been used wi hin he impu a ion p o ocol, he powe o de ec associa ions canno , in gene al, be expec ed o imp o e by using mul i-SNP models. Fo a mo e de ailed compa ison be ween he Bayesian educed ank eg ession and he exhaus i e pai wise es ing, Supplemen a y Figu e S6 shows a Q-Q plo o he sco es (bo h PTVE and PTVE- a e) agains he expec ed sco es ha ha e been ob ained by pe mu a ion. The Supplemen a y Figu e S6 also shows genes de ec able by he simple exhaus i e pai wise sea ch. Bo h Q-Q plo s, bu PTVE in pa icula , indica e an excess o la ge es sco es, e lec ing he ac ha a leas some ue associa ions a e de ec ed by he model. We u he see ha al hough wi h PTVE- a e sco e ewe genes can be de ec ed han wi h PTVE, none o he op-sco ing genes om PTVE- a e a e lagged by he pai wise app oach, making PTVE- a e an a ac - i e sco e o mining associa ions ha migh be missed by he s anda d me hod. 4 DISCUSSION We ha e p esen ed a new s a is ical me hod o in es iga ing associa ions in Genome-wide associa ion s udy (GWAS) da ase s wi h mul i a ia e pheno ypes. The me hod can combine in o - ma ion o e mul iple SNPs, making i pa icula ly sui able o s udying a e a ian s in he high-dimensional pheno ype se ing. Fo his se up, no me hods known o he au ho s ha e been Table 2. Powe compa ison o he di e en me hods Me hod FDR ¼0FDR¼0.1 FDR ¼0.2 FDR ¼0.4 No el PTVE 36 55 103 305 167 PTVE- a e33366 Pai wise 103 176 243 651 300 CCA,singleSNP77 71111 Spa se CCA 37 50 66 117 51 No e: The able shows he numbe s o gene-me abolome associa ions ha had alse disco e y a e below he speci ied h eshold. The las column shows he numbe o pu a i e no el associa ions wi hin genes wi h FDR ¼0.4 a e emo ing he known associa ions as desc ibed in he main ex . 2032 P.Ma inen e al. p esen ed be o e. Ou me hod is based on es ima ing he p opo - ion o o al a iance o he pheno ypes ha is explained by he SNPs unde conside a ion. Fo his pu pose, we ha e de i ed a Bayesian o mula ion o he educed ank eg ession model, which enables us o inco po a e ou knowledge o he expec ed e ec s sizes in he analysis. We used he new me hod o analyze a eal GWAS da ase wi h a mul i a ia e lipop o ein pheno ype. Two no el loci no p e i- ously associa ed wi h he pheno ype we e disco e ed and epli- ca ed in an analysis combining wo addi ional da ase s. Fu he mo e, wo mo e loci we e ound ha eplica ed signi i- can ly in one bu no in he o he es da ase . Possible easons o he lack o success in eplica ing he indings in bo h he da ase s include he ollowing: (i) he associa ions we e alse posi- i e in he i s place, (ii) he associa ions in ol ed a e a ian s ha we e no p esen in su icien numbe s o see he e ec s, (iii) he impu a ion accu acy o he a e a ian s was no su icien in all da ase s, (i ) he pheno ype da a, al hough p ep ocessed in exac ly he same way wi h all he da ase s, ha e no been ully equi alen . Fo example, he scaling o he pheno ypes du ing p ep ocessing has been done using ac o s no exac ly equal, and he pa ame e s lea ned in one da a may hus no ep esen he e ec s adequa ely in ano he da a. Only u he s udies will help o dis inguish be ween he al e na i e explana ions. Fo doing in e ence wi h he model, he cu en implemen a- ion uses MCMC sampling, he compu a ion ime o which is app oxima ely hal an hou pe gene on a 2.3 GHz p ocesso . Thus, analyzing all human genes equi es a clus e compu e o pa allelize he compu a ions o e he genes. Analy ical app oxi- ma ions, such as he a ia ional o Laplace app oxima ions, e.g. Bishop (2006), could be used o speed up he compu a ions and, based on ou expe imen s wi h he cu en me hod, a e wo h doing in he u u e. Al e na i e ways o use he model migh also be conside ed. Fo example, ocusing he analysis on a ian s wi h a p edic ed unc ion could imp o e powe o de ec associa ions and lessen he compu a ional bu den. 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