Variance Components Models for Gene–Environment Interaction in Twin Analysis

“Briefly, the model assumes a quadratic change in the contributions of A, C, and E over time, and has been described in detail elsewhere (18, 19).”

“This is a form of G × E interaction , when the magnitude of genetic influence varies as a function of an environmental exposure, and can be tested using a so-called moderator twin model (Purcell, 2002).”

“If not directly estimated, such interaction effects would be captured in the estimate of nonshared environmental contributions (Purcell, 2002).”

“To address our hypotheses regarding developmental differences in etiology, we fit a series of models in which the path coefficients from the ACE components to internalizing symptoms interacted with age, pubertal status, and both simultaneously (Purcell, 2002).”

“, 2012) are identical to “standard” univariate moderation models (Purcell, 2002) with the exception that the “extended” model accounts for cotwin covariance on the moderator (i.”

“Standard gene 9 environment interaction models (Purcell 2002) specify that the genetic and environmental effects on a phenotype vary as a linear function of a continuous moderator (which produces quadratic variance estimates across the moderator due to squaring the pathway).”

“…study extend this model so as to determine the degree of covariance between the A, C, and E contributions to testosterone level and hippocampal volume, as well as determine the degree to which the A, C, and E contributions to hippocampal volume vary as a function of testosterone (Purcell, 2002).”

“Previous G 9 E twin studies of family SES and child psychopathology have regressed out the main effect of SES on child psychopathology before testing for G 9 E to account for inflation of test statistics due to rGE (Purcell, 2002; van der Sluis, Posthuma, & Dolan, 2012).”

“The methods introduced here can be viewed as complementary to those based in other genetic research designs, such as twin/family (Purcell 2002) and genome-wide molecular methods (Ni et al.”

“Secondly, gene-environment interactions [80] may contribute to the overall effect of an SNP and these may differ by population (for example, in BMI and exercise, [81]).”

“…influences on alcohol use, using a genetically informed design allowed us to model GxE while simultaneously accounting for the possibility of gene-environment correlation (rGE), or the tendency for certain environments to be made up of individuals with certain genetic profile (Purcell, 2002).”

“Third, although our multiple regression approach to moderating variance in BMI has been proposed or used in previous reports (e.g., McCaffery et al. 2009; Purcell 2002), here we demonstrate how this framework may be used to examine the mediating effects of one moderator by another.”

“In the classical twin study design, interactions between genes and shared environment are included in the effect of genes (11).”

“Following previous recommendations (Purcell, 2002), we report unstandardized path and moderator estimates in Table 4 and Fig.”

“We sought to further confirm the above results using the bivariate G×E model (Purcell, 2002), as recommended by van der Sluis et al. (2012).”

“Data We analyzed the Osborne data (Osborne 1980), which include the scores of 328 Caucasian twin pairs and 149 Afro–American twin pairs on various tests of cognitive abilities.”

“Some other methods exist that are able to conduct similar analyses, such as the liability-threshold model (Gottesman and Shields 1973), or models that examine heritability across a second measured child- or family-level variable (e.g., Clifford et al. 1984; LaBuda and DeFries 1990; Purcell 2002).”

“The continuous environmental measure is now modeled as a continuous moderator, in the manner proposed by Purcell (2002).”

“Moreover, any unaccounted-for geneenvironment interaction (ie, increased or decreased genetic sensitivity to certain environmental conditions) may lead to an inflation of individual-specific environment estimates (40,41).”

“Extensions of the SEM model that permit estimation of G × E interactions, including non-linear ones, are available and will permit future research to assess such conjectures (Purcell, 2002; Turkheimer et al., 2003; Bates et al., 2016).”

“In this model, it was testedwhether constraining themeans and variances to be equal across gender led to a significant deterioration of the model fit (Purcell, 2002).”

“While it is well-known that the heritability estimate in twin data is inflated by interactions of genotype with shared environment (Purcell 2002), the extent of this effect is largely unknown for psychiatric conditions or behavioral traits.”

“Turkheimer et al. (2003): A SES and C SES effects In an important study that has generated much interest, Turkheimer et al. (2003) applied the continuous-moderator model of Purcell (2002) in a small sample of 319 pairs of 7-year-old twins.”

“Additionally, twin and pedigree studies also offer an excellent resource for studying the significance of genotype by environment interactions (J. Blangero et al., 2005; S. Purcell, 2002), such as effects of lifestyle, diet or exposure to toxins.”

“Finally, the possibility of heritability changing with increasing or decreasing birth weight or gestational age was studied by using a gene-environment interaction script (31).”

“Instead of estimating genetic contributions to personality in terms of an overall heritability statistic that averages across diverse family circumstances, biometrical moderation models estimate the effect of genetic and environmental factors on individual differences in the presence of gene–environment interaction an…”

“Of note, it would have been possible to formulate models for testing for generenvironment interaction in the presence of gene–environment correlation (Purcell, 2002).”

“This may be testing by extending the present model to include age as a moderator in the manner of Purcell (2002).”

“We were thus sufficiently powered to detect etiologic differences in a two-moderator G E model (see Purcell, 2002 for power analyses of simulated data).”

“, M, the moderator) would moderate the genetic and environmental influence on deviant peer affiliation, the moderation components (b*M) were added in the univariate genetic model (Purcell 2002).”

“We then analyzed the data by forming unit-weighted composite scores for the phenotype for each twin and fitting a biometric model with provisions for G 9 E (Purcell 2002).”

“…from twin data, such as structural equation modelling, offer greater resolution compared to earlier analytical techniques, as they not only allow the modelling of more complex heritability models but also enable the calculation of the confidence intervals for the parameter estimates [13].”

“To investigate these possible moderating effects, we adopted the full bivariate moderation models developed by Purcell [49], and the extended univariate moderation models proposed by van der Sluis et al [23] (Supplementary Figures 4, 5).”

“The association of PRS-D with baseline partner status was tested using logistic regression and the association between PRS-D with baseline social network and social support was tested using linear regression to test for the independence assumption: no GxE correlation (rGE), which could lead to spurious results in GxE…”

“Unmodeled gene–environment correlation can resemble gene–environment interaction (Purcell, 2002), and there is evidence that covariation between family SES and academic achievement is substantially due to shared genes (Krapohl & Plomin, 2015).”

“We chose this model over the univariate model by Purcell (2002) because the latter can produce false-positive effects.”

“Presence of genotype–environment correlation (CorGE) may complicate the statistical procedures necessary for exploring gene–environment interaction (Purcell, 2002).”

“However, simply exploring the importance of genetic as opposed to environmental contributions is not adequate for understanding complex human abilities because genetic contributions are likely to vary as a function of environmental influence (Purcell 2002).”

“Complex traits are strongly influenced by the genotype × environment interaction, which leads to phenotypic variation beyond that caused by the genotype (Purcell, 2002; Long et al., 2007).”

“Mostquantitativegeneticmod-eling makes this assumption (but see Purcell, 2002, for a notable exception to this rule).”

“Additional models that allowed for the contributions of additive genetic and environmental influences to vary as a function of age (30) provided no significant improvement in model fit (P 5 0.”

“The full details of this model can be found in Purcell (Purcell 2002); Fig.”

“Following previous recommendations (Purcell, 2002), unstandardized estimates are reported in figures, as they more accurately depict absolute differences in etiologic effects than standardized estimates that represent differences as proportions of the total variance.”

“variance between a trait and moderator (Purcell, 2002; van der Sluis et al., 2012).”

“A uthor M anuscript A uthor M anuscript A uthor M anuscript A uthor M anuscript variable, in this case age (Purcell, 2002).”

“Another option is to adopt an existing parametric G 3 E interaction model proposed by Purcell in which age can be modeled by adding a moderator in a linear or quadratic form (Purcell 2002).”

“…× environment interaction effects that we did not account for, which could bias the genetic effects; future research should utilize biometric moderation models to examine whether genetic and environmental influences on health differ as a function of level of child maltreatment (e.g., Purcell, 2002).”

“By running structural equation twin model analyses allowing for interaction effects (see Fig. 1; Purcell, 2002), I investigated whether heritability estimates on the basis of peer reports increased with information accuracy of peer assessments.”

“Indeed, consideration of the gene–environment interaction in quantitative and molecular studies will potentially direct and enhance gene-mapping efforts and lead to better understanding of the complexity of joint genetic and environmental factors in the pathogenesis of disease (Purcell 2002; Purcell and Sham 2002).”

“Instead, the model needs to take into account that genetic effects may increase or decrease as a linear function of the environmental moderator [ 15 ].”

“Although this sort of constraint was once standard practice in genetic analyses of Heritability × Phenotype interaction (Purcell, 2002), constraining ACE estimates can bias the results of interaction analyses, deflating interaction effects (Turkheimer et al., 2017).”

“All three forms of rGE have the potential to distort estimates of genetic and environmental effects (Plomin et al., 1977; Purcell, 2002).”

“1) (Purcell 2002).”

“In such cases, extensions of the CTD that deal with GxE and rGE are available and can be utilized (Purcell 2002; Verhulst & Hatemi 2013: 368-369, 371).”

“—Purcell (2002) introduced a model for testing moderation on the variance in A, C, and E while accounting for possible gene-environment correlation (the association of variability in the environment with variability in genetic influences).”

“In the current study, we fitted the ‘univariate GxE’ model (Purcell, 2002), as shown in online Supplementary Fig.”

“Although the modified Purcell model we have used accounted for continuous changes in the variance of GA as a function of parental education, it does not address the root cause of the heteroscedasticity, which is that increasing cognitive ability over time led to a ceiling effect in the measurement of GA, as shown in F…”

“This can be done, for example, by using the genotype-environment parametrization introduced by Purcell (2002) by regressing moderators directly on the genotypic value.”

“More importantly, however, our analysis was based on a much more powerful model that considers both influences common to adiposity and physical activity and unique to each of them (Johnson 2007; Purcell 2002), and compared results to those from recently recommended possible nonlinear-main-effect alternatives (van Hull…”

“Such a possible gene–environment correlation needs to be controlled when testing for potential gene–environment interactions because the same environmental factor may simultaneously be involved in both mechanisms with respect to the developmental outcome (Purcell, 2002).”

“To test for interaction between sex and genetic and environmental influences, the method as proposed by Purcell (2002) was used.”

“…and site, and year were detected for AB reaction, which could be attributed to differences in total precipitation during the growing seasons (Table 2), as also reported also by Kemal et al. (2017), or to differences in virulence spectra of isolates and populations of the pathogen (Purcell, 2002).”

“For this study, we fitted the ‘univariate GxE’ model (Purcell, 2002), as shown in Supplementary Fig.”

“Although the point had been made on several occasions (see e.g. Eaves and Eysenck 1977; Purcell 2002), a recent paper (Eaves 2014) reiterated the implications of common problems of measurement in psychiatric genetics for the detection of interaction between measured environmental covariates and…”