666.17 - Modeling IBD for Pairs of Relatives Biostatistics...

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Modeling IBD for Pairs of Relatives Biostatistics 666 Lecture 17
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Previously … z Linkage Analysis of Relative Pairs z IBS Methods Compare observed and expected sharing z IBD Methods Account for frequency of shared alleles Provide estimates of IBD sharing at each locus
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IBS Linkage Test [ ] ( ) = = = = i i IBS i IBS i IBS df N E N E N ) ( 2 2 2 χ z E(N IBS=i ) depends on N and allele frequencies z Bishop and Williamson (1990)
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Likelihood for Sibpair Data ) pair relative affected | ( ) | ( defines (1990) Risch ) | ( ) | ( 2 0 2 0 i IBD P z j IBD Genotypes P w w z j IBD Genotypes P ASP j IBD P L i i ij j ij j j i = = = = = = =
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MLS Statistic of Risch (1990) algorithm M - E an using estimated be can z ˆ , z ˆ , z ˆ The z , z , z of MLEs at the evaluated LOD the is statistic MLS The 10 ln 2 ˆ ˆ ˆ log ) , , ( 2 1 0 2 1 0 2 2 4 1 1 2 1 0 4 1 2 2 1 1 0 0 10 2 1 0 ∏∑ = + + + + = = i i i i i i i i j ij j w w w w z w z w z LOD w z z z z L χ
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Today … z Predicting IBD for affected relative pairs Modeling marginal effect of a single locus Relative risk ratio ( λ R ) z The Possible Triangle for Sibling Pairs Plausible IBD values for affected siblings Refinement of the model of Risch (1990)
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Single Locus Model 1. Allele frequencies For normal and susceptibility alleles 2. Penetrances Probability of disease for each genotype z Useful in exploring behavior of linkage tests A simplification of reality z Ignore effect of other loci and environment
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Penetrance z f ij = P( Affected | G = ij) z Probability someone with genotype ij is affected z Models the marginal effect of each locus
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Using Penetrances z Allele frequency p z Genotype penetrances f 11 , f 12 , f 22 z Probability of genotype given disease P(G = ij | D) = z Prevalence K =
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Pairs of Individuals z A genetic model can predict probability of sampling different affected relative pairs z We will consider some simple cases: Unrelated individuals Parent-offspring pairs Monozygotic twins z What do the pairs above have in common?
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What we might expect … z Related individuals have similar genotypes z For a genetic disease… z Probability that two relatives are both affected must be greater or equal to the probability that two randomly sampled unrelated individuals are affected
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This note was uploaded on 12/26/2011 for the course BIO 666 taught by Professor Staff during the Fall '06 term at University of Michigan.

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666.17 - Modeling IBD for Pairs of Relatives Biostatistics...

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