Gene-environment interaction models

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Gene-environment interaction models

• Karri Silventoinen

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Interplay between genes and environment

• Genetic models usually make an assumption that
  the genetic and environmental effects are
  independent
• Animal and plant breeding experiments have,
  however, shown that G-E interactions are very
  common
• Rationality behind breeding is usually to develop
  plants and animals who can maximally utilize
  improved nutrition
• There is clear evidence on G-E interactions also
  in humans
• Clinical trials including MZ twins
• Epidemiological settings
• The most famous example is Pima Indians in Arizona

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Conceptualizing G-E interaction in the case of a
single gene
AA
Aa
Trait Value/Risk of Disorder
aa
Protective Predisposing
ENVIRONMENT
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G-E interactions in twin modeling

• In many situations it is reasonable to expect G-E
  interactions also in twin modeling
• For example, the effect of place of residence
  (rural-urban) on the genetics of alcohol
  consumption in Finland (Rose et al, 2001)
• G-E interactions are seen as differences in the
  genetic (or environmental) variation at different
  levels of environmental exposure
• During this course we will use models which need
  measured environmental exposure
• However, also other types of G-E interaction
  models are available
• The most powerful design utilizes information on
  both measures of environmental exposures and
  genomic scans
• The problem is that usually candidate genes
  explain only a small proportion of the phenotypic
  variance

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G-E correlation vs. G-E interaction

• It is important to make distinction between G-E
  interaction and G-E correlation (rGE)
• G-E interaction refers to situation when the
  expression of genes is modified by environment
  or, the other way round, when the effect of
  environment is affected by genotype
• For example, nutrition may modify the effect of
  genes affecting obesity or some genotypes may be
  more sensitive to increase in nutrition intake
• In other words, the effects of genes and
  environment are not independent
• By using the current model we cannot, however,
  make distinction between different causal
  pathways
• Gene-environment correlation refers to situation
  when allele frequencies are not independent of
  environment
• Thus, the environment people are living is partly
  generated by their genotype
• For example, moderate heritability is found for
  experience of negative life events

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Sources of gene-environment correlations

• There are three possible sources of
  gene-environment correlation
• Passive gene-environment correlation
• Parents transmit both their genes and environment
• Genetically musically talented parents more often
  listen music and own musical instruments
• Active gene-environment correlation
• Subjects with a certain genotype actively select
  environments that are correlated with that
  genotype
• Genetically musically talented children like to
  participate musical education
• Reactive gene-environment correlation
• Subjects with a certain genotype evoke certain
  reactions from environment
• Music teachers pick up genetically musically
  talented children for special supervision
• Active and reactive gene-environment correlations
  may be one of the reasons why heritability of
  many personality traits (e.g. intelligence) seem
  to rather increase than decrease during aging
• The possibility of rGE should be taken into
  account in interpretations of results
• For example if ADHD children suffer more
  maltreatment at home the reason may be that their
  parents has also genetic predisposition to
  antisocial behavior

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GE interaction based on multiple group analysis

• A simple way to analyze G-E interactions is to
  stratify the data by the environmental exposure
• Thus, we can simply utilize multiple group
  comparison using univariate models
• Significant differences in genetic and/or
  environmental variance components across the
  categories indicate the existence of G-E
  interaction

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Heritability of height in different birth cohorts
in men
Source Silventoinen et al, Am J Publ Health 2000
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Heritability of height in different birth cohorts
in women
Source Silventoinen et al, Am J Publ Health 2000
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Problems in multiple group comparisons

• Multiple group comparisons have limitations,
  which make them unsuitable to many situations
• Environmental exposure needs to be same for both
  co-twins
• Such as birth cohort or place of residence
• If environmental exposure is continuous,
  categorizing it loses a lot of information if the
  associations are linear
• However if this kind of limitations are not a
  problem, multiple group comparison is a good
  alternative to more sophisticated G-E interaction
  models
• Interpretation of the results is very
  straightforward
• Possible non-linearity is not a problem
• We can accept heterogeneity between the
  categories

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G-E interaction model
A
C
E
cßYM
eßZM
aßXM
M
T
µßMM
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G-E interaction model
A
C
E
cßYM
eßZM
aßXM
M
T
µßMM
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Matrix algebra for G-E interactions

• The equation aßXM is a linear function
• Why this can be used to analyze interactions?
• We are interested in the variance component a2
  instead of the path coefficient a
• Thus (aßXM)2a22aßXM(ßXM)2
• This can be easily generalized to multivariate
  case using matrix algebra rules

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Multivariate G-E interaction model
A1
A2
a1ßY1M
a2ßY2M
a12ßY12M
T
P
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Non-linear interaction effects

• It is also possible that the effect of
  environmental exposure is not linear but
  curvilinear
• For example, genetic variation may be low both at
  low and high level of environmental exposure
• This can be modeled simply by including a new
  moderator term in the model
• Even when curvilinear effects are not difficult
  to model, power may be a problem
• Also the extreme ends of environmental exposures
  may be problematic
• Reporting errors etc.
• Before analyzing curvilinear associations, there
  should be clear theoretical justification why we
  expect this kind of associations
• Sample size should also be large and the
  measurement of environment high quality

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Nonlinear Moderation
AA
Aa
aa
Moderator
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Nonlinear Moderation can be modeled with the
Addition of a quadratic term
A
C
E
e ßZM ßZ2M2
c ßyM ßY2M2
a ßXM ßX2M2
? ßMM
T
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Effect of G-E interactions on heritability

• If G-E interaction is not modeled it naturally
  does not mean that it would not affect the
  results
• In many cases we have not measured relevant
  environmental exposures, but we have to speculate
  whether they can still explain the found results
• G-E interaction may well be one reason why common
  environmental influences are rarely seen even in
  the case when this in counterintuitive
• For example, the lack of common environmental
  effect in many psychological traits
• It may reflect rather that the effect of family
  related factors is modified by genetic factors
  than the lack of this effect

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Contributions of Genetic, Shared Environment,
Genotype x Shared Environment Interaction Effects
to Twin/Sib Resemblance
Shared Environment Additive Genetic Effects Genotype x Shared Environment Interaction
MZ Pairs 1 1 1 x 1 1
DZ Pairs/Full Sibs 1 ½ 1 x ½ ½
In other wordsif gene-(shared) environment
interaction is not explicitly modeled, it will
be subsumed into the A term in the classic twin
model.
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Contributions of Genetic, Unshared Environment,
Genotype x Unshared Environment Interaction
Effects to Twin/Sib Resemblance
Unshared (Unique) Environment Additive Genetic Effects Genotype x Unshared Environment Interaction
MZ Pairs 0 1 0 x 1 0
DZ Pairs/Full Sibs 0 ½ 0 x ½ 0
If gene-(unshared) environment interaction is not
explicitly modeled, it will be subsumed into the
E term in the classic twin model.
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