Backward Haplotype Transmission Association (BHTA) Algorithm. Tian Zheng Department of Statistics Columbia University. February 5 th, 2002

Transcription

1 Backwad Haplotype Tansmsson Assocaton (BHTA) Algothm A Fast ult-pont Sceenng ethod fo Complex Tats Tan Zheng Depatment of Statstcs Columba Unvesty Febuay 5 th, 2002 Ths s a jont wok wth Pofesso Shaw-Hwa Lo n the Depatment of Statstcs at Columba Unvesty. 1

2 Outlne Backgound Genetcs temnology Bologcal bass of genetc mappng Cuent assocaton methods Issues on mappng fo complex tats Intoducton Issues we addessed usng the poposed method. Illustatve example Algothm Detals Dscusson Pefomance of the BHTA algothm Poblem and soluton Futue effots Summay 2

3 Chomosomes and Genes the genetc nfomaton cae Nucleus of body cell One Stand of chomosome Two copes of gene A Alleles Gene 1 One pa of chomosomes Gene 2 Two copes of gene B Alleles 3

4 eoss: Cossove and Recombnaton the bass of genetc mappng Haplotype Cossove Recombnatons 4

5 Lnkage and Lnkage Dsequlbum bass of cuent mappng algothms to locate dsease susceptblty loc utant allele, whch wll make ncease the sk of the dsease Souce: Assocaton Study Desgns Fo Complex Dseases Lon R. Cadon and John I. Bell. Natue Revews Genetcs Volume 2,

6 Assocaton ethods fo the mappng of dsease susceptblty loc Case-contol study Use famly-based contols Tansmsson/Dsequlbum Test (TDT) case-paent to method (Spelman et al. 1993) Assume a make wth alleles and m s studed. Tansmtted Untansmtted m a b m c d The test statstc used s a T = 2 χ statstc wth d.f.=1, ( b c) b+ c 2 6

7 Sceenng fo Complex Tats Complex dseases multfactoal dseases ae caused by multple genes nteactng wth each othe and wth envonmental factos to ceate a gadent of genetc susceptblty to dsease. (Weeks and Lathop 1995) Badet-Bedl Syndome (BBS): Bughes et al (2001) Scence VOL 293:

8 Haplotypc Tansmsson Dsequlbum Assume each make has two alleles ( n, m). Assume a paent of a patent has two haplotypes: h m1 n1 m 2 m 2 =,and h = m9 m9 m n P( h tans., h untans dseased chld) 1 2 P(dseased h tans., h untans) Inteacton among P(dseased) dsease genes P(dseased tans. alleles at loc a, b, c) = P(dseased) 1 2 = Ph ( 1 tans., h2 untans) tans. alleles at loc a, b, c p(tans. alleles at a, b, c, h1 tans. & h2 Lnkage/LD between the makes and the dsease loc untans) 8

9 Cuent Genome Scan methods and ultponts algothms ultple ndvdual Lnkage o Assocaton tests had to establsh sgnfcance, can t handle nteacton among dsease genes. Haplotype TD tests fo tghtly lnked makes the econstucton of the tansmsson matx, the matx s too lage and spase to 2 cay out a vald χ test. The Call fo moe genealzed haplotype based methods thee seems to be a geat need fo the development of multlocus tests of assocaton that make use of haplotype nfomaton, snce these mght pove to be much moe effcent. J. Ptchad and. Pzewosk (June 2001). Am. J. Hum. Genet. 69: 1-14,the most nfomatve and cost effectve method of LD mappng that based on haplotypes. D. Clayton, J. Todd et al (Octobe 2001). Natue Genetcs Volume 29:

10 BHTA Intoducton Backwad Haplotype Tansmsson Assocaton (BHTA) algothm A fast mult-pont sceenng algothm based on haplotypc tansmsson dsequlbum ultpont Sceenng Fast and memoy-effcent Use haplotypc tansmsson nfomaton takng nto account possble nteactons among dsease susceptblty loc Automatcally select a set of mpotant makes as sceenng esult 10

11 Results Fom 2001Pape fo Glles de la Touette Syndom by Ingd Smonc, Jug Ott, et al. Amecan Jounal of edcal Genetcs (Neuopsychatc Genetcs) 105: (2001) Results Summay Fom TDT and HRR Analyses Ognal Case-Contol Study Follow Up Famlal TDT and HRR Study Ch Locus 1-Locus TDT Extended Haplotypes 2- Locus TDT 2-Locus HRR 3-Locus HRR c fom p-tel p p p p p 2 D2S D2S D2S D8S T D8S GATA28F D8S D11S < D11S D11S D20S D20S GATA45C D21S

12 Result fom BHTA algothm 5 akes dentfed by BHTA sceenng: Ch 2 Ch 8 D2S440 GATA28F12 D8S559 Ch 11 D11S1377 Ch 20 D20S469 Evaluated usng pemutatons unde null hypothess: p-value 10 4 Haplotypc Tansmsson Dsequlbum Obseved feq untansmtted Obseved feq tansmtted to the patent Haplotypes ae defned by the 5 makes selected 12

13 Data: genetc nfomaton of a andom sample of n patents and the paents. 2n paent-patent tansmsson pas Each pa conssts of two haplotypes one tansmtted and the othe untansmtted th Fo k pa, let tk be the haplotype tansmtted to the dseased chld, and u k be the untansmtted. Defne n, j= #( tk = h, uk = hj), as the numbe of tansmssons whch tansmtted to the dseased chld and left untansmtted. h j h 13

14 Counts summazng the haplotype tansmssons ae also defned as follows: t n = #( t = h) = n k j u n = #( u = h) = k, j n, j A statstc haplotype tansmsson dsequlbum (HTD) s defned to measue the amount of lnkage/ld nfomaton contaned n the set of makes beng tested: t u 2 ( ), HTD = n n whose expectaton unde the null hypothess s popotonal to the tace of the Fshe s nfomaton matx usng haplotype elatve sks. 14

15 Idea of sceenng: Pck out makes contans lttle amount of lnkage nfomaton, one at a tme untl all the makes emaned ae mpotant n tems of lnkage/ld wth the dsease. Assume m makes S = { 1, 2,..., m} ae beng tested, and we want to evaluate the nfomaton th contaned n the make, whch has 2 alleles a and b. th Consde S = S / ( -deleted make set). Let H = { h, h,..., h } 1 2 H be the set of haplotypes spanned by S, and the t u counts,and can be defned as befoe. n n 15

16 t t Denote by n( a) and n( b), the numbe of tansmssons of the enlaged haplotypes: h a, and h b, espectvely. u u Smlaly, two counts n ( a) and n ( b) ae defned fo the non-tansmssons of the enlaged haplotypes. It s easy to obseve that t t t n = n ( a ) + n ( b ) u u u n = n ( a ) + n ( b ) 16

17 Fo example, T U ABdE 1 AbDe 1 AbdE 1 Abde 1 abde 1 1 abde 1 abde 1 t n t t u u n n ( E ) n () e n ( E ) n () e u ABd AbD Abd abd abd

18 HTD fo m makes, S = { 1, 2,..., m} : HTD( m) = ( n ( a )- n ( a )) + ( n ( b )- n ( b )) h H t u 2 t u 2 HTD fo the m-1 makes n S = S / : th -deleted make set t u HTD ( m 1) = ( n n ) h H 2 t t u u = ( n ( a ) + n ( b ) n ( a )- n ( b )) h H = ( n ( a ) n ( a )) + ( n ( b )- n ( b )) = h H t u 2 t u 2 t u t u + 2 ( n ( a ) n ( a )( n ( b )- n ( b )) HTD( m) t u t u + 2 ( n ( a ) n ( a )( n ( b )- n ( b )) h H h H 2 18

19 Thus, the amount of nfomaton bought by make can be evaluated usng the HTD dffeence the nfomaton dop. HTD ( m 1) = HTD ( m 1) HTD( m) t u t u = 2 ( n( a) n ( a)( n( b)- n ( b) ) h H Haplotype Tansmsson Assocaton (HTA) s ntoduced as follows, h h t u t u HTA ( m) = ( n( a) n ( a)( n( b)- n ( b)) + n( ) a b h H h H 19

20 The popetes of HTA statstc: Expectaton of HTA ( m) ost mpotant contbutes mpotant lnkage Negatve nfomaton to the cuent make set. Zeo only contans edundant lnkage nfomaton what s aleady caed by some makes n the set S ; th -deleted make o no make n the data set s assocated wth any dsease susceptblty loc. Postve contbutes no lnkage nfomaton but nose to the data, and dlutes the tue lnkage/assocaton nfomaton caed by othe makes. Least mpotant 20

21 BHTA algothm based on the HTA statstc Data {,,..., } S = 1 2 K s the total numbe of makes. K m s the numbe of makes etaned n S. Fo each = 1,2,..., m, calculate HTA ( m ) fo. Delete the make wth the hghest HTA ( m ) n S and contnue n the loop. Any postve HTA? Yes No Retun S as sceenng esult wth an HTD scoe. 21

22 Evaluaton of the sgnfcance 1. ultpont TDT tests 2. Pemutaton test (Lazzweon and Lange 1998) th Fo k patent-paent tansmsson pa, ( t, u ), t k was what actually tansmtted to the dseased chld, and u k s the untansmtted. Pemute the tansmtted label unde the null hypothess fo each pa to get a duplcate of the ognal data. * Use ndependent valdaton data snce the BHTA sceenng algothm tends to fnd the maxmal tansmsson dsequlbum n the data. k k 22

23 Smulaton usng the BBS model At each dsease susceptblty locus, assume thee ae thee makes (wth stong lnkage/ld) beng tested. The esult fom ndvdual TDT: agnal TDT pefomance: 150 patents Acceptance egon

24 BHTA s powe detectng tue lnkage: Oveall powe detectng the 3 susceptblty loc (the esultng make set cove all of them) s 75%. Fo each of the loc, the detectng powe of BHTA sceenng algothm usng 150 patents s 90% 30 mk,(nolk) 150 patents, 1000 sceenngs colsums(geneout04.data2)[1:30] Index Oveall powe detectng the 3 loc : 75% 24

25 Infomaton flow dung BHTA sceenng nfomaton steps Red dot: make deleted s unassocated; Blue dot: make deleted s assocated. Black lne: unde tue lnkage (altenatve) Blue/yellow lne: no lnkage/ld (null) Vetcal lnes: whee the sceenng stopped altenatve, null 25

26 Poblem: Sample sze and the numbe of makes affect the pefomance of the sceenng. Spaseness at the begnnng of the sceenng leads to andom deleton. Soluton: two-stage sceenng 100 mk,(lk) 250 patents, 5000 smulatons colsums(geneout04.data2)[1:100] Index 26

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28 Futue effots 1. Extenson to moe genealzed complex tats Quanttatve tats Onset age 2. Futhe nvestgaton of the two-stage sceenng pocedue. Reasonable theshold Pefomance 3. Develop pocedues based on ths algothm, fo lage set of makes, say moe than Desgn of algothm based on the same dea fo patents wth only affected sblng o elatves nfomaton. 5. Possble development of elated softwae 28

29 Summay BHTA algothm A fast haplotype-based algothm able to handle complcated nteacton among dsease loc. Woks wthout specfc dsease model peassumed. Able to handle 100+ makes at the same tme. Tme effcent no e-constucton of tansmsson matx and avods tedous computaton. Especally useful, f some canddate loc o egons have been found. 29