SNP Haplotype Estimation From Pooled DNA Samples

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SNP Haplotype Estimation From Pooled DNA Samples

• Yaning Yang
• Lab of Statistical Genetics
• Rockefeller University
• (yyang_at_linkage.Rockefeller.edu)

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I. Background

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Genotype-phenotype

• Genotype-phenotype association the central
  objective of genetic studies.
• Completion of human genome sequence is the
  foundation (Collin et al. 2003).

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Geno-phenotype

• Genotype
• Internally coded, inheritable information
• Need to be polymorphic (variation)
• Interaction with environmental factors
• Phenotype
• Outward, physical manifestation of the organism
• Disease status, survival times, quantitative
  traits (QTL)
• Complex traits/diseases, simple traits/diseases

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Simple (Mendelian) Traits

• Single gene, simple mode of inheritance.
• Huntington disease, cystic fibrosis.
• Method Linkage analysis
• Co-segregation of marker and disease within
  pedigrees based on recombination events.
• More than 400 simple diseases have been
  genetically mapped.

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Complex Traits

• Polygenic environmental factors Complex
  epistasis (interaction) hard to dissect.
• Polygenic multiple genes each with small to
  moderate effect.
• Enviromental factors race, gender, diet etc.
• Cancer, diabetes, Alzheimers disease (AD) etc.
• Methods association analysis
• population-based
• family-based

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Polymorphism

• A difference in DNA sequence of
• nucleotide among individuals or
• populations.
• P(minor allele)gt0.1, say.
• Genetic mutation is polymorphism.
• Marker locus-specific polymorphism
• Like a (chaining) in approximation
• A significant marker may itself be or close to
  the causal genetic variant

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SNP Single Nucleotide Polymorphism

• The most simple and common genetic polymorphism
• Simple a single base mutation in DNA
• Common 90 of all human DNA variations
• Abundance 0.1
• Biallelic (binary)
• 2 million SNPs reported

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Genotyping
SNP1 (locus 1)
SNP2 (locus 2)
haplotype
G
A
Diploid
T
C
Genotype G/T A/C At each locus, two
possible alleles, e.g, at locus 1, the two
alleles can be G/G, T/T or T/G.
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Association

• Population-based
• Epidemiological methods Case-control cohort
  design
• Stratification control over confounding factors
• Powerful but easily produce spurious associations
  due to population admixture (heterogeneity)
• Family-based
• TDT test (McNemars test for matched pairs)
• No need of stratification, true associations
• Sampling is costly

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Association

• Identification of causal genetic variants.
• Understanding their functions and disease
  etiology.
• Help for disease prevention, diagnostics, drug
  development (e.g.personal medicine).

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Allele Association (marginal)
1. Disease-allele association
G
T
case
control
2. Disease-genotype association
G/G
G/T
T/T
case
control
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Haplotype Association (joint)

• Most genome screen test one locus each time.
• Dependence structure (linkage disequilibrium)
  need to be considered.
• Example Haplotypes for case,control
• Case Control
• ---A-----B--- ---A-----b---
• ---a------b--- ---a-----B---

case
control
---A-----B---
---a-----b---
---A----b---
---a-----B---
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Haplotype

• Total of haplotypes is 2m for m SNPs.
• For example (m3, biallelic at each position
  A/a, B/b, C/c)

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Why Haplotype?

• LD
• Alleles in Linkage disequilibrium (LD) are
  tightly linked and tend to be co-segregated.
• LD plays a fundamental role in genetic mapping of
  complex diseases.
• Haplotypes preserve LD information.

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Why Haplotype?

• Haplotype
• A haplotype is a binary sequence along one
  chromosome.
• Haplotype has a block-wise structure separated by
  hot spots.
• Within each block, recombination is rare due to
  tight linkage and only very few haplotypes really
  occur.

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A Brief Summary

• Genotype-phenotype association analysis for
  complex disease
• Genetic variant/polymorphism/marker
• Genetic variation human variation
• SNP simple, abundant genetic variant/marker
• LD dependence of markers
• Haplotype analysis joint distribution

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II. Haplotype Estimation From Pooled DNA
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Introduction
Key Words Efficiency, EM Algorithm, Haplotype
Frequency, LD Coefficients, Pooling, Variance
estimates.
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Estimating haplotype frequencies from individual
genotypes

• Individual samples are genotyped.
• No phase information.
• Likelihood analysis, (Escoffier Slatkin,1995),
  but no variance estimate.
• Other methods Clarks parsimonious method (Clark
  1990), Bayesian MCMC

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Genotyping individual DNA
Diploid ---A-----B--- haplotype
---a------b--- haplotype
Genotyping A/a B/b observed
genotypes (phase information is lost)
Reconstruct ---A-----B---
---a------b--- haplotype configurations or
---A-----b--- ---a------B---
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Pooling Reduce Genotyping Cost

• Unrelated individual samples are mixed, more
  ambiguities in recovering haplotypes.
• No individual information and no phase
  information.
• Efficient in allele frequency estimation, but is
  it efficient in estimating haplotype frequency?
• Wang et al. (2003), Ito et al. (2003).

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Genotyping pooled DNA
----A------B---- Pooling
----a-------b---- diploid for individual 1
----A------b---- ----a-------B----
diploid for individual 2
Genotyping AAaa BBbb observed
pool-genotypes Hap config ---A-----B--- or
---A----B--- or ---A----b---
---A-----b--- ---A----B---
---A----b--- ---a-----B---
---a----b--- ---a----B---
---a-----b--- ---a----b---
---a----B---
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Pool-genotype of K- pool

• Pool-genotype of allele 1. E.g.
• An individual can be viewed as a pool of two
  independent chromosomes.
• We will say a chromosome is a ½-pool

SNP 1 2 3 4 5
Individual 1

Individual 2
Pool-genotypes
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Missing values

• Pool-genotype at m SNP loci,
• Completely missing no information.
• Partially missing partial information, e.g.,
  only know

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Statistical Methods

• Key Words
• Asymptotic variance , EM, MLE, missing data,
  Relative efficiency,

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Notations

• For m SNPs, each position can take two possible
  alleles. Denote them by 1 0.
• Totally possible haplotypes.
• Haplotype frequencies
• m3

SNP 1 2 3
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Maximum Likelihood Estimate

• Assumptions HWE, random mating
• Likelihood
• where
• When K1/2, multinomial!

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An Example

• m2, K2, observation X(2,1). Consistent
  haplotype configurations are
• Likelihood

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EM algorithm
hkhk(0), k1,2,,2m (initial value)
NO
cJ(k)Number of haplotye k in configuration J
YES
END
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Variance Estimate
Variance matrix for estimated h
and the (k,l) element of matrix is given by
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Asymptotic Variances

• Fisher information matrix

Asymptotic variance of
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Properties
Fisher Information can be represented as
where diag(1/h), ? of the haplotypes, ?
MultiNomial(2K, h), (a latent r.v.).
where
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Reformulation of the Problem

• Let ? MN(2K, h), and 0-1 matrix
• Genotype X can be represented as.
• X A ? (compressed info.)
• From the incomplete observations X, make
  inference on the distribution/parameter h of
  unobservable ?

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Simulated and estimated variances
variances
variances
K
D
Variances decrease with D, increase with
K. (n120, pa0.4,pb0.5)
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Relative efficiency of pooling
Error
Cost
efficient
Error
Cost
inefficient
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Relative Efficiency of Pooling

• Asymptotic relative efficiency (ARE)
• Relative efficiency (RE) (for fixed individual
  number, n, V variance or MSE)

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Asymptotic variances
Table 2 SNPs, pa0.4, pb0.5
K
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Asymptotic Relative Efficiency (ARE)
pa0.4, pb0.5
ARE
Higher LD, higher efficiency.
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Simulations (1,000 replicates)

• 2-locus (a/A, and b/B)
• Different choices of allele frequencies, LD
  coefficients, sample sizes and pool sizes
• pa 0.4, pb 0.5 and pa 0.2, pb 0.3
• D0.25, 0.5, 0.75
• n60, 120, 180
• K1,2,,6.

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Simulations (1,000 replicates)

• 3-locus based on real individual genotype data
• Infinite population
• generate haplotypes according to the known
  haplotype frequencies, then pool 2 haplotypes
  to form individual genotypes, pool K individuals
  to form pool-genotypes.
• Finite population (pseudo-pooling)
• Randomly pooling every K individual genotypes
  to generate pool- genotypes.

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MSE of haplotype estimates
Fig. Two-locus a/A and b/B, pa0.4, pb0.5
n180)

• MSE increases as K increases.
• For SNPs in higher LD, it is easier (less error)
  to estimate haplotype frequencies.

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Relative efficiencies
Fig. Two-locus a/A and b/B, pa0.4, pb0.5 n180

• RE(K) increases with K, but seems to level off
  when K 4.
• The higher the LD, the higher the efficiency of
  pooling.
• V6 2V1

Relative efficiency
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Individual genotype data 3-locus(data provided
by Dr. Kumar)

• 135 unrelated individuals genotyped at 3 SNPs in
  the AGT gene.
• All the individuals are normal Caucasians.
• High LD
• This data set was used for
• Simulation according to the estimated h
• Pseudo-pooling simulation.

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Relative efficiency of pooling (3-locus)
Fig. Haplotypes are generated according to
h(0, 0.082, 0, 0, 0.524,0.283, 0.005, 0.106).

n180

n120
RE
n60
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Pseudo-pooling (table)
Table Haplotype frequency estimates of the
pseudo-pooling experiment based on Kumar data
(n120)
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Influence of missing values on MSE and RE
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Real Data

• Pool-genotypes at 10 SNPs in the AGT gene,
• 15 pools, each with K2 independent individuals.
• Individual genotypes are not available.
• All individuals are unrelated.
• There are 2 completely missing values.

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Haplotype frequency estimates (7 SNPs)
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Case-control study

• Association of haplotypes and diseases.
• Test difference of haplotypes between case and
  control group.
• LRT test
• LRT2log(Lcase)2log(Lcontrol)2log(Lcasecontrol
  ).

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Summary

• Pooling is efficient for m1,2 but not for m ? 2
  when LD is low.
• For m ? 2 and high LD case, pooling is good.
• The variance estimates are good if n/K is large
  (say, ? 30) otherwise, bootstrap.

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Summary (contd)

• Pools may have different pool sizes.
• The algorithm allows for different types of
  missing values.
• Can be applied to case-control design for
  disease-haplotype association.
• Need algorithms for long haplotypes.
• Need considering genotyping errors.

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References

• Clark A (1990) Mol. Biol. Evol. 7, 111-122.
• Collin F et al. (2003) Nature, 422835-847
• Excoffier L Slatkin M (1995) Mol. Biol. Evol.
  12, 921-927.
• Ito et al. (2003) Am . J. Hum. Genet. 72,
  384-398.
• Wang S, Kidd KK Zhao H (2003) Genet. Epidemiol.
  24, 74-82.
• Yang et al. (2003) PNAS 1007225-7230.

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Acknowledgement

• We thank Dr. A. Kumar at the New York Medical
  College in Valhalla for providing the individual
  SNP data.
• Thank You!