Gene x Environment Interactions

Brad Verhulst(With lots of help from slides written

by Hermine and Liz)

September 30, 2014

What does a GxE interaction in a twin model really mean?

• Univariate Analysis: What are the contributions of A, C/D & E to the variance?

• Heterogeneity Analysis: Are the contributions of genetic and environmental factors equal across different groups, such as sex, race, ethnicity, SES, environmental exposure, etc.?

• Moderation Analysis: Are the contributions of genetic and environmental factors to the variance constant across the range of a second (moderator) variable?

Gene-Environment Interaction

GxE• genetic control of sensitivity to the environment• environmental control of gene expression– (environmental modulation of non-genetic paths)

Examples:• Does heritability of IQ depend on SES?• Does heritability of ADHD depend on age?• Does the role parental monitoring depend on

genotype?

Gene-Environment Correlation

rGE• genetic control of exposure to the environment• environmental control of gene frequency

Examples:• Active rGE: Children with high IQ read more books• Passive rGE: High IQ parents give their children books• Reactive/Evocative rGE: Children with ADHD are treated

differently by their parents

Moderating Variables

• Almost any variable can be used as a moderator…… but be careful as not all variables make sense as moderators (or are easy to interpret)

• If a variable has a genetic component (A > 0) interpreting the GxE path is complicated by the fact that the moderator is a function of both G & E.

• Is it a GxG or a GxE interaction?

Heterogeneity Moderation• An easy (but much less powerful) method of conducting GxE

• For categorical variables, estimate separate parameters for each group.– Sex Limitation is a classic case of GxE where separate parameters are

estimated for each group– This can be extended to any number of categories (but quickly gets tedious

and difficult to interpret)

• This approach would not work for continuous variables (as there are no discrete categories)– Age– Factor Scores of X, Y & Z

• Grouping these variables into categories loses a lot of information and power

GxE Model & Theory

Purcell 2002 Twin Research

GxE Application

Turkheimer et al. 2003 Psychological Science

Turkheimer et al. 2003 Psychological Science

Definition Variables in OpenMx

• General definition: Definition variables are variables that may vary per subject/pair and are not dependent variables

• In OpenMx: Specific values of definition variables for a specific individual/pair is read into mxMatrix when analyzing data of that particular individual/pair

Common Use of Definition Variables• To model main effects of on the means (e.g. age and sex)• To model changes in variance components as function of

some moderator variable (e.g. age, SES)

Cautionary Note about Definition Variables

• Definition variables should not be missing if dependent variable is not missing

• Definition variables should not have the same missing values as dependent variable (e.g. use -2.00 for definition variable and -1.00 for dependent variable)

• It is helpful to have very large values for missing definition variables (so that if things go wrong the results are unmistakably funky)

Definition Variables as Main EffectsGeneral model with age and sex as main effects:

yi = α + β1(Agei) + β2(Sexi) + εi

Where:yi is the observed score of individial i

α is the intercept or grand meanβ1 is the regression weight of age

Agei is the age of individual i

β2 is the deviation of females (if sex coded 0:males, 1:females)

Sexi is the sex of individual i

εi is the residual not explained by definition vars

(and can be decomposed further into ACE etc.)

Allowing for Main Effect

M + Xβ M + Xβ

Means Vector

a2 + c2 + e2 H * a2 + c2

H * a2 + c2 a2 + c2 + e2

Covariance Matrix

Allowing for Moderation

M + Xβ M + Xβ

Means Vector

(a + Xϒa)2 + (c + Xϒc)2 + (e+ Xϒe)2

H * (a + Xϒa)2 + (c + Xϒc)2

H * (a + Xϒa)2 + (c + Xϒc)2

(a + Xϒa)2 + (c + Xϒc)2 + (e+ Xϒe)2

Covariance Matrix

Existing Gene-Environment Interaction Models

Classical Twin Design

Pt1 Pt2

1

A

C

E

μ

E

C

A

1

MZ=1

DZ = ½

1

1

1

1

1

1

a + βaM a + βaM

e + βeM

c + βcM c + βcM

e + βeM

+ Mβm μ + Mβm

Purcell (2002)

Means Moderation Model

Basic Means and Variances

Example: Turkheimer Study

• Moderation of unstandardized variance components

• Moderation of standardized variance components

Cautions about interpreting the ParametersUnstandardized (UV) vs Standardized (SV)

Environment 1 Environment 2Unstandardized

VarianceStandardized

VarianceUnstandardized

VarianceStandardized

Variance

Genetic 60 .60 60 .30Common

Environment 35 .35 70 .35Unique

Environment 5 .05 70 .35Total Variance 100 1.00 200 1.00

Cautions about interpreting the ParametersParameters are Conditional

• The estimated values of a, c & e in a Purcell model depend on the value of the intercept (or the mean).

• If the mean is 0, the interpretation of the direct effect of a (or c) on the phenotype is the genetic (or common environment) variance at the mean.

• If the mean is not 0, the interpretation of the direct effect of a (or c) on the phenotype is the genetic (or common environment) variance is more complicated.

• Therefore, it is always suggested that the variance components are plotted across the range of the moderator.

GxE in context of rGE

• If there is a correlation between moderator (environment) and outcome, and you find a GxE effect, it is not clear if:– the environment is moderating the effects of

genesOR

– trait-influencing genes are simply more likely to be present in that environment

Ways to deal with rGE

• Limit study to moderators not correlated with outcome

• Put moderator in means model to remove covariance genetic effects shared by trait and moderator

• Explicitly model rGE in bivariate framework