Gene-environment interaction models

1. Gene-environment interaction models Karri Silventoinen

2. 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

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

4. 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

5. 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

6. 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

7. G*E 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

9. Heritability of height in different birth cohorts in men Source: Silventoinen et al, Am J Publ Health 2000

10. Heritability of height in different birth cohorts in women Source: Silventoinen et al, Am J Publ Health 2000

11. 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

12. G-E interaction model A C E a+βXM c+βYM e+βZM M T μ+βMM

13. G-E interaction model A C E a+βXM c+βYM e+βZM M T μ+βMM

14. Matrix algebra for G-E interactions • The equation a+βXM 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 (a+βXM)2=a2+2*a*βXM+(βXM)2 • This can be easily generalized to multivariate case using matrix algebra rules

15. Multivariate G-E interaction model A1 A2 a12+βY12M a2+βY2M a1+βY1M T P

16. 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

17. Nonlinear Moderation AA Aa aa Moderator

18. Nonlinear Moderation can be modeled with the Addition of a quadratic term A C E e + βZM +βZ2M2 c + βyM +βY2M2 a + βXM +βX2M2  + βMM T

21. 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

22. Contributions of Genetic, Shared Environment, Genotype x Shared Environment Interaction Effects to Twin/Sib Resemblance In other words—if gene-(shared) environment interaction is not explicitly modeled, it will be subsumed into the A term in the classic twin model.

23. Contributions of Genetic, Unshared Environment, Genotype x Unshared Environment Interaction Effects to Twin/Sib Resemblance If gene-(unshared) environment interaction is not explicitly modeled, it will be subsumed into the E term in the classic twin model.