The document provides an introduction to epistasis detection in genome-wide association studies (GWAS). It defines epistasis as the detection of causal SNPs for a disease through their interactions, rather than their individual effects. It outlines the problem of epistasis detection as analyzing large genotype datasets to find combinations of SNPs that maximize an association measure with binary disease status. Popular measures discussed are chi-squared and mutual information statistics. The document reviews computational methods for epistasis detection, including Multifactor Dimensionality Reduction, SNPHarvester, and SNPRuler. It notes the challenges of reducing computational burden and detecting higher-order epistatic interactions.

1. A brief introduction to
epistasis detection in GWAS
2014. 01. 27.
Hyun-hwan Jeong

2. Agenda
• Introduction
• Problem definition
• Computational detection methods
• Challenges
2

3. Introduction

4. Single Nucleotide Polymorphism
• A single letter change in DNA sequence
• DNA sequence : 99.9% identical
• Common type of genetic variation
• ≥ 1% changes in general population
…ATTCGCCGGCTGCAACGTTAGA…
…ATTCGCCGGCTGCAGCGTTAGA…
…ATTCGCCGGCTGCATCGTTAGA…
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5. Genotype, phenotype and Allele
http://en.wikipedia.org/wiki/Phenotype
phenotype
genotype
allele
5

6. Genome Wide Association Study
for relation between Single SNP and disease
Manhattan plot of the GWAS of the discovery cohort comprising
2,346 SSc cases and 5,193 healthy controls. - Nature Genetics 42, 426–429 (2010)
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7. Why is detecting epistasis needed
in GWAS?
An illustration of interaction pattern between two SNPs with no marginal effect. -
Bioinformatics 26, 30-37 (2010)
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8. Problem Definition
8

9. Problem definition
Epistasis detection problem
• Object
• Detection of causative SNPs for disease
• Maximum value for defined measure
• Dataset
• 0.5M ~ 1M SNPs
• 4,000 ~ 5,000 subjects
• Binary disease status(case/control)
• 100MB ~ 1GB genotype data file
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10. Problem definition – Data format
푆푁푃ퟎ 푆푁푃ퟏ 푆푁푃ퟐ 푆푁푃ퟑ 푆푁푃ퟒ 푆푁푃ퟓ 푆푁푃ퟔ 푆푁푃ퟕ 푆푁푃ퟖ 푆푁푃ퟗ 퐶퐿퐴푆푆
1 1 0 0 0 0 1 0 1 1 1
0 0 1 0 0 0 1 1 0 2 1
0 0 0 0 0 0 1 0 0 0 1
1 1 0 0 0 0 0 1 0 2 1
0 0 0 0 0 0 0 1 0 0 1
0 0 0 0 0 0 0 0 0 1 0
1 1 0 1 0 0 0 1 1 1 0
0 0 0 1 1 1 0 1 1 1 0
0 1 0 2 0 0 0 1 0 1 0
0 0 0 1 0 0 1 2 1 0 0
• 3 values for SNP columns - 0(AA), 1(Aa/aA), 2(AA/AA)
• Binary values for CLASS – 1(case/affected subjects), 0(control/normal)
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11. Problem definition – measure(1/3)
• On contingency table
• Popular measure in epistasis detection
• 휒2 − 푡푒푠푡
• Mutual information
Genotype 퐴퐴퐵퐵 퐴퐴퐵푏 퐴퐴푏푏 퐴푎퐵퐵 퐴푎퐵푏 퐴푎푏푏 푎푎퐵퐵 푎푎퐵푏 푎푎푏푏 sum
Case 39 91 95 92 14 31 63 4 71 500
Control 100 15 55 5 22 150 50 93 10 500
sum 139 106 150 97 36 181 113 97 81 1000
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12. Problem definition – measure(2/3)
• 휒2 − 푡푒푠푡 based on 휒2 − distribution
• 퐻0 : no association between SNPs and disease status
휒2 =
(푂푖−퐸푖 )2
퐸푖
Genotype 퐴퐴퐵퐵 퐴퐴퐵푏 퐴퐴푏푏 퐴푎퐵퐵 퐴푎퐵푏 퐴푎푏푏 푎푎퐵퐵 푎푎퐵푏 푎푎푏푏 sum
Case 39 91 95 92 14 31 63 4 71 500
Control 100 15 55 5 22 150 50 93 10 500
sum 139 106 150 97 36 181 113 97 81 1000
Expected contingency table
Genotype 퐴퐴퐵퐵 퐴퐴퐵푏 퐴퐴푏푏 퐴푎퐵퐵 퐴푎퐵푏 퐴푎푏푏 푎푎퐵퐵 푎푎퐵푏 푎푎푏푏 sum
Case 69.5 53 75 48.5 18 90.5 56.5 48.5 40.5 500
Control 69.5 53 75 48.5 18 90.5 56.5 48.5 40.5 500
sum 139 106 150 97 36 181 113 97 81 1000
휒2 − 푣푎푙푢푒 ∶ 379.07, 푝 − 푣푎푙푢푒 = 2.76 × 10−77
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13. Problem definition – measure(3/3)
• Mutual information(1/3)
• Non-parametric measure
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14. Problem definition – measure(3/3)
• Mutual information(2/3)
Genotype 퐴퐴퐵퐵 퐴퐴퐵푏 퐴퐴푏푏 퐴푎퐵퐵 퐴푎퐵푏 퐴푎푏푏 푎푎퐵퐵 푎푎퐵푏 푎푎푏푏 sum
Case 39 91 95 92 14 31 63 4 71 500
Control 100 15 55 5 22 150 50 93 10 500
sum 139 106 150 97 36 181 113 97 81 1000
Frequency Table
Genotype 퐴퐴퐵퐵 퐴퐴퐵푏 퐴퐴푏푏 퐴푎퐵퐵 퐴푎퐵푏 퐴푎푏푏 푎푎퐵퐵 푎푎퐵푏 푎푎푏푏 sum
Case 0.039 0.091 0.095 0.092 0.014 0.031 0.063 0.004 0.071 0.500
Control 0.100 0.015 0.055 0.005 0.022 0.150 0.050 0.093 0.010 0.500
sum 0.139 0.106 0.150 0.097 0.036 0.181 0.113 0.097 0.081 1.000
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15. Problem definition – measure(3/3)
• Mutual information(3/3)
Entropy Table
Genotype 퐴퐴퐵퐵 퐴퐴퐵푏 퐴퐴푏푏 퐴푎퐵퐵 퐴푎퐵푏 퐴푎푏푏 푎푎퐵퐵 푎푎퐵푏 푎푎푏푏 sum
Case 0.183 0.315 0.323 0.317 0.086 0.155 0.251 0.032 0.271 0.500
Control 0.332 0.091 0.230 0.038 0.121 0.411 0.216 0.319 0.066 0.500
sum 0.396 0.343 0.411 0.326 0.173 0.446 0.355 0.326 0.294
퐼 푔푒푛표푡푦푝푒; 푑푖푠푒푎푠푒 = 퐻 푔푒푛표푡푦푝푒 + 퐻 푑푖푠푒푎푠푒 − 퐻 푔푒푛표푡푦푝푒, 푑푖푠푒푎푠푒
= 3.07 + 1.00 − 3.76
= 0.31
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16. Methods to detect
epistasis
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17. Methods – Computational
Approaches
• Multifactor Dimensionality Reduction
(Ritchie et al. 2002)
• SNPHarvester (Yang et al. 2009)
• SNPRuler (Wan et al. 2010)
• Mutual Information With Clustering
(Leem et al. 2014)
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18. Methods
Multifactor dimensionality reduction(1/2)
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19. Methods
Multifactor dimensionality reduction(2/2)
• Model free, non-parametric methods
• Pattern-based method
• Association rule for each combinations of SNPs and
phenotypes
• i.e. 푖푓 푆푁푃10 = 0 푎푛푑 푆푁푃13 = 4 푡ℎ푒푛 푐푙푎푠푠 = 1
• Exhaustive Search
• Computational Burden
• Cross Validation Consistency
• To select best model
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20. Methods
SNPHarvester(1/2)
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21. Methods
SNPHarvester(2/2)
• Local search
• Local optima problem
• PathSeeker algorithm
• Successive Runs
• Score function : 휒2 − 푣푎푙푢푒
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22. Methods
SNPRuler
• Pattern-based method
• Predictive rule
• Branch-and-bound algorithm
• Upper bound of 휒2 − 푣푎푙푢푒 in d.f. is 1
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23. Methods
Mutual Information With Clustering(1/2)
: SNPs
: causative SNPs
d1
d2
distance
Score=d1+d2
Centroid 1
Centroid 2
Centroid 3
3 SNPs with the
highest mutual
information value
m candidates
m candidates
m candidates
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24. Methods
Mutual Information With Clustering(2/2)
• Mutual information
• As distance measure for clustering
• K-means clustering algorithm
• Candidate selection
• Reduce search space dramtically
• Can detect high-order epistatic interaction
• Also, shows better performance (power, execution time)
than previous methods
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25. Challenges in epistasis
detection
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26. Challenges
• Reducing computational burden
• Filtering
• Parallel processing
• Higher-order epistatic interaction detection
• Larger than 2
• Novel measure of association between SNPs and
disease
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