Haplotype analysis of populationbased association studies

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Haplotype analysis of population-based
association studies
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Why study haplotypes?

• Much of common human genetic variation can be
  arranged on relatively few haplotypes within
  blocks of strong LD across the genome that are
  rarely disturbed by meiosis.
• Functional properties of a protein are determined
  by the linear sequence of amino acids,
  corresponding to DNA variation on a haplotype.
• Combination of causal variants in cis in
  HPC2/ELAC2 increase risk of prostate cancer.
• Rare causal variants may reside on specific
  haplotype backgrounds that could not be
  identified through single-locus analysis.
• Here we will consider two specific applications
  of haplotypes in population-based association
  studies
• Testing for association of disease with SNPs in a
  candidate gene or small candidate region.
• Fine-mapping within candidate regions.

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Testing for association of disease with SNPs in
a candidate gene
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Logistic regression framework

• Convenient to model log-odds of disease in a
  logistic regression framework, assuming
  multiplicative haplotype risks.
• Likelihood contribution of individual with
  phenotype yi, carrying pair of haplotypes Hi1 and
  Hi2 given by
• where denotes the additive effect of
  haplotype Hj on the log-odds of disease.
• Can be easily extended to incorporate covariates
  in the same way as for single-locus analysis.

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Testing for haplotype association with disease

• Under null hypothesis of no association, each
  haplotype has the same risk of disease, i.e.
  is constant for all haplotypes Hj.
• Maximise likelihood
• under null and alternative models.
• Deviance has approximate chi-squared distribution
  with n-1 degrees of freedom, where n is the
  number of distinct observed haplotypes in H.

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Unknown phase

• Haplotypes cannot generally be recovered from the
  unphased genotype data generated by current SNP
  typing technology.
• Statistical algorithms exist to infer haplotypes
  from unphased genotype data
• SNPHAP maximum-likelihood via implementation of
  E-M algorithm.
• PHASE pseudo-Bayesian MCMC algorithm using
  population genetics model for haplotype
  evolution.
• Statistical algorithms demonstrated to work well
  in blocks of strong LD.
• Inferred haplotypes are just estimates of the
  true underlying phase, so it is important to
  address the error in the estimation process.

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Unphased genotype data

• Consider all possible haplotype configurations
  consistent with unphased genotype data, weighted
  in likelihood by the corresponding phase
  assignment probability.
• Likelihood contribution of individual with
  phenotype yi, with unphased multi-locus genotype
  Gi given by
• where is estimated by one of
  the haplotype reconstruction algorithms.
• Naturally allows for missing genotype data.
• Deviance has approximate chi-squared distribution
  with n-1 degrees of freedom, where n is the
  number of distinct haplotypes consistent with
  observed unphased genotype data.

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Parsimony issues

• There may be many haplotypes consistent with
  observed unphased SNP genotype data, some of
  which will be very rare.
• Difficult to estimate and interpret disease odds
  for rare haplotypes.
• Each rare haplotype may contribute little
  information about association, but requires an
  additional degree of freedom in the deviance,
  leading to lack of power to detect association.
• Pool together rare haplotypes, and assign the
  same odds of disease to everything in this
  dustbin category. However, may group together
  high- and low-risk rare haplotypes, which may
  mask association with disease.
• More powerful to group haplotypes based on their
  likely evolution with a block of strong LD.

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Haplotype evolution
0 0 0 0 0
Ancestral haplotype
1
2
5
4
3
1 0 0 0 0
1 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 1 0 0 0
0 1 0 0 0
0 1 1 0 0
0 0 0 0 1
0 1 1 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 1 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 1
0 0 0 0 1
0 0 0 0 1
0 1 0 0 0
0 0 0 0 1
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Haplotype clustering

• We expect a pair of haplotypes carrying the same
  disease mutation to share more recent common
  ancestry than a random pair of haplotypes from
  the population.
• Reduce the dimensionality of the problem by
  taking advantage of the expectation that
  similar SNP haplotypes will have comparable
  risks in the region flanking the disease gene.
• Cluster haplotypes according to their similarity.
  Assign the same contribution to log-odds of
  disease to haplotypes in the same cluster, but
  allow haplotype effects to vary between clusters.
• Depends on availability of appropriate metric of
  distance between pairs of haplotypes. A number
  of laternative metrics exist, most based on the
  proportion of SNPs at which pairs of haplotypes
  share the same allele.

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Measuring haplotype similarity

• Assuming that haplotype diversity is driven
  primarily by mutation, as opposed to
  recombination events, score similarity in terms
  of SNP alleles shared in common.
• Similarity between haplotype Hj and Hk defined as
• where
• Could utilise alternative similarity metric. For
  example, incorporate allele frequencies to give
  greater weight to sharing rare alleles.

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Hierarchical clustering

• Standard hierarchical clustering algorithms
  available to group haplotypes according to their
  similarity.
• Haplotypes are successively combined into
  increasingly diverse clusters, until ultimately
  all haplotypes form a single clade (equivalent to
  the null model). Represented as a dendogram.
• Can test for haplotype association with disease
  via the deviance at each level of the dendogram,
  where all haplotypes in the same cluster have the
  same additive effect to the log-odds of disease
  (see Durrant et al. 2004, for example).
• Multiple testing issue can correct maximal
  deviance using Bonferroni correction or by means
  of permutation methods.

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Distance
T1
T2
T4
T5
T6
T7
Th9
h9 clusters of identical haplotypes
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Bayesian partition model
1121
1111
ß1 0.50
Specify number of clusters, K.
2121
Specify K cluster centres, CK.
K 2
Allocate haplotypes to nearest cluster centre.
2122
2222
Allocate log-odds of disease, ß, to each cluster.
2112
ß2 -0.34
Assign prior distribution to K, CK, and ß, and
sample from their joint posterior distribution
given phenotype data and consistent SNP
haplotypes under the logistic regression model.
Implemented in Bayesian MCMC algorithm, GENEBPM,
developed by Morris (2005).
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Prior density function

• Under the null hypothesis of no association,
  there will be a single cluster of haplotypes, all
  with the same risk of disease.
• Assume a prior probability of 0.5 of a single
  cluster (i.e. K 1) of haplotypes, and assume a
  truncate geometric distribution for K gt 1.
• Prior probability of association is 0.5, and
  favours smaller numbers of clusters (i.e. more
  parsimonious models).
• Can reduce prior probability of association to
  account for testing multiple candidate genes or
  regions.
• Assume that each haplotype is equally likely to
  be chosen as a centre for any cluster.
• Assume independent N(µ,sB) distributions for the
  log-odds of disease in each cluster.
• Hyperparameters µ has Uniform density, and sB
  has an exponential distribution with expectation
  1.

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Example CYP2D6

• The gene CYP2D6 on human chromosome 22q13 has an
  established role in drug metabolism.
• Hosking et al. (2002) genotyped 1,018 individuals
  at 32 SNP markers across an 890kb region flanking
  CYP2D6.
• By typing four functional polymorphisms in
  CYP2D6, 41 individuals were found to carry two
  mutations (not necessarily the same variant), and
  hence were predicted to be recessive poor drug
  metaboliser (PDM) cases.
• Standard single-locus analysis of SNP markers
  revealed highly-significant evidence of
  association across 400kb block of strong LD
  flanking the CYP2D6 locus.
• GENEBPM algorithm applied to the 32 SNP markers
  (excluding the known functional polymorphisms) to
  test for association between haplotypes in the
  region flanking CYP2D6 and PDM phenotype.

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GENEBPM analysis

• 878 haplotypes consistent with the observed
  unphased SNP genotype data. 41 common
  haplotypes with relative frequency greater than
  0.5.
• Posterior distribution of the number of clusters
  of haplotypes ranges from 3 to 22, with a mode of
  5. Posterior probability of association gt 99.9.

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Posterior haplotype similarity
Log-odds-ratios (baseline haplotype 1) for
high-risk clusters (A) 7.25-7.28 (B) 2.12-3.05.
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Clustering of cases
Variant 1 associated with cluster (A). Variant 2
associated with cluster (B).
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When is GENEBPM analysis appropriate?

• Use of the GENEBPM algorithm relies on robust
  haplotype estimation, and assumes minimal
  evidence of ancestral recombination in
  calculating the haplotype similarity metric.
• GENEBPM is appropriate for testing for
  association within a strong block of LD, or
  within a single candidate gene subject to limited
  recombination.
• GENEBPM has been demonstrated to perform well,
  even in the presence of ancestral recombination
  (for example CYP2D6 application).
• For larger genetic regions
• Perform sliding window analysis, with independent
  analyses undertaken with overlapping sets of
  SNPs.
• Break into non-overlapping blocks of strong LD,
  with independent analyses performed within each
  block.
• Remember to take account of multiple testing.

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Fine-mapping within candidate regions
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Fine-mapping and the hidden SNP problem

• The goal of fine-mapping studies is to improve
  the resolution of estimates of the location of
  functional polymorphism(s) contributing to
  disease.
• It is possible that we have not typed the
  functional polymorphism itself, but we can use
  genotypes at nearby SNPs and local patterns of LD
  to infer genotypes at the unobserved locus (or so
  called hidden SNP).
• By modelling association between disease and
  genotypes at the hidden SNP for many different
  possible locations across the candidate region,
  we can plot a statistical measure of support for
  association in order to fine-map the functional
  polymorphism.

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Likelihood formulation

• Logistic regression model parameterised in terms
  of the log-odds of disease, ß, for each genotype
  at the hidden SNP.
• Calculate the likelihood of observed phenotype
  data, y, for a case-control sample of
  individuals, given their haplotypes, H, at marker
  SNPs as a summation over possible genotypes at
  the hidden SNP at location z.
• where
• We cannot evaluate the conditional distribution
  of hidden SNP genotypes, f(XH,z), directly.
  However, we can approximate the likelihood by
  taking samples of hidden SNP genotypes, X1, X2,
  , XT, from this conditional distribution using
  population genetics theory.

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Sampling genotypes at the hidden SNP
0 0 0 0 0 0
Ancestral haplotype
z
1
2
5
4
3
1 0 0 0 0 0
1 0 0 0 0 0
1 0 0 0 0 0
0 1 0 0 0 0
0 1 0 1 0 0
0 1 0 1 0 0
0 1 1 1 0 0
0 0 0 0 0 1
0 1 1 1 0 0
0 1 0 1 0 0
0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 0 1 0
0 0 0 0 1 0
0 0 0 0 0 0
0 0 0 0 0 1
0 0 0 0 0 1
0 0 0 0 0 1
0 1 0 1 0 0
0 0 0 0 0 1
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Sampling practicalities

• A common distribution for genealogical trees
  representing the ancestry of a sample of
  chromosomes is given by the coalescent process.
• However, we cannot sample directly from the
  conditional distribution of genealogies, given
  the observed marker SNP haplotype data.
• One attractive solution is to use the product of
  approximate conditionals (PAC) likelihood
  introduced by Li and Stephens (2003).
• Conditional on the estimated fine-scale
  recombination rate, ?, across the candidate
  region, it follows that
• Haplotypes are not observed directly from
  unphased SNP genotype data. However, PHASE can
  be used to infer haplotypes, and obtain estimates
  of the recombination rate across the candidate
  region.

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Localisation

• Consider many positions, Z z1, z2, , zP, for
  the functional polymorphism.
• Sample from the conditional distribution of
  hidden SNP genotypes at each position, given the
  observed haplotype data.
• Obtain the likelihood f(yH,zj) at each position
  by integration over the hidden SNP genotype odds
  of disease, ß.
• Posterior probability that the functional
  polymorphism is located at position zj given by
  Bayes theorem
• where f(zj) denotes the prior probability
  that the functional polymorphism is located at
  position zj.
• Assuming all positions to be equally likely, a
  priori, we can approximate the posterior
  probability by

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Example cystic fibrosis (CF)

• CF is a fully penetrant recessive disease, most
  common in white populations with an incidence of
  one case in each 2500 live births.
• Preliminary linkage analysis had suggested a
  1.8Mb candidate region for a single CF gene on
  chromosome 7q31.
• More recently, a 3bp deletion, ?F508, has been
  identified within this region in the CFTR gene.
• It is now well established that ?F508 accounts
  for 66 of all chromosomal mutations in
  individuals with CF, with the remainder made up
  of many rare mutations in the same gene.
• Kerem et al. (1989) obtained marker haplotypes
  from 94 case chromosomes and 92 control
  chromosomes using 23 RFLPs in the candidate
  region.
• Of the case chromosomes, 62 have now been
  confirmed as carrying the ?F508 mutation.
• Single locus analysis revealed strong evidence of
  association with CF of RFLPs in 300kb region
  flanking CFTR.

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Comments

• Flexibility of logistic regression modelling
  framework allows for covariates including
  environmental risk factors, polygenic effects and
  indicators of population structure.
• Can allow for a range of different genetic models
  of disease at the hidden SNP.
• Hidden SNP need not be fixed as binary. Could
  easily extend the method to allow for genetic
  heterogeneity by considering a multi-allelic
  hidden locus, or several tightly linked SNPs
  coding for risk haplotypes at functional
  polymorphisms.
• With accurate estimation of haplotypes, method
  can be used to fine-map functional polymorphisms
  across entire chromosomes.
• The hidden SNP approach can also be used to test
  for association between disease and an unobserved
  functional polymorphism at a fixed location by
  comparison of f(yH,z) with the likelihood under
  the null model of no association.
• With accurate information regarding patterns of
  LD from the International HapMap project, we can
  use the hidden SNP approach to test for
  association between polymorphisms in HapMap that
  have not been typed in the association study
  (i.e. IMPUTATION).

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Summary

• Haplotype analysis of population-based
  association studies may have greater power than
  single-locus tests
• Take account of background patterns of LD between
  loci.
• Correspond to the block-like structure of common
  genetic variation.
• Haplotypes can be reconstructed from unphased
  genotype data within blocks of strong LD using
  statistical algorithms.
• Power of haplotype-based tests of association can
  be improved by clustering haplotypes according to
  their similarity, used as a proxy for recent
  shared ancestry.
• Fine-mapping of disease loci can be implemented
  by treating the functional polymorphism(s) as
  hidden SNP(s), and simulating the distribution of
  genotypes at these loci using population genetics
  theory.
• Within a logistic regression framework, we can
  incorporate covariates to account for non-genetic
  risk factors, polygenic effects, and indicators
  of population structure.

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References

• Durrant C, Zondervan KT, Cardon LR, Hunt S,
  Deloukas P, Morris AP (2004). Linkage
  disequilibrium mapping via cladistic analysis of
  SNP haplotypes. Am J Hum Genet 75 35-43.
• Hosking LK et al. (2002). Linkage disequilibrium
  mapping identifies a 390kb region associated with
  CYP2D6 poor drug metabolising activity.
  Pharmacogenomics J 2 165-175.
• Kerem BS et al. (1989). Identification of the
  cystic fibrosis gene genetic analysis. Science
  245 1073-1080.
• Li N, Stephens M (2003). Modelling linkage
  disequilibrium, and identifying recombination
  hotspots using SNP data. Genetics 165
  2213-2233.
• Morris AP (2005). Direct analysis of unphased
  SNP genotype data in population-based association
  studies via Bayesian partition modeling of
  haplotypes. Genet Epidemiol 29 91-107.