Shaun Purcell

Psychiatric & Neurodevelopmental Genetics UnitCenter for Human Genetic Research

Massachusetts General Hospital

http://pngu.mgh.harvard.edu/~purcellspurcell@pngu.mgh.harvard.edu

Gene-environment & gene-gene Gene-environment & gene-gene interaction in association studies: interaction in association studies:

a methodologic introductiona methodologic introduction

Finding disease-causing variation

The Human Genome

chromosome 4 DNA sequenceSNP (single nucleotide polymorphism)

…GGCGGTGTTCCGGGCCATCACCATTGCGGGCCGGATCAACTGCCCTGTGTACATCACCAAGGTCATGAGCAAGAGTGCAGCCGACATCATCGCTCTGGCCAGGAAGAAAGGGCCCCTAGTTTTTGGAGAGCCCATTGCCGCCAGCCTGGGGACCGATGGCACCCATTACTGGAGCAAGAACTGGGCCAAGGCTGCGGCGTTCGTGACTTCCCCTCCCCTGAGCCCGGACCCTACCACGCCCGACTA…

Rare disease, major gene effect

Genotype Risk of diseaseDD 0.001

Dd 0.001

dd 0.95

Disease prevalence ~1 in 1000

Individuals with dd are ~1000 times more likely to get disease

Frequency of d in controls ~ 5%Frequency of d in cases ~ 96%

Disease prevalence ~1 in 1000

Individuals with dd are ~1000 times more likely to get disease

Frequency of d in controls ~ 5%Frequency of d in cases ~ 96%

Common polygenic disease

Genotype Risk of diseaseDD 0.01

Dd 0.012

dd 0.0144

Common disease, polygenic effects

Disease prevalence ~1 in 100

Each extra d allele increases risk by ~1.2 times

Frequency of d in controls ~ 5%Frequency of d in cases ~ 6%

Disease prevalence ~1 in 100

Each extra d allele increases risk by ~1.2 times

Frequency of d in controls ~ 5%Frequency of d in cases ~ 6%

?

GenotypeGenotype

EnvironmentEnvironment

PhenotypePhenotype

?

Gene-environment correlation

Gen

e ef

fect

Environmental effect

The environment modifies the effect of a gene

A gene modifies the effect of an environment

G x E interactionG x E interaction

Gene-environment interaction

Linkage disequilibrium (LD)

Epistasis

Gene effect

Gen

e ef

fect

Epistasis: one gene modifies the effect of another

Gene Gene ×× gene interaction gene interaction

Classical definition of epistasis

The aa genotype masks the effect of the bb genotype

AA

Aa

aa

BB Bb bb

Separate analysis

• locus A shows an association with the trait

• locus B appears unrelated

AA Aa aa BB Bb bb

Marker A Marker B

Joint analysis

• locus B modifies the effects of locus A

BB Bb bb

AA

Aa

aa

Two locus genotypes Locus A

Locus B AA Aa aa

BB AABB AaBB aaBB

Bb AABb AaBb aaBb

bb Aabb Aabb aabb

Epistasis & haplotypes

• Two-locus genotype A/a B/b (AaBb)A and B need not even be on same chromosome

• Haplotype AB / abA and B on same chromosome; effect could appear as “interaction”

• cis versus trans effectsAB haplotype causes disease A and B interact to cause disease

A

a

B

b

A

a

b

B

A

a

B

b

A

a

b

B

disease

no disease

disease

disease

Two locus genotypes Locus A

Locus B AA Aa aa

BB fAABB fAaBB faaBB

fBB

Bb fAABb fAaBb faaBb

fBb

bb fAabb fAabb faabb

fbb

fAA fAa faa f

“Penetrance” = probability of developing disease given genotype

Genotype Risk of diseaseDD 0.01

Dd 0.012

dd 0.0144

Common disease, polygenic effects

Disease prevalence ~1 in 100

Each extra d allele increases risk by ~1.2 times

Frequency of d in controls ~ 5%Frequency of d in cases ~ 6%

Disease prevalence ~1 in 100

Each extra d allele increases risk by ~1.2 times

Frequency of d in controls ~ 5%Frequency of d in cases ~ 6%

Small single SNP effectsmight represent larger epistatic effects

AA

Aa

aa

BB Bb bb

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.20

Risk of developing disease

0.01 0.01 0.012

Frequency a = b = 0.1

Interaction may be a common feature of genetic variation

• Brem et al (2005) Nature– gene expression phenotypes in yeast

– two-stage approach to find pairs of loci

• 65% of these pairs showed significant interaction

• many secondary loci would be missed by standard approaches though

Examples of interactions?Risk Environment Outcome

phenylalanine hydroxylase deficiency

dietary phenylalanine

mental retardation

debrisoquine metabolism

smoking lung cancer

fair skin sun exposure skin cancer

Lewis blood group alcohol intake coronary atherosclerosis

APOE genotype head injury Alzheimer's disease

The rest of this talk…

• Statistical issues

• Study designs

• Examples

AA AC

AA CC AA

AA

AC

AA

AA AC CCAA

AA AA AA AC AA AC CC CC

Family-based transmission disequilibrium test (TDT)

Population-based case/control

Odds ratio: measure of association

A aCase a bControl c d

Odds of A in cases = a/bOdds of A in controls = c/d

Odds ratio = (a/b)/(c/d) = ad / bc

E- E+

A a A a

Case 80 20 60 40

Control 80 20 80 20

Odds ratio 1.00 0.375(80*20)/(80*20) (60*20)/(80*40)

Z = ( ln(ORE-) – ln(ORE+) ) / sqrt( VE- + VE+)

V( ln(OR) ) = 1/a + 1/b + 1/c + 1/d

Regression modeling of interaction

Y = bXX + e

Y = bXX + bZZ + bIXZ + e

Y = ( bX + bIZ )X + bZZ + e

interaction component

effect of X on Y is modified by Z

Y = b0 + b1G + b2E +b3G×E

Y

0 1 2

• Linear for continuous outcomes

• Logistic regression for yes/no outcomes

G = 0, 1, 2 copies of allele “A”

E = yes/no exposure (0/1)

continuous measure

E-

E+

Gene dosage

The “Interactome”

Definitions of epistasisBiological Statistical

Individual-levelphenomenon

Population-level phenomenon

BB Bb bb

AA

Aa

aa

BB Bb bb

AA

Aa

aa

Requires:1) Variation between individuals2) Effect on disease

BB Bb bb

AA

Aa

aa

Requires:1) Correct statistical definition of effect

What do interactions mean?

• TEST MAIN EFFECT – Null hypothesis straightforward

• TEST INTERACTION– Null hypothesis is a mathematical model describing

joint effects

A- A+

B- 1 a

B+ b ?

A- A+ RR(A)

B- 1 a a/1 = a

B+ b ab ab/b = a

Additive risk differencesAdditive risk differences

A- A+ RD(A)

B- 1 a a-1 = a-1

B+ b a+b-1 a+b-1-b = a-1

Multiplicative risk ratiosMultiplicative risk ratios

“…we defined interaction as departure from a multiplicative model…”

• Multiplicative model (a×b)– common, easy to implement, logistic

regression• additive on log-odds scale• multiplicative on risk scale

• Other common models (on risk)– additive (a + b)– heterogeneity model (a + b – ab )

A- A+

B-

B+

10

20

20

30

LENGTH = A + B

A- A+

B-

B+

100

400

400

900

AREA = A + B + A×B

Original Log-transform

0.1

.2.3

De

nsity

-5 0 5p0

0.5

11.

5D

ens

ity

-2 -1 0 1 2p1

0.0

2.0

4.0

6.0

8D

ens

ity

-100 -50 0 50 100 150p2

0.5

11.

52

De

nsity

0 1 2 3 4 5p3

0.1

.2.3

De

nsity

0 2 4 6 8p4

Cubic-transform Censored 7-point scale

G1

G2

G1G2

OR(A) = 2

OR(B) = 2

1 2 3 4 51/21/3

Additive (3.00)

Multiplicative (4.00)???

OR(A) = 1.2

OR(B) = 1.2

1 2 3 4 51/21/3

Additive (1.40)

Multiplicative (1.44)?

AA AA

AA AC

No controls(Case-only design)

Population-based controls

Family-based controls

More robust, fewer assumptions

More efficient, powerful

v.s.

Case-only design• Detect interaction only, no main effects

Risk factors Prevalence

G- E- p0

G+ E- pG

G- E+ pE

G+ E+ pGE = p0 ∙ pG /p0 ∙ pE /p0

Case-only design• Detect interaction only, no main effects

Risk factors Prevalence

G- E- p0

G+ E- pG

G- E+ pE

G+ E+ pGE = p0 ∙ pG /p0 ∙ pE /p0

Leads to ORINT = ORGE / (ORG ∙ ORE)

It turns out, ORINT = ORCase / ORControl

where ORCase is the association of G and E in cases

and ORControl is the association of G and E in controls

0

10

20

30

40

50

60

70

80

90

100

100 cases, 100 controls

200 cases, 200 controls

200 cases only

200 controls only

No interaction Interaction0

10

20

30

40

50

60

70

80

90

100

100 cases, 100 controls

200 cases, 200 controls

200 cases only

200 controls only

0

10

20

30

40

50

60

70

80

90

100

% r

epli

cate

s si

gnif

ican

t at p

=0.

05

Case-only designs offer efficient detection of interaction

Case-only design isn’t always valid

• Chromosomal proximity

• Multiple ethnicities in case sample

Gene A Gene B

Gene A Gene B

stratification

Epistasis:

LD in cases ≠ LD in controls

Cases(Scz)

Controls

Genes in 5q GABA cluster

Pamela SklarTracey PetryshenC&M Pato

Pamela SklarTracey PetryshenC&M Pato

TDT requires independence assumption

aa Aa

aa

aa Aa

Aa

AA Aa

Aa

AA Aa

AA

Stratify for bb probands Stratify for BB probands

→100% →0% → 0% →100%

If variants A and B are in LD (common haplotypes AB / ab)

→ false positive interactions (due to linkage or population stratification)

An “all pairs of SNPs” approach to epistasis does not scale well

# SNPs # pairs

5 10

10 45

50 1,225

100 4,950

500 124,750

500000 124,999,750,000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45 50

Multiple testing increases false positives

Number of independent tests performed

P(a

t lea

st 1

fals

e po

siti

ve) per test false positive

rate 0.05

per test false positive rate0.001 = 0.05/50

Tests for interaction have low power

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Increasing sample N

Stat

isti

cal p

ower

Epistasis test

Standard association test

• DTNBP1 & 7 other genes encode proteins that make up the BLOC1 protein complex– biogenesis of lysosome-related organelles complex 1

• DTNBP1’s effect on Scz mediated via BLOC1?– if so, an analysis including all 8 genes

might help to resolve inconsistent studies

Dysbindin-1 (DTNBP1) & schizophrenia

Derek MorrisAiden CorvinMichael Gill

Derek MorrisAiden CorvinMichael Gill

DTNBP1 association studies

rs10

47

63

1

P1

32

8

P1

33

3

rs734129 P

12

87

rs38

29

89

3

P1

65

5

P1

63

5

rs26

19

54

2

P1

32

5

rs26

19

55

0

P1

76

5

P1

75

7

P1

32

0

P1

76

3

P1

57

8

P1

79

2

P1

79

5

P1

58

3

rs27

43

85

2

rs26

19

53

8

A A T

G G C

C C C

G C A A T C C

A C A T T

T G T C A

C A

C A T

C A T C T C

G G

G G

1 2 3 4 5 6 7 8 9 10

Exons

Straub et al. (2002)

SNPs

Schwab et al. (2003)

Van den Oord et al. (2003)

Van den Bogaert et al. (2003)

Tang et al. (2003)

Kirov et al. (2004)

Williams et al. (2004)

Funke et al. (2004)

Numakawa et al. (2004)

Li et al. (2005)

Types of interaction

G+

G-

G+

G-

G+

G-

Direction of effect Presence of effect Magnitude of effect

Duplicate gene action

Example: Kernel Color in Wheat

Only 1 dominant allele required, either A or B

A_B_ NormalA_bb NormalaaB_ Normalaabb No product

AA Aa aa

BB

Bb

bb

Complementary gene action

Example: Flower color in sweet pea

One recessive genotype at either gene would increase disease risk

i.e. genes A and B required

A_B_ NormalA_bb No productaaB_ No productaabb No product

AA Aa aa

BB

Bb

bb

AA Aa aa

BB

Bb

bb

Complementarygene action

Duplicategene action

Heterogeneity

model“Checkerboard”

model

Negative feedback: a common biological mechanismNegative feedback: a common biological mechanism

-/- +/- +/+

-/-

+/-

+/+

Negative feedback: simple model of dysregulationNegative feedback: simple model of dysregulation

-/- +/- +/+

-/-

+/-

+/+0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Frequency of one locus(other locus fixed p=0.4)

Single markerrelative risk

Negative feedback: single marker analysis leads toNegative feedback: single marker analysis leads tothe “opposite allele” problemthe “opposite allele” problem

0

0.5

1

1.5

2

2.5

Standard single SNP analyses

DTNBP1 MUTED PLDN SNAPAP CNO BLOC1S1 BLOC1S2 BLOC1S3

-log

10(p

-val

ue)

p=0.05

Dysbindin-1 by itself shows no evidence of association with Scz

373 Irish schizophrenics

812 controls

ABCDEFGHIJ

12345678

A 1A 2A 3A 4A 5A 6A 7A 8B 1B 2B 3B 4B 5B 6B 7B 8

…….J 6J 7J 8

A single gene-based test

80 allele-based tests

0

0.5

1

1.5

2

2.5

MUTED genotype

DTNBP1 DTNBP1 DTNBP1

Odd

s ra

tio

An independent replication? DTNBP1 MUTED epistasis (Straub et al. WCPG meeting Oct 2005.)

An independent replication? DTNBP1 MUTED epistasis (Straub et al. WCPG meeting Oct 2005.)

DTNBP1

MUTED

BLOC1S2

CNO

PLDN

SNAPAPBLOC1S1

BLOC1S3

Known protein interactions in BLOC-1 complex

Gene-based p = 0.0009Correcting for multiple tests, p = 0.025

Gene-based p = 0.0009Correcting for multiple tests, p = 0.025

Methylenetetrahydrofolate reductase (MTHFR) polymorphisms and serum folate interact to influence negative symptoms

and cognitive impairment in schizophrenia

Joshua Roffman, Donald Goff, et al

• Folic acid deficiency may contribute to negative symptoms and cognitive impairment in schizophrenia– underlying mechanism remains

uncertain

• A cohort of 159 outpatients

with schizophrenia measured:– negative symptoms– frontal lobe deficits

0

5

10

15

20

25

30

35Low folate

High folate

PA

NS

S N

egat

ive

Sym

pto

ms

C/C & C/T

T/T

0

10

20

30

40

50

60

Low folate

High folate

C/C & C/T T/T

Ver

bal

Flu

ency

0

10

20

30

40

50

60

Low folate

High folate

C/C & C/T T/T

WC

ST

% P

erse

vera

tive

Err

ors

•Interaction of low serum folic acid and homozygosity for the MTHFR 677T allele confers risk.

•Patients homozygous for the MTHFR 677T allele may therefore benefit specifically from folic acid supplementation.

Further reading

• Cordell HJ (2002) Human Molecular Genetics 11: 2463-2468.

– a statistical review of epistasis, methods and definitions

• Clayton D & McKeigue P (2001) The Lancet, 358, 1357-60.

– a critical appraisal of GxE research

• Marchini J, Donnelly P & Cardon LR (2005) Nature Genetics, 37, 413-417

– epistasis in whole-genome association studies