Informative SNP Selection Based on Multiple Linear Regression

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Informative SNP Selection Based on Multiple
Linear Regression

• Jingwu He
• Alex Zelikovsky

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Outline

• SNPs, haplotypes, and genotypes
• Tagging problem formulation
• Tagging based on multiple linear regression
• Experimental results

3
Human Genome

• Length of Human Genome (DNA)
• ? 3 billion base pairs A,C,G, or T.
• Our DNA is similar.

99.9 of DNA is common.
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SNPs

• Genome difference between any two people ? 0.1
  of genome
• These differences are Single Nucleotide
  Polymorphisms (SNPs).
• Total number of SNPs in human genome ? 107

SNP
SNP
SNP
A C C G . . . .
A A C A
G C C A . . . . T T C G
G G T C . . . . A G T C
C
G
G
A C C G . . . .
A A C A
G C C A . . . . T T C G
G G T C . . . . A G T C
C
A
A
A C C G . . . .
A A C A
G C C A . . . . T T C G
G G T C . . . . A G T C
T
G
A
A C C G . . . .
A A C A
G C C A . . . . T T C G
G G T C . . . . A G T C
C
G
G
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Haplotyes and Genotypes

• Human diploid organism two different copies
  of each chromosome, one from mother, one from
  father.

One copy from A
A C C G . . . .
. . . C A
G C C A . . . . T T C G
G G T C . . . . A G T C
C
G
G
C
G
G
Another copy from A
C
A
A
A C C G . . . .
. . . C A
G C C A . . . . T T C G
G G T C . . . . A G T C
T
G
A
One copy from B
T
G
A
Another copy from B
G
A C C G . . . .
. . . C A
G C C A . . . . T T C G
G G T C . . . . A G T C
C
G
G
C
G

• Since individuals differ in SNPs, we keep only
  SNPs.
• Haplotype SNPs in a single copy of a
  chromosome
• Genotype A pair of haplotypes

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Cause of Variation Mutations and Recombinations
Mutation
Recombinations
One nucleotide is replaced with other G -gt A
One chromatid recombine with another.
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Encoding

• SNPs are generally bi-allelic
• only two alleles in single SNP wild type and
  mutation
• 0 stands for wide type, 1 stands for mutation

homozygous
Heterozygous
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Outline

• SNPs, haplotypes, and genotypes
• Tagging problem formulation
• Tagging based on multiple linear regression
• Experimental results

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Tagging Motivation

• Decrease SNP genotyping cost and data analysis
• Many SNPs are linked (strongly correlated)
• Genotype only informative SNPs ? tag SNPs, other
  SNPs are inferred from tag SNPs
• Perform data analysis only on tag SNPs.
• Cost-saving ratio m/k

Use only tag SNPs to infer non-tag SNPs
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Tagging Problem
Step 1 Find tags (SNP position) in sample
Find tags (0, 1, 2)
Step 2 Reconstruct complete haplotype
Computation Methods

• Problem formulation
• Given the full pattern of all SNPs in a sample
• Find the minimum number of tag SNPs that will
  allow the reconstruction of the complete
  haplotype for each individual.
• Tag Selection Algorithm
• SNP Prediction Algorithm

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Tagging Methods

• Tagging Methods
• HapBlock (K. Zhang, M.S. Waterman, et al.)
• Greedy algorithm for tag selection
• Majority voting for prediction
• V. Bafna, B.V. Halldorson et al.
• Graph algorithm for tag selection
• Majority voting for prediction
• STAMPA (E. Halperin and R. Shamir)
• Dynamic programming for tag selection
• Majority voting for prediction
• ..
• Tagging based on Multiple Linear Regression
• Greedy Selection
• Multiple Linear Regression for Prediction

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SNP Prediction Algorithm
Predicting
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Tag Selection based on Prediction

• Choose the optimal k tags
• It is NP-hard, m choose k
• (m No. of total SNPs, k No. of tags)
• Use Stepwise (greedy) Tag Selection Algorithm
  (STA) to reduce the cost and time
• Starts with the best tag t0, i.e., tag that
  minimizes error when predicting with Ak all other
  tags.
• Then STA finds such tag t1, which would be the
  best extension of t0, and continues adding best
  tags until reaching the set of tags of the given
  size k.

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Projection Method forSNP Prediction
possible resolutions
s0
0 . . .
2 . . .
s2
1 . . .
s1
d0
d2
d1
tag t2
projections
span(T)
0
tag t1

• Choose resolution minimizing its distance d to
  spanning of tag space span (T)

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Data Sets

• Daly et al
• 616 kilobase region of human Chromosome 5q31
  genotyping 103 SNPs for 129 trios.
• Seven ENCODE regions from HapMap.
• Regions ENr123 and ENm010 from 2 population 45
  singles Han Chinese (HCB) and 44 singles
  Japanese(JPT).
• Three regions (ENm013, ENr112, ENr113) from 30
  CEPH family trios obtained from HapMapSTAMPA (E.
  Halperin and R. Shamir)
• Two gene regions STEAP and TRPM8
• genotyping 23 and 102 SNPs for 30 trios

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Experimental Results
Directly to genotype data
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Multivariate Linear Regression Tagging

• Genotype tagging
• uses fewer tags (e.g., up to two times less tags
  to reach 90 prediction accuracy) than STAMPA (E.
  Halperin and R. Shamir, ISMB 2005 and
  Bioinformatics)
• Statistical tagging
• Linear recombination of tags statistically cover
  non-tag SNPs
• Traditional methods use single tag to cover
  non-tag SNPs
• uses on average 30 fewer tags than IdSelect
  (C.S. Carlson et al. 2004) for statistical
  covering all SNPs.

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Thank youAny Questions?