666.18 - Multipoint Analysis for Sibling Pairs...

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Multipoint Analysis for Sibling Pairs Biostatistics 666 Lecture 18
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Previously … z Linkage analysis with pairs of individuals “Non-parametric” IBS Methods “Maximum Likelihood” IBD Based Method Possible Triangle Constraint
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ASP Methods Covered So Far … z Increasing degrees of sophistication and complexity z In each case, only a single marker is evaluated…
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IBS Based Linkage Test [ ] 10 ln 2 ) ( ) ( 2 2 2 2 χ = = = = = LOD N E N E N i i IBS i IBS i IBS df z Expect counts calculated using: Allele frequencies for marker Relationship for affected individuals
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Likelihood for a Single ASP ij i ij j ij j j i w j IBD Genotypes P w w z j IBD Genotypes P ASP j IBD P L ate proportion need only We ) | ( defines (1990) Risch ) | ( ) | ( 2 0 2 0 = = = = = = = =
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MLS Linkage Test 2 1 0 2 4 1 1 2 1 0 4 1 2 2 1 1 0 0 10 2 1 0 z , z , z of MLEs at the evaluated LOD the is statistic MLS The log ) , , ( ∏∑ + + + + = = 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
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Possible Triangle Constraint z For any genetic model, we expect ASPs to be more similar than unselected pairs of siblings. z More precisely, Holmans (1993) showed that for any genetic model z 2 ¼ z 1 ½ and z 1 2 z 0 z 0 ¼
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Further Improvements … z All these methods lose information when a marker is uninformative in a particular family… z Today, we will see how to use neighboring markers to extract more information about IBD.
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Intuition For Multipoint Analysis z IBD changes infrequently along the chromosome z Neighboring markers can help resolve ambiguities about IBD sharing z In the Risch approach, they might ensure that, effectively, only one w is non-zero 22 21 12 11 1 1
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Today … z Framework for multipoint calculations
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666.18 - Multipoint Analysis for Sibling Pairs...

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