STA6178_2005(10) - Special topic for Rebecca and Amys...

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Linkage Disequilibrium Mapping of Complex Binary Diseases Two types of complex traits Quantitative traits –continuous variation Dichotomous traits –discontinuous variation o Binary , e.g., presence (1) or absence (0) of a disease o Multiple outcomes, e.g., none, moderate or severe disease Special topic for Rebecca and Amy’s project
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Consider a nature population One marker with two alleles M and m, Prob(M)=p, Prob(m)=1-p One QTL (affecting a binary trait) with two alleles A and a, Prob(A)=q, Prob(a)=1-q Four haplotypes: Prob(MQ)=p 11 =pq+D p=p 11 +p 10 Prob(Mq)=p 10 =p(1-q)-D q=p 11 +p 01 Prob(mQ)=p 01 =(1-p)q-D D=p 11 p 00 -p 10 p 01 Prob(mq)=p 00 =(1-p)(1-q)+D D is the linkage disequilibrium between the marker and underlying QTL
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Data structure Sample Binary (y i ) Marker (j) 1 1 MM (2) 2 1 Mm (1) 3 1 Mm (1) 4 1 mm (0) 5 0 MM (2) 6 0 Mm (1) 7 0 Mm (1) 8 0 mm (0)
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Arrange the data in a 2 x 3 contingency table Marker genotype 2 1 0 Affected (1) n 12 n 11 n 10 n 1 . Normal (0) n 02 n 01 n 00 n 0 . n. 2 n. 1 n. 0 n Affected (1) g 12 g 11 g 10 g 1 . Normal (0) g 02 g 01 g 00 g 0 . g. 2 g. 1 g. 0 1
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Independence test χ 2 df=2 = Σ l=0 1 Σ j=0 2 (n lj - m lj ) 2 /m lj = n Σ l=0 1 Σ j=0 2 (g li - g l .g. j ) 2 /(g l .g. j ) where m lj is the expected value of n lj , m lj =ng l .g.j. H0: g li = g l .g. j H1: g li g l .g.
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