666.19 - Checking Pairwise Relationships Lecture 19 Biostatistics 666 Last Lecture Markov Model for Multipoint Analysis X1 X3 X2 P X 1 | I1 P X 2 |

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Checking Pairwise Relationships Lecture 19 Biostatistics 666
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Last Lecture: Markov Model for Multipoint Analysis 1 X 2 X 3 X M X 2 I 3 I M I 1 I ) | ( 1 2 I I P ) | ( 2 3 I I P (...) P ) | ( 1 1 I X P ) | ( 2 2 I X P ) | ( 3 3 I X P ) | ( M M I X P IBD states along the chromosome are modeled using a Markov Chain …
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The Likelihood of Marker Data ∑∑ ∑ = = = 12 1 2 1 1 ) | ( ) | ( ) ( ... II I M i i i M i i i M I X P I I P I P L z General, but slow unless there are only a few markers. z Combined with Bayes’ Theorem allows us to estimate probability of IBD states at any marker.
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Worked Example z Consider two loci separated by θ = 0.1 z Each loci has two alleles, each with frequency .50 z If two siblings have the following genotypes: Sib1 Sib2 Marker A: 1/1 2/2 Marker B: 1/1 1/1 z What is the probability of IBD=2 at marker B when… You consider marker B alone? You consider both markers simultaneously?
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Solution I 1 I 2 P(I 1 )P ( I 2 |I 1 ( X 1 |I 1 ( X 2 |I 2 ) Prob 00 01 02 10 11 12 20 21 22
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Solution I 1 I 2 P(I 1 )P ( I 2 |I 1 ( X 1 |I 1 ( X 2 |I 2 ) Prob 0 0 0.25 0.67 0.0625 0.0625 0.00066 0 1 0.25 0.30 0.0625 0.125 0.00058 0 2 0.25 0.03 0.0625 0.25 0.00013 1 0 0.5 0.15 0 0.0625 0.00000 1 1 0.5 0.70 0 0.125 0.00000 1 2 0.5 0.15 0 0.25 0.00000 2 0 0.25 0.03 0 0.0625 0.00000 2 1 0.25 0.30 0 0.125 0.00000 2 2 0.25 0.67 0 0.25 0.00000
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Solution z Taking into account all available genotype data… P(I 1 = 2) = 0.09 P(I 1 = 1) = 0.42 P(I 1 = 0) = 0.49 z Considering only one marker, the corresponding probabilities would be 0.44, 0.44 and 0.11. Quite a difference!, but which value do you expect to be more accurate?
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The Likelihood of Marker Data ∑∑ ∑ = = = 12 1 2 1 1 ) | ( ) | ( ) ( ... II I M i i i M i i i M I X P I I P I P L z General, but slow unless there are only a few markers. z How do we speed things up?
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Extending the MLS Method … z We just change the definition for the “weights” given to each configuration! ) ( ) ( ) | ( ) | ... ( ) | ... ( ) | ( 1 1 1 j j j j j j j M j j j j j j I R I L I X P I X X P I X X P I X P w = = +
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Today … z Checking accuracy of reported relationships Why is this an important problem?
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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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666.19 - Checking Pairwise Relationships Lecture 19 Biostatistics 666 Last Lecture Markov Model for Multipoint Analysis X1 X3 X2 P X 1 | I1 P X 2 |

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