Let us now return to Eq. (28.11), where the terms that capture the interactive effects between the genetic and environmental factors (AxE, AxC) were "conveniently" set to zero. The classical twin design needs to assume these terms to be zero simply because it is not possible to estimate the contribution of these effects to the total phenotypic variance with a twin study unless the environmental factors are measured or experimentally controlled. If the assumption on the absence of gene-environment interaction
is wrong, the estimates for a2, c2, and e2 may be biased. True AxC effects that are not modeled will inflate heritability estimates as well as the effects of the shared environment, whereas true AxE effects that are not modeled will act to inflate the estimates of the unique environmental contribution (Purcell, 2002). Perhaps counter-intuitively, the latter means that twin studies will underestimate the importance of genetic variance, if the relevant environmental factor is a person-specific factor, like the amount of life stress or level of job strain.
Fortunately, if the relevant environmental factors have been measured they can be readily incorporated in the twin design. Their interaction with genetic effects can be formally tested and the relative contribution of gene-environment interaction effects to the total trait variance estimated. There are a number of ways to do this. First, the classic twin analyses can be stratified for the measured environmental factor, such that the analyses are performed in subgroups of MZ and DZ twins that are concordant for the degree of environmental exposure (Heath et al, 1998). Significantly different heritability estimates in these subgroups signal gene-environment interaction. An example for blood pressure is provided by McCaffery and colleagues (2008) who investigated Ax E gene-environment interaction in hypertension by examining the extent to which educational attainment modifies the heritability of hypertension in Vietnam-era twins. Thousands of MZ and DZ male twins provided data on their education and self-report physician diagnosis of hypertension or medication usage. From these, the MZ and DZ pairs were selected to be concordant for low or high educational attainment such that either both of them had received more than 14 years of education or both of them had received less than 14 years of education. Heritability of hypertension was 63% in the higher educated twins versus 46% in the lower educated twins. In view of the higher incidence of hypertension in lower educational attainment groups, individual differences in genetic vulnerability to hypertension seem to be swamped by the environmental risk factors in subjects with lower education levels. In contrast, in subjects with high educational attainment only those at high genetic risk will develop hypertension.
A second way to test gene-environment interaction is to add the observed environmental factor as a moderator variable to the path loadings of the genetic factor on the observed variable. This extension of the twin model does not need to be restricted to the interaction of genetic with shared or unique environmental factors and can also be used to test for interaction within the two types of environment, i.e., Cx E or Ex E interactions (Purcell, 2002). Figure 28.7 depicts two ways of doing this. The left-hand side is a modified version of the models used by studies that aimed to detect possible moderating effects of regular physical activity on the genetic risk for obesity (McCaffery et al, 2009; Mustelin et al, 2009). A classical ACE decomposition is used, but now the effects of the latent factors are allowed to be modified by the measured environmental variable. Physical activity was allowed to act as an environmental modulator of the genetic effects on BMI (^1) as well as of the unique and shared environmental effects (^2, ^3). Significance of, for instance, the gene-physical activity interaction can be tested by comparing this full model to a model with set to zero.
The moderator variable in this model can be dichotomous, for instance, by contrasting non-exercisers (activity = 0) versus vigorous exercisers (activity = 1) based on the endorsement of one or more of five common vigorous intensity aerobic exercises (McCaffery et al, 2009).6 The moderator can also be continuous for instance when a physical activity index is calculated from the product of self-reported exercise intensity, duration, and frequency as was done in thousands of Finnish twin pairs (Mustelin et al, 2009). Of note, both approaches showed that physical activity significantly modified the heritability of BMI, with a high level of physical activity decreasing the
6 In the latter case the model resembles the approach above in that it computes the heritability separately in non-exercisers (a2/Vp) versus and vigorous exercisers ((a2 + ^1*activity)/Vp).
additive genetic component in BMI (Mustelin et al, 2009; McCaffery et al, 2009). This suggests that genetic variation significantly influences variation in adiposity in sedentary subjects, but that in physically active individuals the effects of this genetic variation is diminished. The often-replicated effect of the FTO gene on BMI appears to be one of the genes modified by physical activity, as the association between FTO and BMI was blunted in people with high physical activity assessed either by self-report (Andreasen et al, 2008) or 7-day accelerometry (Rampersaud et al, 2008).
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