2006.666.21 - The Lander-Green Algorithm in Practice...

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The Lander-Green Algorithm in Practice Biostatistics 666 Lecture 21
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Last Lecture: Lander-Green Algorithm z Similar multipoint sib-pair analysis, but with: More general definition for I, the "IBD vector" Probability of genotypes given “IBD vector” Transition probabilities for the “IBD vectors” = = = 1 1 2 1 1 ) | ( ) | ( ) ( ... I m i i i I m i i i I X P I I P I P L m
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Lander-Green Recipe z 1. List all meiosis in the pedigree There should be 2n meioses for n non-founders z 2. List all possible IBD patterns Total of 2 2n possible patterns defined by setting each meiosis to one of two possible outcomes z 3. At each marker location, score P(X|I) Evaluate using each possible founder allele graph I
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Lander-Green Recipe z 4. Build transition matrix for moving along chromosome Patterned matrix, built from matrices for individual meioses = + n n n n n T T T T T ) 1 ( ) 1 ( 1 θ
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Lander-Green Recipe z 5. Run Markov chain Start at first marker, m =1 Build a vector listing P(G first marker |I) for each I Move along chromosome Multiply vector by transition matrix Combine with information at the next marker Multiply each component of the vector by P(G current marker |I) Repeat previous two steps until done
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Pictorial Representation z Forward recurrence z Backward recurrence z At an arbitrary location
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Today: Lander-Green Algorithm in practice z Common applications of the algorithm Non-parametric linkage analysis Parametric linkage analysis Information content calculations z Refining the Lander-Green algorithm Speeding up transition step Reducing size of inheritance space
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Part I: Common Applications z Non-parametric linkage analysis z Parametric linkage analysis z Information content calculation Time permitting!
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Nonparametric Linkage Analysis z Model-free z Does not require specification of a trait model z Tests for excess IBD sharing among affected individuals
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Non-parametric Analysis for Arbitrary Pedigrees z Must rank general IBD configurations Low scores correspond to no linkage High scores correspond to linkage z Multiple possible orderings are possible Especially for large pedigrees z Under linkage, probability for vectors with high scores should increase
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Nonparametric Linkage Statistic z Let S(I) be a statistic that ranks IBD vectors z Then, following Whittemore and Halpern (1995) [] ) 1 , 0 ( ~ ) ( ) ( ) ( ) ( ) ( ) | ( ) ( ) ( 2 2 N G S Z G P G S G P G S G I P I S G S G G I σ µ = = = =
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Nonparametric Linkage Statistic z Original definition not useful for multipoint data… z Kruglyak et al (1996) proposed: [] ) 1
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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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2006.666.21 - The Lander-Green Algorithm in Practice...

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