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Heterogeneity II

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Heterogeneity II

Danielle Dick, Tim York,

Marleen de Moor, Dorret Boomsma

Boulder Twin Workshop

March 2010

- Standard Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance?
- Heterogeneity: Are the contributions of genetic and environmental factors equal for different groups, such as sex, race, ethnicity, SES, environmental exposure, etc.?

- Multiple Group Models
- Sex Effects
- Divorced/Not Divorced
- Young/Old cohorts
- Urban/Rural residency
- Etc…

Females

Males

Females

Males

aF = aM ? cF = cM ? eF = eM ?

Divorced

Not Divorced

aD = aND ? cD = cND ? eD = eND ?

- Many variables of interest do not fall into groups
- Age
- Socioeconomic status
- Regional alcohol sales
- Parental warmth
- Parental monitoring
- Grouping these variables into high/low categories may lose information

- General definition: Definition variables are variables that may vary per subject and that are not dependent variables
- In Mx:The specific value of the def var for a specific individual is read into a matrix in Mx when analyzing the data of that particular individual

create dynamic var/cov structure

- Common uses:
- To model changes in variance components as function of some variable (e.g., age, SES, etc)
- As covariates/effects on the means (e.g. age and sex)

- Means vector
- Covariance matrix

A

C

E

A

C

E

c

a

e

a

c

e

m

m

Twin 1

Twin 2

M

M

A

C

E

A

C

E

c

a+XM

e

a+XM

c

e

m

m

Twin 1

Twin 1

Twin 2

Twin 2

M

M

A

C

E

A

C

E

c

a+XM1

e

a+XM2

c

e

m

m

Twin 1

Twin 1

Twin 2

Twin 2

M

M

A

C

E

A

C

E

c+YM1

c+YM2

a+XM1

a+XM2

e+ZM1

e+ZM2

m

m

Twin 1

Twin 1

Twin 2

Twin 2

M

M

Definition Variables in Mx

X

a

M1

Total genetic variance = a+XM1

- Classic Twin Model:
Var (P) = a2 + c2 + e2

- Moderation Model:
Var (P) =

(a + βXM)2 + (c + βYM)2 + (e + βZM)2

Purcell 2002,

Twin Research

Var (T) = (a + βXM)2 + (c + βYM)2 (e + βZM)2

Where M is the value of the moderator and

Significance of βX indicates genetic moderation

Significance of βY indicates common environmental moderation

Significance of βZ indicates unique environmental moderation

A

C

E

A

C

E

c+YM1

c+YM2

a+XM1

a+XM2

c+cM*D1

c+cM*D2

e+ZM1

e+ZM2

a +aM*D1

a+aM*D2

e+eM*D2

e+eM*D1

Twin 1

Twin 2

M

M

m

m

mu

mu

create dynamic var/cov structure

- Common uses:
- To model changes in variance components as function of some variable (e.g., age, SES, etc)
- As covariates/effects on the means (e.g. age and sex)

General model with age and sex as covariates:

yi = + 1(agei) + 2 (sexi) +

Where yi is the observed score of individual i, is theintercept or grand mean, 1is the regression weight of age, ageiis the age of individual i, 2 is the deviation of males (if sex is coded 0= female; 1=male), sexiis the sex ofindividual i, and is the residual that is not explained by the covariates (and can be decomposed further into ACE etc).

- Means vector
- Covariance matrix

- Incorporating covariates (sex, age, etc)
- Testing the effect of SNPs (association)
- In the context of GxE, controlling for rGE

A

C

E

A

C

E

c

a

e

a

c

e

m+MM1

m+MM2

Twin 1

Twin 2

M

M

A

C

E

A

C

E

c+YM1

c+YM2

a+XM1

a+XM2

c+cM*D1

c+cM*D2

e+ZM1

e+ZM2

a +aM*D1

a+aM*D2

e+eM*D2

e+eM*D1

Twin 1

Twin 2

M

M

m+MM2

m+MM1

mu+b*D2

mu+b*D1

Main effects and moderating effects