Association analysis

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Association analysis

• Shaun Purcell
• Boulder Twin Workshop 2004

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Overview

• Candidate gene association
• Haplotypes and linkage disequilibrium
• Linkage and association
• Family-based association

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What is association?

• Categorical traits
• disease susceptibility genes
• Continuous traits
• quantitative trait loci, QTL

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Disease traits
Is there a difference in allele/genotype
frequency between cases and controls?

• Case Control
• AA n1 n2
• Aa n3 n4
• aa n5 n6

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Disease traits
Is there a difference in allele/genotype
frequency between cases and controls?

• Case Control
• AA 30 25 p2
• Aa 50 50 2p(1-p)
• aa 20 25 (1-p)2

, p-value
Test for independence
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Disease traits
General model
Additive model
Dominant model for A
1 df
1 df
2 df
Effect sizes calculated as odds ratios
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Relative risk

• D D-
• E a b
• E- c d
• Risk in E a / ( a b )
• Risk in E- c / ( c d )
• Relative risk of exposure (a /( a b )) / (c
  /(c d ))

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Odds ratio

• D D-
• E a b
• E- c d
• Odds in D a/c
• Odds in D- b/d
• Odds ratio (a/c) / (b/d)

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Quantitative traits
ID Y G A D 001 0.34 aa -1 0 002 1.23 Aa 0 1 003 1
.66 Aa 0 1 004 2.74 AA 1 0 005 1.33 AA 1 0

Y aA dD e
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Some web resources

• BGIM
• http//statgen.iop.kcl.ac.uk/bgim/
• Introductory tutorials on twin analysis, primer
  on maximum likelihood, Mx language.
• GxE moderator models
• http//statgen.iop.kcl.ac.uk/gxe/
• Power calculation
• http//statgen.iop.kcl.ac.uk/gpc/
• Case/control association tools
• http//statgen.iop.kcl.ac.uk/gpc/model/

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Relative risk
P(DAA) / P(Daa) labelled RR(AA) P(DAa) /
P(Daa) labelled RR(Aa)
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Genetic models
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Tests
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Multiple samples

• Constrain frequencies across samples
• Constrain effects across samples
• Can test genetic models with effects and/or
  frequencies constrained to be equal
• Can perform tests of homogeneity of effects
  and/or frequencies across samples

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An example2 case/control samples

• Population frequency 5

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• Homogeneous effects across samples
• Homogeneous allele frequencies across samples
• Model p RR(Aa) RR(AA) -2LL
• ----- - ------ ------ ----
• Gen 0.367 1.979 3.663
• 0.367 1.979 3.663 793.143
• Mult 0.367 1.911 3.651
• 0.367 1.911 3.651 793.199
• Dom 0.401 1.990 1.990
• 0.401 1.990 1.990 802.927
• Rec 0.405 1.000 1.921
• 0.405 1.000 1.921 805.064
• None 0.442 1.000 1.000
• 0.442 1.000 1.000 815.628

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• Heterogeneous effects across samples
• Homogeneous allele frequencies across samples
• Model p RR(Aa) RR(AA) -2LL
• ----- - ------ ------ ----
• Gen 0.367 1.235 2.136
• 0.367 2.890 5.547 786.498
• Mult 0.367 1.440 2.073
• 0.367 2.282 5.208 788.262
• Dom 0.401 1.216 1.216
• 0.401 2.936 2.936 796.422
• Rec 0.405 1.000 1.519
• 0.405 1.000 2.195 803.849
• None 0.443 1.000 1.000
• 0.443 1.000 1.000 815.628

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• TESTS OF GENETIC MODELS -- ASSUMING EQ EFFECTS
  EQ FREQS
• 
  
• Gen vs None (2 df) 22.485 p 0.000
• Mult vs None (1 df) 22.429 p 0.000
• Dom vs None (1 df) 12.701 p 0.000
• Rec vs None (1 df) 10.564 p 0.001
• Gen vs Mult (1 df) 0.056 p 0.813
• Gen vs Dom (1 df) 9.784 p 0.002
• Gen vs Rec (1 df) 11.921 p 0.001
• TESTS OF GENETIC MODELS -- ASSUMING UNEQ EFFECTS
  EQ FREQS
• 
  
• Gen vs None (4 df) 29.130 p 0.000
• Mult vs None (2 df) 27.366 p 0.000
• Dom vs None (2 df) 19.205 p 0.000
• Rec vs None (2 df) 11.779 p 0.003
• Gen vs Mult (2 df) 1.764 p 0.414

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Indirect association
Genotyped markers
QTL
Ungenotyped markers
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Recombination
Homologous chromosomes in one parent
Paternal chromosome
Maternal chromosome
Recombination event during meiosis
Recombinant gamete transmitted, harboring mutation
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Recombination
Homologous chromosomes in one parent
Paternal chromosome
Maternal chromosome
No recombination event during meiosis
Nonrecombinant gamete transmitted, not harboring
mutation
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Linkage affected sib pairs
Paternal chromosome
Maternal chromosome
First affected offspring, no recombination
Second affected offspring, recombinant gamete
IBD sharing from this one parent (0 or 1)
1
0
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Association analysis

• Mutation occurs on a red chromosome

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Association analysis

• Mutation occurs on a red chromosome

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Association analysis

• Association due to linkage disequilibrium

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Haplotypes

• A a
• M AM aM
• m Am am
• This individual has aa and Mm genotypes
• and am and aM haplotypes

a
m
M
a
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Haplotypes

• A a
• M AM aM
• m Am am
• This individual has Aa and Mm genotypes
• and AM and am haplotypes
• but given only genotype data,
• consistent with Am/aM as well as AM/am

a
m
A
M
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Haplotypes

• A a
• M AM aM
• m Am am
• This individual has AA and Mm genotypes
• and AM and Am haplotypes

A
m
A
M
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Equilibrium haplotype frequencies

• A a
• M pr ps p
• m qr qs q
• r s

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Linkage disequilibrium

• A a
• M pr D ps - D p
• m qr - D qs D q
• r s
• DMAX Min(qs, pr)
• D D /DMAX
• r2 D / pqrs

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Haplotype analysis

• Estimate haplotypes from genotypes
• Associate haplotypes with trait
• Haplotype Freq. Odds Ratio
• AAGG 40 1.00
• AAGT 30 2.21
• CGCG 25 1.07
• AGCT 5 0.92
• baseline, fixed to 1.00

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Linkage Association
Trait
aa
Aa
AA
QTL genotype
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Variance Components

• Means
• M1 M2
• Variance-covariance matrix
• V1 C21
• C12 V2

ASSOCIATION
LINKAGE
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Variance Components

• Means
• M1 bG1 M2 bG2
• Variance-covariance matrix
• V1 C21 q(?-½)
• C12 q(?-½) V2

ASSOCIATION b regression coef. G individuals
genotype
LINKAGE q regression coef. ? IBD sharing
0 , ½ , 1
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Components of a Genetic Theory

• POPULATION MODEL
• Allele genotype frequencies
• Demographics population history
• Linkage disequilibrium, haplotype structure
• TRANSMISSION MODEL
• Mendelian segregation
• Identity by descent genetic relatedness
• PHENOTYPE MODEL
• Biometrical model of quantitative traits
• Additive dominance components

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Linkage without association
3/5
2/6
3/5
2/6
3/2
3/6
5/2
5/6
Both families are linked with the marker but
a different allele is involved.
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Linkage and association
3/6
2/4
3/5
2/6
4/6
2/6
3/2
3/6
6/2
5/6
6/6
6/6
All families are linked with the marker and
allele 6 is associated with disease
Linkage is just association within families
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Association without linkage
Controls
Cases
6/6
6/2
3/5
3/4
3/6
5/6
2/4
3/2
3/6
2/2
4/6
2/6
2/5
5/2
Allele 6 is more common in the GREEN
population The disease is more common in the
GREEN population a spurious association
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TDT

• Transmission disequilibrium test
• test for linkage and association

aa
Aa
AA
AA
AA
Aa
Aa
AA
Aa
Aa
Aa
AA
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TDT A disease allele

• AA x Aa AA x Aa aa x Aa aa x Aa
• AA Aa
  Aa aa
• -
  -
• 0.5 0.5
  -
• -
  0.5 0.5

Additive
Dominant
Recessive
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Between and within components
Sib1
Sib2
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Between and within components

• Fulker et al (1999)

Note W S1 B
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Parental genotypes

• Use parental genotypes to generate B
• Examples
• AA from AAxAA W 0
• Aa from AAxAa W -0.5
• Aa from AaxAa W 0

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assoc.mx

• Sibling pair sample
• B and W components precalculated in input file
• Single SNP genotype
• Quantitative trait

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assoc.dat
s1 s2
g1 g2 b
w1 w2

• -0.007 -0.972 -1 0 -0.5
  -0.5 0.5
• -0.829 -0.196 1 1 1
  0 0
• 0.369 0.645 1 1 1
  0 0
• 0.318 1.55 0 1 0.5
  -0.5 0.5
• 1.52 0.910 0 0 0
  0 0
• -0.948 -1.55 1 1 1
  0 0
• 0.596 -0.394 1 0 0.5
  0.5 -0.5
• -1.91 -0.905 0 1 0.5
  -0.5 0.5
• 0.499 0.940 1 0 0.5
  0.5 -0.5
• -1.17 -1.29 1 0 0.5
  0.5 -0.5
• -0.16 -1.81 1 1 1
  0 0

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• ! Mx script for QTL association sib pairs,
  univariate
• Group 1
• Calc NG2
• Begin Matrices
• ! Parameters
• B Full 1 1 free ! association between
  component
• W Full 1 1 free ! association within
  component
• M Full 1 1 free ! mean
• S Full 1 1 free ! Shared residual variance
• N Full 1 1 free ! Nonshared residual variance
• ! Definition variables
• C Full 1 1 ! association between
• X Full 1 1 ! association within, sib 1
• Y Full 1 1 ! association within, sib 2
• End Matrices

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• Group2 Data Group
• Data NI7 NO0
• RE fileassoc.dat
• Labels Sib1 Sib2 g1 g2 b w1 w2
• Select Sib1 Sib2 b w1 w2 /
• Definition b w1 w2 /
• Matrices Group 1
• Means M BC WX M BC WY /
• Covariance
• S N S _
• S S N /
• Specify C b /
• Specify X w1 /
• Specify Y w2 /

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Models

• B W
• B Full 1 1 free
• W Full 1 1 free
• !Equate W 1 1 1 B 1 1 1
• B W
• B Full 1 1 free
• W Full 1 1 free
• Equate W 1 1 1 B 1 1 1
• B
• B Full 1 1 free
• W Full 1 1
• !Equate W 1 1 1 B 1 1 1
• BW0
• B Full 1 1
• W Full 1 1
• !Equate W 1 1 1 B 1 1 1

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Tests

• Test HA H0
• Standard association test B W BW0
• Test of stratification B W B W
• Robust association test B W B

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assoc.mx

• Model B W -2LL df
• B W -0.478 -0.365 2103.96 795
• B W -0.420 -0.420 2105.05 796
• B -0.4778 2127.01 796
• BW0 2163.34 797

Test of total association HA BW 2105.05
H0 BW0 2163.34 ?-2LL 58.29, df
1, p lt 1e-14
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assoc.mx

• Model B W -2LL df
• B W -0.478 -0.365 2103.96 795
• B W -0.420 -0.420 2105.05 796
• B -0.4778 2127.01 796
• BW0 2163.34 797

Test of stratification HA B W 2103.96
H0 B W 2105.05 ?-2LL 1.09, df
1, p 0.29
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assoc.mx

• Model B W -2LL df
• B W -0.478 -0.365 2103.96 795
• B W -0.420 -0.420 2105.05 796
• B -0.4778 2127.01 796
• BW0 2163.34 797

Test of within association HA B W 2103.96
H0 B 2127.01 ?-2LL 23.06,
df 1, p lt 1e-6
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Implementation

• QTDT
• Abecasis et al (2001) AJHG
• extends between/within model to general pedigrees
• multiple alleles
• covariates
• combined test of linkage and association
• discrete as well as quantitative traits

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Linkage Association

• families
• detectable over large distances gt10 cM
• large effects OR gt3, variancegt10

• unrelateds or families
• detectable over small distances lt1 cM
• small effects ORlt2, variancelt1