1. POLYMORPHISMS & ASSOCIATION TESTS
Arián Avalos
Mayo-Illinois Computational Genomics Workshop
June 22, 2017

2. OUTLINE Molecular Markers Genome Wide Association Studies (GWAS)
Beyond Single Locus
Functional Effects

3. Individuals I2 and I5 have a variation (T → A). This position is both.
MOLECULAR MARKERS
What is a SNP and a SNV?
Single Nucleotide Polymorphysm
Single Nucleotide Variant
I1: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT
I2: AACGAGCTAGCGATCGATCGACAACGACTACGAGGT
I3: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT
I4: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT
I5: AACGAGCTAGCGATCGATCGACAACGACTACGAGGT
I6: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT
I7: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT
I8: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT
Individuals I2 and I5 have a variation (T → A). This position is both.

4. MOLECULAR MARKERS
A SNV is any change (e.g. a somatic mutation, even an artifact).
A SNP has defining criteria
Polymorphic SNV, have “Major” and “minor” alleles
Sometimes defined by frequency level (e.g. minimum allele frequency of 5%)
Segregating sites, germplasm polymorphism in a population
For reference, the 1000 Genomes project identified ~41 Million SNPs across ~1000 Individuals.

5. MOLECULAR MARKERS
Both types of variants are relevant depending of the field
Population geneticists conducting association test will focus on SNPs
Cancer geneticists will instead be interested in SNVs
The terminology is further complicated in non-human biology (e.g. polyploidy, horizontal gene transfer, etc.)

6. GWAS: Resources
Zhang X. et al. (2012). PLoS Comput Biol 8(12): e  
Bush W. S. & Moore J. H. (2012) PLoS Comput Biol 8(12): e

7. GWAS Example: Approach: Genetic Linkage Analysis
Cystic Fibrosis and the CFTR gene mutations
Approach: Genetic Linkage Analysis
Genotype family members (some individuals carrying the disease)
Find a marker that correlates with the disease
Disease gene lies close to this marker

8. GWAS
Concept:
When a marker is correlated with a trait, it is likely to be genetically linked to the locus in a family analysis

9. GWAS

10. GWAS Limitations of Genetic Linkage Analysis
Requires data from entire families, preferably large ones, where the trait is segregating
Linkage analysis less successful with common diseases, e.g., heart disease or cancers.
Requires single, large effect loci

11. GWAS
Hypothesize that common diseases are influenced by common genetic variation in the population
Implications:
Any individual variation (SNP) will have relatively small correlation with the disease
The combinatorial effect of many alleles is what influence the disease phenotype
This argues for population- rather than family-based studies.

12. GWAS
Bush W. S. & Moore J. H. (2012) PLoS Comput Biol 8(12): e

13. GWAS: Genotyping Microarray – can assay 0.5 – 1.0 Million or more SNPs
Whole-genome sequencing (WGS) – assays (near) complete SNP profile
In non-human genetics, reduced-representation methods provide a middle-ground.

14. GWAS: Phenotyping
Case / Control – qualitative, usually binary measure (e.g. disease vs. no disease)
Quantitative – continuous measure usually complex phenotypes (e.g. blood pressure, LDL levels)
Possible to look at more than one phenotype?

15. GWAS Case / Control Disease?
I1: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I2: AACGAGCTAGCGATCGATCGACAACGACTACGAGGT +
I3: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I4: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I5: AACGAGCTAGCGATCGATCGACAACGACTACGAGGT +
I6: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I7: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I8: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -

16. GWAS Before analysis and interpretations a few considerations:
Correlation is not causation

17. GWAS Before analysis and interpretations a few considerations:
Correlation is not causation
Linkage disequilibrium (see later)
Population structure (see later)
Phenotyping

18. GWAS
Further consider that even if the analysis is successful, findings can be hard to interpret
Example:
SNP correlates well with heart disease
Biochemical link? Behavioral link (you particularly like bacon…)?

19. GWAS: Statistics Case vs. Control A T3 1
Control 9
Case vs. Control
I1: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I2: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I3: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I4: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I5: AACGAGCTAGCGATCGATCGACAACGACTACGAGGT +
I6: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I7: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I8: AACGAGCTAGCGATCGATCGACAACGACTACGAGGT +
I9: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I10: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT +
I11: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I12: AACGAGCTAGCGATCGATCGACTACGACTACGAGGT -
I13: AACGAGCTAGCGATCGATCGACAACGACTACGAGGT -
I14: AACGAGCTAGCGATCGATCGACAACGACTACGAGGT +

20. GWAS: Statistics 3 All 14 Case 4 A p-value < 0.05 Case vs. Control
The Fisher’s Exact Test 3
All 14
Case 4 A A T
Case 3 1
Control 9
p-value < 0.05

21. GWAS: Statistics
An favored alternative to the Fisher’s Exact Test is the Chi-Squared Test.
We conduct this test on EACH SNP separately, and get a corresponding p-value.
The smallest p-values point to the SNPs most associated with the disease.

22. GWAS: Statistics
Either Fisher’s or the Chi-Squared Test are considered an allelic association test, i.e. we test if A instead of T at the polymorphic site correlates with the disease.
In a genotypic association test each position is a combination of two alleles, e.g. AA, TT, AT
We therefore correlate genotype with phenotype of the individual

23. GWAS: Statistics
There are various options for a Case vs. Control genotypic association test
Example:
Dominant Model
AA or AT TT
Case ?
Control

24. GWAS: Statistics
There are various options for a Case vs. Control genotypic association test
Example:
Dominant Model
Recessive Model AA
AT or TT
Case ?
Control

25. GWAS: Statistics
There are various options for a Case vs. Control genotypic association test
Example:
Dominant Model
Recessive Model
2x3 Table AA AT TT
Case
O11
O12
O13
Control
O21
O22
O23
Χ 2 = 𝑖 𝑗 𝑂 𝑖𝑗 − 𝐸 𝑖𝑗 𝐸 𝑖𝑗
Chi-Squared Test

26. GWAS: Statistics Quantitative Phenotypes 𝑌=𝑎+𝑏𝑋
If no association, 𝑏 ≈0
The more 𝑏 Δ 0, the stronger the association
This is called linear regression

27. GWAS: Statistics Quantitative Phenotypes
Another statistical test commonly used on GWAS matrices is Analysis of Variance (ANOVA)
Statistical models for GWAS can get quite involved (can give references on request)

28. GWAS: Statistics
Lambert et al., 2013: Nature Genetics 45, 1452

29. GWAS: Statistics Multiple Hypothesis Correction
What does p-value = 0.01 mean?
It means that the observed Genotype x Phenotype correlation has only 1% probability of happening just by chance.
What if we repeat the test for 1 Million SNPs? Of those tests, 1% (10,000 SNPs) will show this level of correlation, just by chance (and by definition)

31. GWAS: Statistics Multiple Hypothesis Correction Bonferroni
Multiply the p-value by the number of tests
So if the original SNP had p-value 𝑝, the new p-value is defined as 𝑝 ′ =𝑝 ×𝑁
With 𝑁= , a p-value of 10 −9 is downgraded to:
𝑝 ′ = 10 −9 × = 10 −3
This is quite good!

32. GWAS: Statistics Multiple Hypothesis Correction False Discovery Rate
Given a threshold 𝛼 (e.g. 0.05)
Sort all p-values (𝑁 of them) in ascending order (i.e. 𝑝 1 ≤ 𝑝 2 ≤ … ≤ 𝑝 𝑛 )
Count for each group of 𝑁:
Require 𝑝 ′ <𝛼
This ensures the expected proportion of false positives in the reported association is <𝛼
𝑝 𝑖 ′ = 𝑝 𝑖 × 𝑁 𝑖

33. BEYOND SINGLE LOCUS
So far we have tested each SNP separately, however recall our hypothesis that common diseases are influenced by common variants
Maybe considering two SNPs together will identify a stronger correlation with phenotype
Main problem: Number of pairs ~ 𝑁 2

34. BEYOND SINGLE LOCUS
Further consider, in genotyping we may be using a Microarray (e.g. 0.5 – 1 Million SNPs)
But there are many more sites in the human genome where variation may exist, will we then miss any causal variant outside the panel of ~1 Million?
Not necessarily

35. BEYOND SINGLE LOCUS
Two sites close to each other may vary in a highly correlated manner, this is Linkage Disequilibrium (LD)
In this situation, lack of recombination events have made the inheritance of those two sites dependent
If two such sites have high LD, then one site can serve as proxy for the other

36. BEYOND SINGLE LOCUS
So if sites X & Y have high LD, and X is in the Microarray, then knowing the allelic form of X informs the allelic form at Y
In this way a reduced panel can represent a larger number (all?) of the common SNPs

37. BEYOND SINGLE LOCUS
Impact of LD

38. BEYOND SINGLE LOCUS
A problem is that if X correlates with a disease, the causal variant may be either X or Y

39. BEYOND SINGLE LOCUS
Impact of Population Structure.

40. BEYOND SINGLE LOCUS
In many cases, able to find SNPs that have significant association with disease.
GWAS Catalog
Yet, final predictive power (ability to predict disease from genotype) is limited for complex diseases.
Finding the Missing Heritability of Complex Diseases

41. BEYOND SINGLE LOCUS
Increasingly, whole-exome and even whole-genome sequencing used for variant detection
Taking on the non-coding variants. Use functional genomics data as template
Network-based analysis rather than single-site or site- pairs analysis
Complement GWAS with family-based studies

42. FUNCTIONAL EFFECTS
How do we predict how a variant is likely to be affecting protein function?

43. FUNCTIONAL EFFECTS Case:
I found a SNP inside the coding sequence. Knowing how to translate the gene sequence to a protein sequence, I discovered that this is a non-synonymous change, i.e., the encoded amino acid changes. This is an nsSNP.
Will that impact the protein’s function?
(And I don’t quite know how the protein functions in the first place ...)

44. FUNCTIONAL EFFECTS Two popular approaches: PolyPhen 2.0 SIFT
Adzhubei, I. A. et al. (2010). Nat Methods 7(4):
SIFT
Kumar P. et al., (2009). Nat Protoc 4(7):

45. FUNCTIONAL EFFECTS
PolyPhen 2.0

46. FUNCTIONAL EFFECTS
The PolyPhen 2.0 pipeline uses existing data sets for training and later evaluation of target data.
Specifically the HumDiv data base which is
A compilation of all the damaging mutations with known effects of molecular function
A collection of non-damaging differences between human proteins and those of closely related mammalian homologs

47. FUNCTIONAL EFFECTS
PolyPhen 2.0 features:

48. FUNCTIONAL EFFECTS
A look at the Multiple Sequence Alignment (MSA) part of the PolyPhen 2.0 pipeline:

49. FUNCTIONAL EFFECTS
Of interest is the Position Specific Independent Count (PSIC) Score.
This score reflects the amino acid’s frequency at the specific position in the sequence given an MSA

50. FUNCTIONAL EFFECTS
Example:

51. FUNCTIONAL EFFECTS
To derive the PSIC score we first calculate the frequency of each amino acid:
p 𝑎, 𝑖 = 𝑛 𝑎, 𝑖 𝑒𝑓𝑓 𝑏 𝑛 𝑏, 𝑖 𝑒𝑓𝑓

52. FUNCTIONAL EFFECTS p 𝑎, 𝑖 = 𝑛 𝑎, 𝑖 𝑒𝑓𝑓 𝑏 𝑛 𝑏, 𝑖 𝑒𝑓𝑓 The idea:
𝑛 𝑎, 𝑖 𝑒𝑓𝑓 is not the raw count of amino acid “𝑎” at position 𝑖 but rather it is adjusted for the many closely related sequences in the MSA
The PSIC score of a SNP 𝑎 →𝑏 at position 𝑖 is given by:
p 𝑎, 𝑖 = 𝑛 𝑎, 𝑖 𝑒𝑓𝑓 𝑏 𝑛 𝑏, 𝑖 𝑒𝑓𝑓
PSIC 𝑎→𝑏, 𝑖 ∝ln 𝑝 𝑏, 𝑖 𝑝 𝑎, 𝑖

53. FUNCTIONAL EFFECTS
Ultimately your derived score can be compared with the existing scores from HumDiv

54. FUNCTIONAL EFFECTS Classification Naive Bayes method
A type of classifier. Other classification algorithms include “Support Vector Machine”, “Decision Tree”, “Neural Net”, “Random Forest” etc.
Sometimes called “Machine Learning”
What is a classification algorithm?
What is a Naive Bayes method/classifier?

55. FUNCTIONAL EFFECTS 𝑥 11 , 𝑥 12 , …, 𝑥 1𝑛 + 𝑥 21 , 𝑥 22 , …, 𝑥 2𝑛 + …
𝑥 11 , 𝑥 12 , …, 𝑥 1𝑛 +
𝑥 21 , 𝑥 22 , …, 𝑥 2𝑛 + …
𝑥 𝑖+1, 1 , 𝑥 𝑖+1, 2 , …, 𝑥 𝑖+1𝑛 -
𝑥 𝑖+2, 1 , 𝑥 𝑖+2, 2 , …, 𝑥 𝑖+2𝑛 -
Positive examples
Negative examples
Training Data
MODEL
“Supervised Learning”

56. FUNCTIONAL EFFECTS
Data Vector
𝑥 1 , 𝑥 2 , …, 𝑥 𝑛
MODEL
Yes or No

57. FUNCTIONAL EFFECTS Naïve Bayes Classifier Bayesian Inference: + or −
Training Data
Bayesian Inference:
Expresses how a subjective assessment of likelihood should rationally change to account for evidence
+ or −

58. FUNCTIONAL EFFECTS
In statistics, frequentists and Bayesians often disagree.
A frequentist is a person whose long-run ambition is to be wrong 5% of the time.
A Bayesian is one who, vaguely expecting a horse, and catching a glimpse of a donkey, strongly believes he has seen a mule.

59. Or…

60. FUNCTIONAL EFFECTS Evaluating a classifier: Cross-validation
PREDICT AND EVALUATE
ON THESE
TRAIN ON THESE
FOLD 1

61. FUNCTIONAL EFFECTS Evaluating a classifier: Cross-validation
PREDICT AND EVALUATE
ON THESE
FOLD 2

62. FUNCTIONAL EFFECTS Evaluating a classifier: Cross-validation
PREDICT AND EVALUATE
ON THESE
FOLD k

63. Collect all evaluation results (from k “FOLD”s)
FUNCTIONAL EFFECTS
Evaluating a classifier: Cross-validation
Collect all evaluation results (from k “FOLD”s)

64. FUNCTIONAL EFFECTS
Evaluating Classification Performance
Wikipedia

65. FUNCTIONAL EFFECTS The Receiver Operating Characteristic (ROC) curve
True +ve vs False +ve

66. FUNCTIONAL EFFECTS What about those SNPs outside the coding regions?
Generally hard enough to predict within coding regions – regulatory sequences notoriously hard to pin down (see ENCODE controversy)
One interesting new approach uses Support Vector Machine (SVM) classifiers to describe damage to cell-specific regulatory motif vocabularies.

67. FUNCTIONAL EFFECTS