ASSOCIATION ANALYSES of the MAS-QTL DATA SET using GRAMMAR, PRINCIPAL COMPONENTS and BAYESIAN NETWORK METHODOLOGIES

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1 OSL ASSOCATO AALYSS of the MAS-QTL DATA ST using GAMMA, PCPAL COMPOTS and BAYSA TWOK MTODOLOGS Burak Karacaören, Tomi Silander, José M. Álvarez- Castro, Chris S. aley, Dirk Jan de Koning OSL STTT and (D)SVS, VSTY of DBG SCOTLAD, K T O F D V B S T Y G BC aster Bush esearch Consortium

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3 k n GWAS, genetic relations between and within cases and controls need to be taken into account 500 cases & 500 controls markers For isolated oulation with few founders roblem increases. Possible Solutions GAMMA(Aulchenko et al, 007) STAT (Price et al, 006) Fig. The actual significance level of the allele test as a function of the coefficient of inbreeding. Siegmund and Jakir, 007, The Statistics of Gene Maing, Sringer

4 Slajd 3 k er ikisi de onemlilik, ama akrabaligin artmasina dayali olarak seviye dusuyir, boylece diyelim bir isaretci 0.0 cikiyor onemlilik, akrabalik arttikca buna onemlidir demen gerekiyor. karacao;

5 OSL LKAG DSQLBM TOP SPs FOM GWAS Many significant SPs from GWAS in LD Co-linearity among these SPs. Wang and Abbott (008) suggested using (PCeg) aroach. T O F D V B S T Y G BC aster Bush esearch Consortium

6 Malovini et al, 009, BMC Bioinformatics, 0: S7 Most GWAS studies do not model correlations: Among SPs Between SPs and environmental variables Bayesian networks are models that resent statistical deendencies and indeendencies in the joint robability distribution of the data.

7 OSL STMATO of SPs ffects esiduals may be used, but these may not be normally distributed. The atural and Orthogonal interactions model (OA) (Castro et al, 008) could be useful to decomose effects orthogonally. T O F D V B S T Y G BC aster Bush esearch Consortium

8 GAMMA/ STAT PCeg Bayesian etwork OA

9 Genome-wide aid Association using Mixed Model and egression y = Xb + Za + e () y = Xb + η + e () Princial comonent analyses. Princial comonents analyses used to orthoganize the genomic sace; y y y = a = a = a x x x + a + a + a M x x x + K + a + K+ a + K + a x x x with the coefficients being chosen so that y,, y, K y account for most of the exlanatory roortions of the total variance of the original variables, x, x, K, x, (veritt et al., 00).

10 BAYSA TWOK An imortant roerty of Bayesian network models is that the joint robability distribution over the model variables factorizes to a roduct of n conditional robability distributions: n,, X n ) = P X i i= ( ) P( X K, where denotes the arents of variable i i X i (Myllymaki etal, 00). SP3 SP SP SP4

11 qtscore(feno, df, gaussian) GAMMA SLTS qtscore(formula, data, snsubset, idsubset, strata, trait.tye, times, qu log0(p value) log 0 (P value) Chromosome Chromosome Before ermutation After 000 ermutations

12 Scree Plot of m3-m836 Loading Plot of A4,..., A9764 igenv alue Comonent umber Second Comonent A803 A475 A843A88 A8480 A8474 A795 A7993 A7995 A8486 A836 A7988A95 A5668 A8584 A8583 A9587 A7844 A3870 A4 A3435 A7399 A97 A96 A8880 A8573 A934 A8437 A844 A6040 A5866 A390 A73 A945 A93 A84 A946 A938 A69 A4999 A4675 A8389 A7870 A5004 A485 A345 A3439 A49 A490 A8338 A8395 A956 A98 A340A3 A540 A870 A856 A7664 A853 A8400 A7608 A896 A9590 A958 A8873 A843 A807 A603 A67 A855 A7530 A759 A63 A964 A89 A683 A950 A945 A937 A88 A09 A988 A03 A764A76 A7595 A8 A783 A5579 A4958 A08 A33 A483 A4834 A8535 A6454 A644 A656 A955 A486 A9309 A599 A7764 A94 A857 A765 A6569 A489 A3679A367 A736 A3444A309 A46 A06 A487A75 A670 A8953 A8963 A847 A365 A8 A795 A6546 A6543 A776 A59 A95 A48 A7480 A7495 A7486 A934 A0 A735 A3 A084 A66 A083 A6536 A7607 A690 A8005A57 A39 A8458 A808 A36 A738 A767 A745 A304 A798 A8 A9000 A8955 A8003 A954 A734 A389 A497 A496 A8960 A794 A653 A643 A64 A73 A6559 A69 A784 A9707 A70 A648 A6500 A649 A785 A8508 A969 A9694 A970 A9679 A9687 A808 A8879 A6578 A795 A857 A8948 A8945 A A4059 A4058 A4063 A4056 A First Comonent 0.0 A9684 A9677 A9688 A9764A9703 A97 A968 A975 A97A970 A9756 A975 A965 A9698 A9693A9 A9760 A9755 A975 A9763 A Scree lot from rincial comonents of To SPs based on GAMMA. Loading lot for first rincial comonents.

13 igenvalue -log() Comonents Scree lot using 0 rincial comonents for Binary trait. Position esults of rincial comonent stratification based on 0 rincial comonents.

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15 OSL Marker A8 A8363 A8 A8 A8035 A839 V S Y T T O F Chi BC G Marker A900 A900 A8363 A835 A839 A835 D B aster Bush esearch Consortium P(Chi) D CorrCoeff Drime AC ex(arc)

16 Marker Marker ChiSq ProbChi D CorrCoeff Drime Delta ProDiff YulesQ AC A599 A A599 A A30 A A30 A

17 Linear Model OA esidual(%) Phenotye(%) esidual(%) Phenotye(%) First00SPs andom00sps Table. stimation of SPs effects for first 00 and random 00 SPs with linear and OA model. SP LA(%) OA(%) Frequency istogram of esidual_ esidual_ 0 5 Table. stimates of exlanatory roortions for to SPs from linear and OA models.

18 DSCSSOS/COCLSOS GAMMA can be used to accommodate genetic relationshi among cases and controls in GWAS. n ractice OA could be used to redict SPs effects with dominant effects. PCeg is useful to choose most imortant SPs from list of SPs in linkage disequilibrium. Bayesian Tree Structured etworks useful to introduce and investigate relationshis within/ among SPs and other environmental effects.

19 OSL FCS Myllymaki, P., Silander, T., Tirri,., ronen, P. B-Course: A Web-Based Tool for Bayesian and Causal Data Analysis. (00) nternational Journal on Artificial ntelligence Tools, Vol, o. 3, Siegmund D. and Yakir, B. (007) The statistics of gene maing. Sringer. Wang, K., and Abbott, D. (008) A rincial comonent aroach to multilocus genetic association studies. Genetic idemiology 3:08-8. T O F D V B S T Y G BC aster Bush esearch Consortium

20 OSL TAKS FO YO ATTTO T O F D V B S T Y G BC aster Bush esearch Consortium

21 OSL BC aster Bush esearch Consortium T V S T Y O F D B G The natural and orthogonal inter-actions (OA) model (Álvarez-Castro and Carlborg 007) is a genotye-to-henotye ma that unifies the so-called functional and statistical aroaches (see ansen and Wagner 00). ere, we are interested in the statistical formulation of OA for two alleles, a arameterization of the exected henotye of each genotye, i.e. the genotyic values G=(G ij ), in terms of genetic effects (additive and interaction effects). For one locus, this arameterization is G=S exanding to: = δ α µ 4 G G G The vector of genetic effects,, entails the oulation mean, µ, the additive, α, and the dominance, δ, effects. The arameterization is given by the genetic-effect design matrix, S, exressed as a function of the genotyic frequencies of the oulation