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Hypothetical examples of an Environmental moderator (left) or a genetic moderator (right) of total variance in a phenotype producing the impression of GxE. Left: Residuals of the regression of the Phenotype on the Measured Environment are heteroscedastic. High, average, and low polygenic scores (PGSs) are associated with constant percentiles of the phenotype at any given location along the x axis. However, because variance of the phenotype expands across the range of the Measured Environment, the PGS accounts for increasing unstandardized variance across this range. Right: A variance quantitative trait locus (vQTL) in which the effect allele is associated with greater variance in the phenotype. Unstandardized scores on the phenotype that are associated with high, average, and low levels of the measured environment (E) become more distinct with increasing number of effect alleles. However, because the total variance in the phenotype expands across the x axis, the percentile locations of these scores within each genotype (0, 1, or 2) is constant across all levels of the genotype
Source publication
Genotype-by-environment interaction (GxE) studies probe heterogeneity in response to risk factors or interventions. Popular methods for estimation of GxE examine multiplicative interactions between individual genetic and environmental measures. However, risk factors and interventions may modulate the total variance of an epidemiological outcome tha...
Citations
... However, because a statistically significant interaction does not provide enough information for understanding the actual interaction pattern, beside the traditional recommendation of plotting effects, several methodological guidelines have been proposed, giving rise to a lively debate (e.g. Belsky & Widaman, 2018;Del Giudice, 2017;Zhang, Widaman, & Belsky, 2023) also into the genetic field (Domingue, Kanopka, Mallard, Trejo, & Tucker-Drob, 2022;Tucker-Drob & Harden, 2013). Among different recommendations for exploring patterns of interactions, when it comes to theories under the environmental sensitivity umbrella (Pluess, 2015), probably two of the most often used approaches to follow-up interactions are the ones of Widaman et al. (2012) and Roisman et al. (2012). ...
Background
For investigating the individual–environment interplay and individual differences in response to environmental exposures as captured by models of environmental sensitivity including Diathesis‐stress, Differential Susceptibility, and Vantage Sensitivity, over the last few years, a series of statistical guidelines have been proposed. However, available solutions suffer of computational problems especially relevant when sample size is not sufficiently large, a common condition in observational and clinical studies.
Method
In the current contribution, we propose a Bayesian solution for estimating interaction parameters via Monte Carlo Markov Chains (MCMC), adapting Widaman et al. (Psychological Methods, 17 , 2012, 615) Nonlinear Least Squares (NLS) approach.
Results
Findings from an applied exemplification and a simulation study showed that with relatively big samples both MCMC and NLS estimates converged on the same results. Conversely, MCMC clearly outperformed NLS, resolving estimation problems and providing more accurate estimates, particularly with small samples and greater residual variance.
Conclusions
As the body of research exploring the interplay between individual and environmental variables grows, enabling predictions regarding the form of interaction and the extent of effects, the Bayesian approach could emerge as a feasible and readily applicable solution to numerous computational challenges inherent in existing frequentist methods. This approach holds promise for enhancing the trustworthiness of research outcomes, thereby impacting clinical and applied understanding.
... This gene-environment interaction remained significant when applying a heteroscedasticity model to assess whether this interaction term is specific to the measured predictor or whether it represents a general pattern of variation in the outcome ( Table 2; cf. Domingue et al., 2022). ...
... Significant ²-tests of indicate that the gene-by-environment interaction is not driven by heteroscedasticity in the environment or education-genetics (cf. Domingue et al., 2022). H0: = 0; gene-byenvironment interaction is driven by dispersion in outcome related to G or E. H1: ≠ 0; GxE interaction is not driven by dispersion in outcome related to G or E. Note. ...
Here we examine geographical and historical differences in polygenic associations with educational attainment in East and West Germany around reunification. We test this in n = 1902 25-85-year-olds from the German SOEP-G[ene] cohort. We leverage a DNA-based measure of genetic influence, a polygenic index calculated based on a previous genome-wide association study of educational attainment in individuals living in democratic countries. We find that polygenic associations with educational attainment were significantly stronger among East, but not West, Germans after but not before reunification. Negative control analyses of a polygenic index of height with educational attainment and height indicate that this gene-by-environemt interaction is specific to the educational domain. These findings suggest that the shift from an East German state-socialist to a free-market West German system increased the importance of genetic variants previously identified as important for education.
One Sentence Summary
We find that polygenic associations with educational attainment were significantly stronger among East, but not West, Germans after but not before reunification.
... Previous studies have demonstrated that genotype-protein interaction (GPI) and correlation effects are important factors contributing to complex phenotype traits, such as AD [7][8][9][10][11][12]. From a biological standpoint, there are two distinct types of relationships between protein and genetic variations. ...
Integrating and analyzing multiple omics data sets, including genomics, proteomics and radiomics, can significantly advance researchers’ comprehensive understanding of Alzheimer’s disease (AD). However, current methodologies primarily focus on the main effects of genetic variation and protein, overlooking non-additive effects such as genotype–protein interaction (GPI) and correlation patterns in brain imaging genetics studies. Importantly, these non-additive effects could contribute to intermediate imaging phenotypes, finally leading to disease occurrence. In general, the interaction between genetic variations and proteins, and their correlations are two distinct biological effects, and thus disentangling the two effects for heritable imaging phenotypes is of great interest and need. Unfortunately, this issue has been largely unexploited. In this paper, to fill this gap, we propose $\textbf{M}$ulti-$\textbf{T}$ask $\textbf{G}$enotype-$\textbf{P}$rotein $\textbf{I}$nteraction and $\textbf{C}$orrelation disentangling method ($\textbf{MT-GPIC}$) to identify GPI and extract correlation patterns between them. To ensure stability and interpretability, we use novel and off-the-shelf penalties to identify meaningful genetic risk factors, as well as exploit the interconnectedness of different brain regions. Additionally, since computing GPI poses a high computational burden, we develop a fast optimization strategy for solving MT-GPIC, which is guaranteed to converge. Experimental results on the Alzheimer’s Disease Neuroimaging Initiative data set show that MT-GPIC achieves higher correlation coefficients and classification accuracy than state-of-the-art methods. Moreover, our approach could effectively identify interpretable phenotype-related GPI and correlation patterns in high-dimensional omics data sets. These findings not only enhance the diagnostic accuracy but also contribute valuable insights into the underlying pathogenic mechanisms of AD.
... Intriguingly, the observed small change in the proportion of variance explained by SEP as group-level BMI differences have increased is consistent with a model in which the effects of risk factors for high BMI have uniformly increased in strength over the obesity epidemic [40] -one study in Sweden found that genetic effects have similarly increased, while heritability has remained almost stable [41]. However, there are reasons to expect changes in the variation explained by education, including the changing distribution of education itself as the population has become more highly educated (see Fig. 1) and variation in the returns to education (i.e. through period and cohort effects in the effect of education on earnings) which could lead to differences in effect size, e.g. from changes in relative access to healthy foodstuffs. ...
Background
The widening of group-level socioeconomic differences in body mass index (BMI) has received considerable research attention. However, the predictive power of socioeconomic position (SEP) indicators at the individual level remains uncertain, as does the potential temporal variation in their predictive value. Examining this is important given the increasing incorporation of SEP indicators into predictive algorithms and calls to reduce social inequality to tackle the obesity epidemic. We thus investigated SEP differences in BMI over three decades of the obesity epidemic in England, comparing population-wide (SEP group differences in mean BMI) and individual-level (out-of-sample prediction of individuals’ BMI) approaches to understanding social inequalities.
Methods
We used repeated cross-sectional data from the Health Survey for England, 1991–2019. BMI (kg/m²) was measured objectively, and SEP was measured via educational attainment, occupational class, and neighbourhood index of deprivation. We ran random forest models for each survey year and measure of SEP adjusting for age and sex.
Results
The mean and variance of BMI increased within each SEP group over the study period. Mean differences in BMI by SEP group also increased: differences between lowest and highest education groups were 1.0 kg/m² (0.4, 1.6) in 1991 and 1.3 kg/m² (0.7, 1.8) in 2019. At the individual level, the predictive capacity of SEP was low, though increased in later years: including education in models improved predictive accuracy (mean absolute error) by 0.14% (− 0.9, 1.08) in 1991 and 1.05% (0.18, 1.82) in 2019. Similar patterns were obtained for occupational class and neighbourhood deprivation and when analysing obesity as an outcome.
Conclusions
SEP has become increasingly important at the population (group difference) and individual (prediction) levels. However, predictive ability remains low, suggesting limited utility of including SEP in prediction algorithms. Assuming links are causal, abolishing SEP differences in BMI could have a large effect on population health but would neither reverse the obesity epidemic nor reduce much of the variation in BMI.
... This violation is not uncommon in GxE models. New conceptual frameworks are being developed to articulate the distinction between a significant GxE effect due to the environmental variable amplifying/suppressing the PGS effect or the environmental variable amplifying the total variation in the phenotype [63]. We addressed the heteroscedasticity problem with weighted linear regression in which each percentile of the ADI contributed equally to the models. ...
IMPORTANCE
Behavioral problems in children are influenced by environmental and genetic factors, but it is still unclear how much each contributes and if there are gene-by-environment interactions (GxE).
OBJECTIVE
Our object was to investigate how environmental adversity moderates the effects of polygenic scores (PGS) on childhood behavioral problems through additive and interaction effects.
DESIGN, SETTING, AND PARTICIPANTS
Participants were N = 7, 191 children aged 7-15 years (50% autistic) from two United States cohorts, ABCD and SPARK.
MAIN OUTCOMES AND MEASURES
The main outcomes were five dimensional subscales from the Child Behavior Checklist (CBCL). The genetic variables were 20 behavior-related PGS, including psychiatric diagnoses, substance use disorders, cognition, and personality PGS. Environmental adversity was estimated by the Area Deprivation Index (ADI). The ADI is a composite variable of neighborhood adversity based on education, income, and housing.
RESULTS
Thirteen out of the 20 PGS were significantly associated with the ADI. PGS for psychiatric and substance use disorders were positively associated with the ADI, and PGS for educational attainment and cognitive performance were negatively associated. The ADI had significant SNP heritability: h ² = 0.33 [0.24, 0.42], with the estimate similar between ABCD and SPARK. The ADI was positively associated with more behavioral problems and explained more variance than any PGS, but this effect was reduced after accounting for these potential genetic confounders. Several GxE effects were identified, including: 1.) the positive associations of the cannabis and alcohol dependency PGS with externalizing problems increased as the ADI increased, 2.) the positive associations of the anorexia PGS with thought and internalizing problems increased as the ADI increased, 3.) the positive associations of the autism PGS with internalizing problems decreased as the ADI increased, 4.) the negative associations of the educational attainment and cognitive performance PGS with several behavioral problems increased as the ADI increased, and 5.) the extraversion PGS association with social problems was negative in an advantaged environment but positive in a disadvantaged environment.
CONCLUSIONS AND RELEVANCE
Environmental adversity estimated by the ADI moderates the effects of some PGS on childhood behavioral problems through additive and interaction effects. This highlights the importance of considering both genetic and environmental factors in understanding childhood behavioral problems. Our findings emphasize the need to include PGS of personality and cognitive traits, in addition to psychiatric PGS.
... However, their analysis also included several variables directly related to health, such as healthcare utilization. Intriguingly, the observed small change in the proportion of variance explained by SEP as group level BMI differences have increased is consistent with a model in which the effects of risk factors for high BMI have uniformly increased in strength over the obesity epidemic [47] -genetic effects have similarly increased, while heritability has remained almost stable [22,48,49]. ...
Background: Socioeconomic differences in body mass index (BMI) have widened alongside the obesity epidemic. However, the utility of socioeconomic position (SEP) indicators at the individual level remains uncertain, as does the potential temporal variation in their predictive value. Examining this is important in light of the increasing incorporation of SEP indicators into predictive algorithms and the possibility that SEP has become a more important predictor of BMI over time. We thus investigated SEP differences in BMI over three decades of the obesity epidemic in England and compared population-wide (SEP group differences in mean BMI) and individual-level (out-of-sample prediction of individuals' BMI) approaches.
Methods: We used repeated cross-sectional data from the Health Survey for England, 1991-2019. BMI (kg/m2) was measured objectively, and SEP was measured via educational attainment and neighborhood index of deprivation (IMD). We ran random forest models for each survey year and measure of SEP adjusting for age and sex.
Results: The mean and variance of BMI increased within each SEP group over the study period. Mean differences in BMI by SEP group also increased across time: differences between lowest and highest education groups were 1.0 kg/m2 (0.4, 1.6) in 1991 and 1.5 kg/m2 (0.9, 1.8) in 2019. At the individual level, the predictive capacity of SEP was low, though increased in later years: including education in models improved predictive accuracy (mean absolute error) by 0.14% (-0.9, 1.08) in 1991 and 1.06% (0.17, 1.84) in 2019. Similar patterns were obtained when analyzing obesity, specifically.
Conclusion: SEP has become increasingly important at the population (group difference) and individual (prediction) levels. However, predictive ability remains low, suggesting limited utility of including SEP in prediction algorithms. Assuming links are causal, abolishing SEP differences in BMI could have a large effect on population health but would neither reverse the obesity epidemic nor explain the vast majority of individual differences in BMI.
... In either case, statistical observations of an interaction could arise from mechanisms other than the differential susceptibility interpretation advanced by the authors. For example, environmental effects on phenotypic variance can produce this pattern of interaction (5). A clear next step following from this analysis is to conduct a trial in which levels of social support are experimentally increased, for example, by providing some interns with access to peer support groups or soliciting nominations of friends and relatives at baseline and later prompting these ...
... We do not consider analysis using techniques such as structural equation modeling or mixed models. There are also outcome types that we do not consider (e.g., skewed outcomes; Domingue et al., 2022). In addition, we do not consider spline-based approaches that may allow for nonparametric analysis of outcome response surfaces as a (potentially nonlinear) function of predictors. ...
... A score of zero would be equivalent to a z-score of À1.3 given the mean and SD for the SCL-90-R(Table 1 inde Castro-Catala et al., 2017). Alternatively, the measure could be heavily skewed but that introduces other problems for interaction studies(Domingue et al., 2022).BIAS, FALSE DISCOVERY, AND INTERACTIONS3 This document is copyrighted by the American Psychological Association or one of its allied publishers.This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. ...
Studies of interaction effects are of great interest because they identify crucial interplay between predictors in explaining outcomes. Previous work has considered several potential sources of statistical bias and substantive misinterpretation in the study of interactions, but less attention has been devoted to the role of the outcome variable in such research. Here, we consider bias and false discovery associated with estimates of interaction parameters as a function of the distributional and metric properties of the outcome variable. We begin by illustrating that, for a variety of noncontinuously distributed outcomes (i.e., binary and count outcomes), attempts to use the linear model for recovery leads to catastrophic levels of bias and false discovery. Next, focusing on transformations of normally distributed variables (i.e., censoring and noninterval scaling), we show that linear models again produce spurious interaction effects. We provide explanations offering geometric and algebraic intuition as to why interactions are a challenge for these incorrectly specified models. In light of these findings, we make two specific recommendations. First, a careful consideration of the outcome's distributional properties should be a standard component of interaction studies. Second, researchers should approach research focusing on interactions with heightened levels of scrutiny. (PsycInfo Database Record (c) 2022 APA, all rights reserved).
... Moreover, statistically significant G × E results from linear regression models might be attributable to a violation of the homoscedasticity assumption in linear regression models (Domingue et al., 2022). We assessed this possibility in our analysis. ...
This study is aimed to investigate how paternal incarceration moderates the genetic association with children’s educational attainment. Based on gene-environment interaction (G × E) models, we hypothesize that exposure to paternal incarceration, a critical source of health and social disadvantages, may reduce children’s genetic potential for educational attainment. To test the hypothesis, we conduct an analysis based on a whole-genome polygenic score for educational attainment using data from participants of European ancestry in the National Longitudinal Study of Adolescent to Adult Health (Add Health). To guard against false-positive findings due to passive gene-environment correlation, we replicated the analysis based on participants raised by a social (i.e., non-biological) father. We find that the association between the education polygenic score and educational attainment observed at Wave 5 is significantly lower among Add Health participants who experienced paternal incarceration than those who never experienced paternal incarceration. This study provides evidence that social and genetic factors jointly and interactively influence educational attainment. It demonstrates how developmental and life-course criminology can be integrated with socio-genomic research to improve our understanding of the consequences of criminal justice involvement.
Genotype × environment interactions (GxE) have long been recognized as a key mechanism underlying human phenotypic variation. Technological developments over the past 15 years have dramatically expanded our appreciation of the role of GxE in both gene regulation and complex traits. The richness and complexity of these datasets also required parallel efforts to develop robust and sensitive statistical and computational approaches. Although our understanding of the genetic architecture of molecular and complex traits has been maturing, a large proportion of complex trait heritability remains unexplained. Furthermore, there are increasing efforts to characterize the effect of environmental exposure on human health. We therefore review GxE in human gene regulation and complex traits, advocating for a comprehensive approach that jointly considers genetic and environmental factors in human health and disease.
