IBD%20Estimation%20in%20Pedigrees

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IBD Estimation in Pedigrees

• Gonçalo Abecasis
• University of Oxford

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3 Stages of Genetic Mapping

• Are there genes influencing this trait?
• Epidemiological studies
• Where are those genes?
• Linkage analysis
• What are those genes?
• Association analysis

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(No Transcript)
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Relationship Checking
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Where are those genes?
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Tracing Chromosomes
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Sometimes it is easy
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Sharing, or Not?
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Data

• Polymorphic markers
• Eg. Microsatellite repeats, SNPs
• Allele frequency
• Location
• Task
• Phase markers
• Place recombinants

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Complexity of the Problem

• For each meiosis
• In a pedigree with n non-founders, there are 2n
  meioses each with 2 possible outcomes
• For each location
• One for each of m markers
• Up to 4nm distinct outcomes

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Elston-Stewart Algorithm

• Factorize likelihood by individual
• Each step assigns phase
• for all markers
• for one individual
• Complexity ? n 4m
• Small number of markers
• Large pedigrees
• With little inbreeding

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Lander-Green Algorithm

• Factorize likelihood by marker
• Each step assigns phase
• For one marker
• For all individuals in the pedigree
• Complexity ? m 4n
• Large number of markers
• Assumes no interference
• Relatively small pedigrees

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Markov-Chain Monte-Carlo

• Approximate solutions
• Explore only most likely outcomes
• Remove restrictions
• Pedigree size
• Number of markers
• Inbreeding
• Assuming no interference
• Computationally intensive

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Popular Packages

• Elston-Stewart Algorithm
• LINKAGE / FASTLINK (Lathrop et al, 1985)
• VITESSE (OConnell and Weeks, 1995)
• Lander-Green Algorithm
• Genehunter (Kruglyak et al, 1995)
• Allegro (Gudbjartsson et al, 2000)
• MCMC
• Simwalk2 (Sobel et al, 1996)
• LOKI (Heath, 1998)

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1. Enumerate Possibilities

• Enumerate gene-flow patterns
• Gene-flow pattern
• Sets transmitted allele for each meiosis
• Implies founder allele for each individual

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2. Founder Allele Sets

• For each gene flow pattern v
• Enumerate set A(G,v)
• All allele states a a1, , a2f
• Compatible with both
• Gene flow v
• Genotypes G
• The likelihood is L(vG) 2-2n?a?i f(ai)
• f(ai) is the frequency of allele ai

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For example ...
Genotypes
Gene Flow
Founder Alleles
Four meioses. Three one alleles
required. Likelihood ½4 f(a1)3
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Single Marker Probabilities

• We now have ...
• Likelihood for each gene flow pattern
• Conditional on genotypes
• Conditional on allele frequencies
• Conditional on a single marker
• Probability for each gene-flow pattern
• P(v) L(v) / ?vL(v)

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3. Allowing for Recombination

• Transition Probability
• T(va?vb, ?) (1-?)nr(Va,Vb)?r(Va,Vb)
• Transition Matrix

Location A
Location B
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Moving along chromosome

• Input
• Vector v of likelihoods at location A
• Matrix T of transition probabilities A?B
• Output
• Vector v of likelihoods at location B
• Conditional on likelihoods at A
• For k vectors, requires k2 operations

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Elston and Idury Algorithm

• Requires k log2 k operations

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Moving Along Chromosome
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Markov-Chains

• Single Marker
• Left Conditional
• Right Conditional
• Full Likelihood

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MERLIN

• Fast multipoint calculations
• Non-parametric linkage analyses
• Error detection
• e.g., unlikely obligate recombinants
• Haplotyping
• most likely, exhaustive lists, sampling

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Sparse Gene Flow Trees
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Dense maps

• Computational challenge
• Require more memory
• Require Lander-Green algorithm
• Limited pedigree size
• Computational advantages
• Reduced recombination between markers
• Approximate solutions possible if steps with many
  recombinants are ignored

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MERLIN Example Pedigrees
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MERLIN Timings
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MERLIN Memory Usage
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Command Line Options
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Effect of Genotyping Error

• Modest levels are likely
• Up to 1 may be typical
• Mendelian inheritance checks
• Detect up to 30 of errors for SNPs
• Effect on power
• Linkage vs. Association
• SNPs vs. Microsatellites

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Affected Sib Pair Sample
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Unselected Sample
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Association Analysis
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Error Detection

• Genotype errors can introduce unlikely
  recombinants
• Change likelihood
• Replace (1-q) with q
• Test sensitivity of likelihood to each genotype
• Detects errors that have largest effect on linkage

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Practical Exercise

• Lon Cardon
• Stacey Cherny

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Tracing Chromosomes

• Get Picture of Monogenic Pedigree
• Comment how
• Individuals sharing some variant are similar
• Have disease
• Effects might be more subtle
• Mention challenge reconstructing chromosomes

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Error Detection

• Using all the data
• Lfull using known recombination fractions
• Ufull assuming unlinked markers
• Excluding a single genotype
• Lno geno using known recombination fractions
• Uno geno assuming unlinked markers
• Calculate R (Lno genoUfull)/(LfullUno geno)
• Large R imply recombinants
• not supported by other data