Variance Components Models for Gene–Environment Interaction in Twin Analysis

“Newer biometric modeling techniques are able to overcome these statistical obstacles (Purcell, 2002).”

“Following previous recommendations [50], however, we also report the unstandardized parameter estimates for the best-fitting model.”

“Newer computational and analytical strategies (Purcell, 2002; Rathouz, Van Hulle, Rodgers, Waldman, & Lahey, 2008), however, allow BG researchers to demonstrate that the degree to which genes influence behavior often depends on the environment and vice versa.”

“This residualization facilitates unbiased regression-based tests for G 9 E interactions (Purcell 2002; G. Carey, personal communication).”

“For example, external factors may be correlated with the genetic effects on complex traits (rGE), and this rGE can appear as gene–environment interaction (G × E) if the rGE is not accommodated explicitly in the model (Purcell 2002).”

“…intensity of four METs, and the total time spent on all such activities was at least 60 minutes a week; in Norway, they exercised during leisure time between one and two times a week at sufficient intensity to build up a sweat for 30–60 minutes in duration; in Sweden, they had to exercise…”

“All the covariates with a unique environmental component, besides gestational age, must either explain differences between twins or describe gene environment interactions (Purcell 2002; van der Sluis et al. 2006).”

“Current behavioral genetic models are able to test gene-byenvironment interaction in combination with genetic pleiotropy (Purcell, 2002; Purcell & Sham, 2002), but models that incorporate behavioral feedback loops, for example, the effects of acute mood effects on future exercise behavior, have yet to be developed.”

“Analogous to the modelling of a moderating effect on the additive genetic path, a, in the twin model (Purcell, 2002), the QTL path q is simply modified to (q+βQM) or even (q+βQM+δQM (2)) to incorporate Q × M interaction, representing linear and nonlinear interactions, respectively, between the additive genetic value a…”

“For these analyses, a series of GxE interaction or r GE correlation models will be tested against the univariate ACE twin model (Purcell, 2002).”

“Measuring these kinds of transactions between genetic and environmental influences involving pairs of traits can be very helpful in uncovering the causal patterns involved in the association between the traits, and new statistical modelling approaches make this possible (Purcell, 2002).”

“In order to test for the effect of breastfeeding on the genetic architecture of cognitive abilities a moderator model (Purcell 2002) was used.”

“This process is not limited to twins, i.e., the behavior or personality of any family member may contribute to the environment of his or her cohabitants and such covariance between additive genetic and household effects will also contribute to a household effect (Purcell 2002) if it is not modeled.”

“In addition to additive influences of individual genetic variants, these estimates reflect non-additive dominance and epistatis effects due to interactions between and within genetic loci, effects of rare variants and person-environment correlations (Purcell, 2002), and they are possibly confounded with environmental…”

“Typically, changes in unstandardized genetic variance are examined in studies of latent G × E because changes in standardized genetic variance (i.e., heritability, or the proportion of overall variance accounted for by genetic factors) can be misleading (Purcell, 2002; Young-Wolff et al., 2011).”

“To facilitate interpretation of the unstandardized values (Purcell, 2002), we standardized our log-transformed child AGG and RB scores to have a mean of 0 and a standard deviation of 1 prior to analysis.”

“Behavioral genetic models are also particularly sensitive to skewness (Purcell, 2002).”

“As a first step, we tested for gene-environment interactions on motivation and math achievement separately, using a univariate behavioral genetic model that decomposes between-person variation in a given phenotype, Y, into variation accounted for by genes, the environment, and their interactions with SES (Purcell, 200…”

“…genetics has only recently been made feasible by the development of both biometric approaches, which provide overall tests for the existence of G×E (Purcell, 2002), and measured genotype approaches, which test hypotheses about the interaction of specific functional genetic polymorphisms with…”

“For further explanation of these models see Kremen et al. (2005) and Purcell (2002).”

“If heritability estimates are conditional on the value of a quantitative trait such as age or socioeconomic status, the estimates can be obtained across the total scale of a quantitative trait (Purcell, 2002).”

“Finally, given that several studies have shown that gene–environment interactions can be confounded by the presence of gene–environment correlations (rGE; [83,84]), as suggested by Richards et al.”

“Moreover, themodel includes amain—ormediating—effect of the moderator upon the phenotype’s mean/thresholds [Purcell, 2002] which is mapped by the bM parameter, even though the decomposition of variance is not influenced by this effect.”

“Behavioral geneticists have long known that that the genetic and non-shared environmental variance components in traditional behavioral genetic models contain main effects as well as G × E interactions [6].”

“Over 50 twin and adoption studies have found similar results for antisocial behaviour (Rhee & Waldman 2002).”

“As Purcell (2002) detailed, GE-interplay affects the A parameter.”

“In addition, the continuous data (from which the binary and ordinal data arose) were also analyzed using a standard moderated regression script for continuous data (after Purcell 2002 ).”

“Whereas LOSEM estimates local heritability and environmentality across the moderator, parametric approaches specify genetic and environmental influences to vary as a function of the moderator (Purcell, 2002).”

“Parametric moderation models (Purcell, 2002) allow Hormonal markers of chronic hypothalamic–pituitary–adrenal function 1393 for sets of the acn, ccn, ecn, ac, cc, ec and ra, rc and re parameters to vary as functions of the moderator tested in the form p = p0 + p1×m, where p is the parameter and m…”

“Shared environment is of specific interest in the current study, because the Gene × Shared Environment interaction is subsumed within the additive genetic variance in twin studies, inflating the typical heritability estimate (Purcell, 2002).”

“The effects of gene by shared environment interaction, if any, would be captured in A, and the effects of gene by nonshared environment interaction, if any, would be captured in E (Purcell 2002).”

“…address such interesting (and tricky) questions as whether one can simultaneously estimate both G 9 E interaction and GE correlation from twin data (Purcell 2002; Price and Jaffee 2008; Rathouz et al. 2008), or whether a one-generation study can separate out the genetic and environmental…”

“The conditional term may is used here in recognition that nonshared environmental factors could also reflect population heterogeneity to the extent that gene-environment correlations play a role in nonshared environmental experiences (Purcell, 2002).”

“We ruled out mediation effects by fitting “GxE in the presence of rGE” models (Purcell, 2002) and finding that the parameter testing rGE (i.e., the moderation of the covariance path) was nonsignificant and could be constrained to 0 (comparison with full model: v2D(3) 5 5.38, p 5 .15).”

“It is interesting that, in recent neurogenetics studies, researchers have begun to address G G interactions and the likely cumulative nature of different genetic variants by constructing cumulative/polygenic genetic profiles (Cicchetti & Rogosch, 2012; Holmes et al., 2012; Nikolova, Ferrell, Manuck, & Hariri, 2011; Pu…”

“In order to assess the moderation of the aetiological influences on diurnal preference as a function of age as a continuous moderator, a series of linear and non-linear (quadratic) moderation models were run in order to assess GxE of rMEQ by age (see Purcell, 2002, for more information).”

“A modified Cholesky decomposition model is provided in the right side of Figure 2 (Dick & York, 2010; Purcell, 2002), again shown only for one twin in the pair.”

“Correlation between genetic and shared environmental influences acts to increase the proportion of shared environmental influence; correlation between genetic and nonshared environmental influences acts to increase the proportion of genetic influence (Purcell, 2002).”

“An interaction between A and E would inflate the E estimate, and a correlation between A and E is part of the variance attributable to the A estimate (50).”

“…mating (people choose to marry persons similar to themselves; Eaves et al. 1984; Loelin and DeFries 1987), gene–environment correlation (Plomin et al. 1977; Eaves et al. 1977), and gene–environment interaction (Plomin et al. 1977; Eaves et al. 1977; Purcell 2002; Eaves and Erkanli 2003).”

“…(Kendler and Eaves, 1986; Plomin et al., 1977) in which exposure to and the experience of specific environmental conditions mediate genetic variability (e.g., indexed by changes in h2) in a population (e.g., Kendler and Eaves, 1986; Plomin et al., 1977; Purcell, 2002; Purcell and Sham, 2002).”

“2; Purcell, 2002).”

“…evaluate for potential confounds due to heteroscesdacity in ROI variance (e.g., changes in heritability of cortical thickness with age or sex), we repeated our ACE models with additional parameters allowing for variance components to vary with our covariates (Purcell, 2002; Wallace et al., 2006).”

“This possibility should be directly investigated in future studies that have adequate sample sizes to test gene-environment interaction twin models.(43)”

“factors” are only viable when teamed with environmental risk (known as gene–environment interaction [Purcell, 2002]).”

“…1998 Longitudinal or temporal data Kwok et al., 2008 Random effects or coefficients Dunton, Gajewski, Taunton, & Moore, 2004 Variance components Purcell, 2002 Growth curve Gross et al., 2009 Clustered Livert, Rindskopf, Saxe, & Stirratt, 2001 Spatial Mather et al., 2006 Latent variable Unruh &…”

“Our study also relied in part on the ‘GrE in the presence of rGE’ model described by Purcell (2002).”

“Unstandardized parameter estimates are favored here in order to examine absolute (rather than proportional) shifts in each parameter across each level of the moderator (as recommended by Purcell 2002).”

“Joint examination of these effects is necessary to correctly discriminate between correlation and interaction [57].”

“Therefore, we utilized a model that allows for a continuous moderator (Purcell, 2002) to examine the data for evidence of genotypic moderation in the presence of genotype-environment correlation.”

“2011; Purcell 2002).”

“Indeed, there is an increasing effort to devise statistical models that can accommodate these complicating effects (Dick & Rose, 2002; Purcell, 2002; Eaves & Erkanli, 2003).”

“To estimate whether the relative importance of genetic effects changes across the life course, additional models were fitted which omitted adjustment for age, age squared and birth year and instead fitted age as a moderator variable (Purcell 2002) where the magnitude of the A, C and E effects was allowed to vary with…”

“…significant moderators that were often in opposing directions) is not in line with what would be expected if skewed data were driving our results (i.e., similar moderation effects in the same direction across genetic, shared environmental, and nonshared environmental factors) (Purcell, 2002).”

“Its omission is parallel to the situation in latent variable interaction models for twin studies (Purcell 2002), where non-additive effects of the genotype can mimic or obscure G × E interaction (Van Hulle et al. 2013).”

“If these assumptions are violated, however, it has systematic influences on the parameter estimates (Purcell, 2002).”

“For example, alcohol risk genes, as well as risky environments are passed down from parents to offspring living in the household: these are the conditions under which the dissection of GXE effects, for a variety of technical reasons, is most challenging (e.g. Purcell 2002; Rathouz et al. 2008).”

“In that case, it may be better to use the approach of Purcell (2002) who introduces moderator effects in the structural model, explaining the factor’s distribution, rather than that of the loadings.”

“The expression of genes and thus also the genetic variance, however, may depend on environmental circumstances (Purcell, 2002).”

“We are also able to test for moderation of the ACE variance components of BMI by SES, a form of G E interaction, by extending the model described above (Purcell, 2002).”

“We used standard univariate moderation models to examine possible moderating effects of age on the etiology of thin-ideal internalization, as these are the recommended models when the moderator is a family-level variable that is shared within twin pairs, as is true for age.(37,38) For puberty moderation models, we use…”

“…phenotypic association between the moderator and the outcome has no substantive bearing on the extent of etiologic moderation (as described by Purcell, 2002), with the lone exception of reducing concerns about possible gene-environment correlational confounds (Rathouz, Van Hulle, Rodgers,…”

“The nonshared environmental component contains the effects of all Gene × Environment interactions where the envi ronmental moderator is a nonshared environmental factor (Purcell, 2002).”