A new multipoint method for genomewide association studies by imputation of genotypes

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A new multipoint method for genome-wide
association studies by imputation of genotypes

• Marchini, J., Howie, B., Myers, S., McVean, G.
  Donnelly, P.
• Nature Genetics 906-913 (2007)
• Presented by Yixuan Chen
• 10/12/2007

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Contents

• Introduction
• Methods
• Results

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Association Study
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Association Test
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Disease Mapping
Disease Gene
Disease status
S2
...
SNP1
...
a ? 2 1 1 a ? 1
2 1
1 2 2 1 1 2 1 2 1 2 1 1
2 2
1 2 2 1 2 1 1
2
2 1 1 1 1 1 1
1
c 2 1 ? ?c 1 1
? ?
1 2 2 1 1 2 1 1 2 2 2 1
1 1
1 1 2 1 1 2 2 2 2 2 1 1
2 1
2 2 ? 1 1 1 ?
1
a 1 1 2 1a 1 1
1 2

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Haplotype
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Enhancement by Imputation

• Dense genotypes by commercial genotyping chips
• Unlikely to include the true causal variant
• Based on the observed data, impute the missing
  data
• These in silico genotypes can then be used as
  if the SNPs involved were directly genotyped
• Multipoint instead of single-SNP approaches

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Methods

• HH1,,HN denotes a set of N known haplotypes
• HiHi1,,HiL is a single haplotype
• H is set to be the 120 CEU haplotypes in the
  HapMap project
• GG1,,GK denotes the genotype data on the K
  individuals in a new study
• GiGi1,,GiL

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Hidden Markov Model for each genotype

• The model for Pr(GiH) is a HMM
• The hidden states are a sequence of pairs of the
  N known haplotypes in the set H

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The HMM Model

• Pr(Zi(1), Zi(2)H) defines the prior probability
  on how the sequences of hidden states, Z(1) and
  Z(2), change along the sequence.
• The switching rates depend upon an estimate of
  the fine-scale recombination map based upon the
  HapMap Phase II Data.

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The HMM Model (c1)
The effective population size
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The HMM Model (c2)
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Imputation of Missing SNPs

• Association test at an unobserved SNP
• Simulate M realizations of this SNP in H
• Treat the SNP as known in H and can be
  conditioned upon to simulate the unknown in G

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Imputation of Missing SNPs (c1)

• Suppose the jth sites in the set H are all missing

A product of approximate conditionals (PAC)
model. Given an ordering of H(1), , H(N), the
missing H(1)j, , H(N)j, are simulated
sequentially.
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Imputation of Missing SNPs (c2)

• Probabilistically choosing a haplotype to which
  to apply the first mutation
• pr denotes the probability of the first mutation
  occurring on the (r1)th haplotype in the ordering

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Imputation of Missing SNPs (c3)

• If mth haplotype carries the first mutation
• The alleles are simulated using higher order
  approximate conditionals

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Results

• The imputation at a particular SNP can
  theoretically combine information from all typed
  SNPs on the same chromosome.
• The influence of these SNPs decreases with
  increasing genetic distance from the locus of
  interest.

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Datasets

• CEU HapMap samples
• Known haplotypes
• Individuals from the 1958 British Birth Cohort
  that were typed at 500,000 SNPs on the
  Affymetrix 500K chip
• Evaluation imputation
• Separately typed 15,000 SNPs on a custom Illumina
  chip
• Imputation

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Summary

• Combine data from studies that use different
  genotyping chips to facilitate these
  meta-analytic approaches
• The imputation of other types of genetic variants
  that may show substantial association with
  phenotypes
• Imputation of genotypes for different study
  designs such as trio designs for association
  mapping and mapping by admixture LD (MALD)
  studies
• Development of statistical information measures
  for untyped variants