ibdreg: An R package fr Genetic Linkage with Cvariates Jasn Sinnwell Daniel Schaid August 10, 2007
ibdreg: utline Intr t Linkage (brief) Why d linkage with cvariates? Methdlgy in ibdreg Dem f ibdreg n prstate cancer data 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 2
Linkage Intr: Genetic Analysis Types Segregatin Analysis - Use family data t determine the extent t which a disease is genetic Linkage Analysis Use family data t lcate a chrmsme segment that is inherited jintly with a disease lcus Assciatin Analysis Use unrelated data t find a genetic effect f a particular DNA marker(s) n a disease 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 3
Intr t Linkage: Recmbinatin Mendel prpsed genes (n peas) are inherited independently f ne anther Nt quite right -- genes / markers which are clse tgether shw assciatins During meisis, crrespnding DNA segments can recmbine in any lcatin Recmbinatin is smewhat cnstant ver the whle genme In general, clse markers have fewer recmbinatins 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 4
Intr t Linkage, basic plt 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 5
Linkage with Cvariates: illustrated Nuclear family with 4 children, 3 affected with disease ped1, early age-f-nset 1 2 If genetic linkage: persns 3,5 share mre alleles near disease lcus persns 3,4 share fewer alleles at disease lcus 3 age=30 4 5 age=31 6 age=24 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 6
Linkage with Cvariates: IBD Sharing Identity-By-Descent (IBD): alleles that have been inherited frm the same ancestr Estimate prbability f sharing 0, 1, and 2 alleles IBD: f 0, f 1, f 2 Use Merlin, Genehunter, etc. Estimated IBD sharing fr a relative pair: s = + r 2 f 1f r, 2 r,1 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 7
Linkage with Cvariates: illustrated ped2, late age-f-nset Nuclear family, tw affected siblings Late-nset frm f the disease 1 2 3 age-60 4 5 age-55 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 8
Linkage with Cvariates Ped1 and Ped2 culd be tw frms f disease: early and late nset Mixture f gene and envirnment effects, i.e. disease hetergeneity Assume the early nset is genetically linked at lcus L IBD sharing at L is: ped1: greater than null ped2: smewhere near null 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 9
Linkage with Cvariates The mre alike the cvariates, the mre allele sharing is expected Cnsider a functin f the age f nset fr affected siblings: 1. age1 + age2 2. age1 * age2 3. ( age1-60 * age2-60 ) 2 Define any functin that applies t the disease and cvariate impact 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 10
Linkage with Cvariates Intuitively, affected relative pairs with similar cvariates share mre alleles than the null Linear relatinship fr IBD sharing and pair-specific cvariates (X): m r, m r : Expected s r under linkage, n linkage = scaling factr fr the relatinship types c r X * r = c r 0 r m = m + c Xβ = [1 r X ] r X * r β 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 11
ibdreg methd Quasi-likelihd scre functin: n T 1 U = Di Vi ( Si Mi) i= 1 where i = 1..n pedigrees S i, M i : vectrs f estimated and expected (H ) allele sharing D i : derivative f M i with respect t β V i : cvariance matrix f the S i vectr 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 12
ibdreg methd Develp a chi-square test: where V u T n = X i= 1 * T i = V 1 0, i U T V 1 U u With q degrees f freedm: X * i q=1 fr intercept-nly (linkage) q=2 fr intercept with 1 cvariate etc. 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 13
ibdreg methd Available tests (degrees f freedm) 1. Linkage withut cvariates (q=1) 2. Linkage with p cvariates (q=1+p) 3. Effect f p cvariates n IBD sharing, adjusting fr linkage (p) 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 14
ibdreg applied Data: sample f pedigrees ascertained at May Clinic (SE MN) fr having multiple cases f prstate cancer 159 pedigrees (max 21 peple) 495 affected relative pairs (ARPs) Cvariate: age-f-nset (dxage) 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 15
ibdreg applied LODPAL, f S.A.G.E., apprximates a pseud-likelihd f IBD sharing prbabilities by a trinmial lgistic regressin mdel (blue line) Cmpare t ibdreg (green line), bth using sum(dxage) as a cvariate Als include ibdreg, linkage-nly (black line) Same c scale (genetic effect between dminant and recessive) 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 16
Ibdreg, applied 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 17
ibdreg applied Fr figure abve, nte a few things: LODPAL and ibdreg generally clse Differences: 1. Narrw peaks (ch6, ch20) 2. Ends f chrmsmes (ch5) Bth may be attributable t instability f maximizing pseudlikelihd f LODPAL 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 18
ibdreg applied: R cde # lad the library R> library(ibdreg) # lad cvariate data, cntaining ped id and persn id t match file R> cv.data <- read.table("cv.data.csv", sep=",") # create data.frame with id (ped and persn) and IBD data with Merlin results R> ibd.dat.bj <- create.ibd.dat(pstfile="chr20.pst.ibd", prirfile="chr1.prir.ibd") # simulate ibd.var bject using gene-drpping # requires a.pre file fr pedigree specs R> ibd.var.bj <- sim.ibd.var("ch.20.pre", n.sim=10000) 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 19
ibdreg applied: R cde # define a functin fr the sum f cvariates R> pairsum <- functin(cv1,cv2) {cv1+cv2} # run ibdreg fr AA relatives, # with cvariate sum(dxage), minimax c scaling R> sum.dxage.aa <- ibdreg(frmula=~pairsum(dxage), status.methd="aa", c.scale="minimax", status=pcstat, ped.id=ped.id, persn.id=persn.id, data=cv.data, ibd.dat=ibd.dat.bj, ibd.var=ibd.var.bj) 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 20
ibdreg applied: chrmsme 20 Linkage signal different lcatin frm linkage w/cv In nn-peak, linkage w/cv is smaller --1 mre deg. f freedm Cv Effect has small cntributin t linkage signal 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 21
ibdreg applied: all ARPs Disregarding cvariates, we can test linkage n all 495 relative pairs in the example, which cntain sub-grups AA: Affected-Affected (429) UU: Unaffected-Unaffected (7) AU: Affected-Unaffected (59) Sharing under linkage is expected as AA: Mre than null UU: Mre than null, but less than AA UU: Less than null 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 22
Ibdreg applied, all ARPs Linkage tests fr all relative pairs Test fr linkage in directin expected under linkage: AA-mre UU-mre AU-less Overall linkage is driven by AA pairs 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 23
ibdreg applied: unexpected sharing IBD allele sharing can be invalid by: 1. Mis-specify marker allele freq when parents missing 2. Incrrect pedigree relatinships 3. Unaccunted inbreeding The χ 2 test fr linkage given as bth uncnstrained and cnstrained t favr linkage (1-sided, smaller p-value) If p uncnstrained < p cnstrained, indicates unexpected IBD sharing (chrms 1, 7, 12) 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 24
8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 25
ibdreg, cncluded Allws multiple tests fr linkage Prvides ptins fr specifying cvariates and scaling (c r ) Scaling avids fitting new regressin line fr each relatinship type Linear regressin is easy t fit, and easy t apply weights t accunt fr dependence f variance n cvariates Returned S3 bject with print and plt methds Perl scripts supplied t wrk with Merlin. 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 26
Thank Yu Fr mre details and references see: Schaid DJ, Sinnwell JP, Thibdeau SN. Testing genetic linkage with relative pairs and cvariates by quasilikelihd scre statistics. Hum Hered. 2007;64(4):220-33. Epub 2007 Jun 12. 8/10/2007 Divisin f Bistatistics, May Clinic Cllege f Medicine 27