Single Nucleotide Polymorphism Analysis Predictive Analytics and Data Science Conference May 27-28 Asst. Prof. Vitara Pungpapong, Ph.D. Department of Statistics Faculty of Commerce and Accountancy Chulalongkorn University

1. Single Nucleotide Polymorphism
Analysis
Asst. Prof. Vitara Pungpapong, Ph.D.
Department of Statistics
Faculty of Commerce and Accountancy
Chulalongkorn University
1

2. Outline
• What is SNP array?
• Typical SNP analysis
• Challenges
• The ICM/M Method
• Results
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3. Microarray
• Usually known as Chip-chip.
• First publication in 1999
• Each known gene is a one spot on the
chip.
• Laser induced fluorescence (LIF) is used to
obtain color and intensity of each gene.
• Varying colors show varying levels of gene
activity.
• A microarray chip can contain 10,000 –
20,000 genes.
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4. Single Nucleotide Polymorphism
• Usually called chip-seq or SNP.
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(https://en.wikipedia.org/wiki/Single-nucleotide_polymorphism)

5. Microarray vs SNPs
• Microarray is more suitable for small genomes
• More bias in microarray
• SNPs generally produces profiles with a better
signal-to-noise ratio, and allows detection of
more peaks and narrower peaks.
• SNPs generate more high-throughput data (>
1Tb) which requires more effort in analysis.
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6. 1000 Genome Project
• http://www.1000genomes.org/
• The 1000 Genome Project provide the largest public catalog of
human genetic variation.
• The Project ran from 2008 and completed in 2015.
• The human genome consists of approximately 3 billion DNA
base pairs and is estimated to carry around 20,000 protein
coding genes.
• The samples for the 1000 Genomes Project are anonymous
and have no associated medical or phenotype data.
• The project holds self-reported ethnicity and gender.
• All participants declared themselves to be healthy at the time
the samples were collected.
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7. 1000 Genome Project
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(http://www.1000genomes.org/)

8. dbGaP database
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• http://www.ncbi.nlm.nih.gov/gap

9. Maize Genome
• http://www.panzea.org/
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10. Vitara Pungpapong 10
Genome-wide Association Study (GWAS)
Goal:
Identify genetic variants associated with phenotype of interest.

11. Typical(Simple) GWAS Analysis
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Preprocessing
Data
Univariate
Analysis
Controlling
FWER or FDR
GWAS Gold Standard: 5 x 10-8

12. Preprocessing Data in GWAS
• SNP Call Rate (98-99%)
• Sample Call Rate (98-99%)
• Data Imputation
• Minor Allele Frequency (Remove extremely rare
SNPs, i.e., <5% frequency)
• Hardy-Weinberg Equilibrium
• Recode SNPs to the count of minor allele (0, 1, 2)
• For more information, refer to Turner et. Al.
(2011).
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13. Biological Pathways
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Databases:
- KEGG
(http://www.genome.jp/kegg
/pathway.html)
- Ingenuity
(http://www.ingenuity.com/)
- etc.

14. Challenges in GWAS
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- Want to incorporate biological pathway in GWAS
- Want to analyze all SNPs at once

15. High-dimensional Regression
• Regression with n < p
• Challenges in high-dimensional regression
– Large p small n problem
– Multicollinearity
– Sparsity
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16. Bayesian Model Setup
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𝐘 = 𝐗𝛽 + 𝜀, 𝜀~𝑁 0, 𝜎2
𝐼 𝑛
Consider a normal regression model:
Prior to capture sparsity in regression coefficient:
𝛽𝑗|𝜏𝑗 ~ 1 − 𝜏𝑗 𝛿0 𝛽𝑗 + 𝜏𝑗 𝛾𝛼 𝛽𝑗 𝜎 .
where 𝛿0 . is a Dirac delta function at zero
𝜏𝑗 = 1 𝛽 𝑗≠0
𝛾𝛼 𝛽𝑗 𝜎 =
𝛼 𝑛 − 1
2𝜎
exp −
𝛼 𝑛 − 1
𝜎
|𝛽𝑗|

17. Bayesian Model Setup
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18. Bayesian Model Setup
• The Ising model is employed to model relationship among
SNPs.
• The Ising model assumes that the relationship lies in an
undirected graph G = (V, E) where V is a set of vertices and E is
a set of edges.
• The Ising prior for 𝜏 = 𝜏1, … , 𝜏 𝑝
𝑡
where 𝜏𝑗 = 1 𝛽 𝑗≠0
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𝑃 𝜏 =
1
𝑍(𝑎, 𝑏
exp 𝑎
𝑗
𝜏𝑗 + 𝑏
<𝑗,𝑘>∈𝐸
𝜏𝑗 𝜏 𝑘 𝜏1
𝜏2
𝜏3 𝜏4
𝜏5

19. The ICM/M Algorithm
• Pungpapong et. al. (2015).
• Idea: The conditional distributions are used to obtain
parameters
• The ICM/M consists of two main parts:
– Conditional median for each regression coefficient
– Conditional mode for hyperparameters and auxiliary parameters
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20. The ICM/M Algorithm
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Obtain initial estimate ( 𝛽, 𝜎2
)
Obtain 𝜏 = 𝜏1, … , 𝜏 𝑝
𝑡
where 𝜏𝑗 = 1 𝛽 𝑗≠0
𝑎, 𝑏 = mode 𝑖=1
𝑝
𝑃 𝜏𝑗 𝜏−𝑗; 𝑎, 𝑏 ) =
mode 𝑖=1
𝑝
𝑃( 𝜏𝑗|{ 𝜏 𝑘: < 𝜏𝑗, 𝜏 𝑘 >∈ 𝐸}; 𝑎, 𝑏
𝛽𝑗 = median 𝛽𝑗 𝐘, 𝐗, 𝛽−𝑗, 𝜎2
, 𝑎, 𝑏 , 𝑗 = 1, … , 𝑝,
where 𝛽−𝑗 = ( 𝛽1, . . , 𝛽𝑗−1, 𝛽𝑗+1, … , 𝛽 𝑝 .
𝜎2 = mode(𝜎2|𝐘, 𝐗, 𝛽, 𝑎, 𝑏
Convergence in 𝜷? Stop

21. The ICM/M Algorithm
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Obtain initial estimate ( 𝛽, 𝜎2
)
Obtain 𝜏 = 𝜏1, … , 𝜏 𝑝
𝑡
where 𝜏𝑗 = 1 𝛽 𝑗≠0
𝑎, 𝑏 = mode 𝑖=1
𝑝
𝑃 𝜏𝑗 𝜏−𝑗; 𝑎, 𝑏 ) =
mode 𝑖=1
𝑝
𝑃( 𝜏𝑗|{ 𝜏 𝑘: < 𝜏𝑗, 𝜏 𝑘 >∈ 𝐸}; 𝑎, 𝑏
𝛽𝑗 = median 𝛽𝑗 𝐘, 𝐗, 𝛽−𝑗, 𝜎2
, 𝑎, 𝑏 , 𝑗 = 1, … , 𝑝,
where 𝛽−𝑗 = ( 𝛽1, . . , 𝛽𝑗−1, 𝛽𝑗+1, … , 𝛽 𝑝 .
𝜎2 = mode(𝜎2|𝐘, 𝐗, 𝛽, 𝑎, 𝑏
Convergence in 𝜷? Stop

22. Generalized Linear Models (GLMs)
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23. Iteratively Reweighted Least Squares
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24. Extension of the ICM/M to GLMs
• Borrow the idea of an iteratively reweighted least squares
(IRLS).
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25. Simulation Studies
• A total of 1,782 SNPs were randomly selected from
the Framingham dataset (Cupples et. al. 2007)
• 24 human regulatory pathways were retrieved from
KEGG database which involved 1,502 genes.
• 311 SNPS involved in 5 pathways were assumed to
have nonzero effect where the effect sizes were
randomly generated from Uniform[0.5, 3].
• Phenotype were simulated from the normal
regression model with the error variance = 5.
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26. Simulation Studies
• Results
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Method Prediction
Error
False
Positive
False
Negative
Lasso 30.7 (.41) .69 (.0004) .02 (.0004)
Adaptive
Lasso
206.2 (.57) .07 (.0017) .13 (.0002)
ICM/M 21.7 (.23) .03 (.0015) .04 (.0003)

27. Framingham Data Analysis
• Dataset: Framingham heart study (Cupples et. al. 2007)
• Phenotype: log transformation of vitamin D level
• Sample size: 952 for training set and 519 for test set
• The gene-pathway information relevant to vitamin D
level is obtained from the KEGG database
• There are 84,834 SNPs resided in 2,167 genetic regions in
112 pathways.
• Univariate tests were applied for screening process
resulting in 7,824 SNPs left for the analysis.
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28. Framingham Data Analysis
• Prediction errors and no. of identified SNPs
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Method Prediction
Error
No. of Identified
SNPs
Lasso .2560 14
Adaptive
Lasso
.2085 5
ICM/M .2121 5

29. Framingham Data Analysis
Chromosome - SNP
1-3887 4-0894 4-1174 5-2773 8-5143 17-
3907
17-
9089
𝛽 Lasso .0412 0 .0355 .0402 0 0 0
Adaptive
Lasso
.1521 0 .0434 .1539 -.0200 0 .0167
ICM/M .2417 -0.0512 0 .3047 -.0857 .1093 0
P-value* Lasso .2694 1 1 .6050 1 1 1
Adaptive
Lasso
.2060 1 1 .0031 1 1 1
ICM/M .0837 1 1 .0034 1 1 1
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* From multi-sample split method (Meinhausen et. al. (2009))

30. Parkinson’s Disease Data Analysis
• Data come from 3 different studies on PD
– Autopsy-Confirmed Parkinson Disease GWAS Consortium
(APDGC) (dbGaP Study Accession: phs000394.v1.p1)
– Genome-Wide Association Study of Parkinson Disease:
Genes and Environment (dbGaP Study Accession:
phs000196.v2.p1)
– NINDS-Genome-Wide Genotyping in Parkinson's Disease:
First Stage Analysis and Public Release of Data (n=1741)
– dbGaP Study Accession: phs000089.v3.p2
• Combined three data sets and obtained overlapping
SNPs (𝑛 = 6,704, 𝑝 = 888,398
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31. Parkinson’s Disease Data Analysis
• Pathway related to PD were retrieved from Ingenuity© IPA.
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32. Parkinson’s Disease Data Analysis
• ICM/M found 46 SNPs having nonzero
regression coefficients across 22
chromosomes.
• 8 genes known to PD were identified (e.g.,
TLR4, TNF, …).
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33. References
• Cupples, L. A.et al. (2007). The framingham heart study 100k snp genome-
wide association study resource: Overview of 17 phenotype working group
reports. BMC Medical Genetics, 8(Suppl 1):S1.
• Ho et. al. (2011). ChIP-chip versus ChIP-seq: Lessons for experimental
design and data analysis, BMC Genomics 2011 12:134.
• Meinshausen et. al. (2009). P-values for high-dimensional regression.
Journal of the American Statistical Association, 104:1671–1681.
• Pungpapong et. al. (2015). Selecting Massive Variables Using An Iterated
Conditional Modes/Medians Algorithm, Electronic Journal of Statistics 9 :
1243-1266.
• Turner, S. (2011). Quality control procedures for genome-wide association
studies. Curr Protoc Hum Genet 2011;68:1–19.1.18.
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