Specification, Testing, and Interpretation of Gene-by-Measured-Environment Interaction Models in the Presence of Gene–Environment Correlation

Abstract

Purcell (2002) proposed a bivariate biometric model for testing and quantifying the interaction between latent genetic influences and measured environments in the presence of gene-environment correlation. Purcell's model extends the Cholesky model to include gene-environment interaction. We examine a number of closely-related alternative models that do not involve gene-environment interaction but which may fit the data as well Purcell's model. Because failure to consider these alternatives could lead to spurious detection of gene-environment interaction, we propose alternative models for testing gene-environment interaction in the presence of gene-environment correlation, including one based on the correlated factors model. In addition, we note mathematical errors in the calculation of effect size via variance components in Purcell's model. We propose a statistical method for deriving and interpreting variance decompositions that are true to the fitted model.

Gene × environment interaction of vigorous exercise and body mass index among male Vietnam-era twins

“…However, we chose not to examine such models because the joint distribution of VE and BMI is no longer a bivariate normal once VE is allowed to moderate both common and specific additive genetic paths (41).…”

Dependence of Gene-by-Environment Interactions (GxE) on Scaling: Comparing the Use of Sum Scores, Transformed Sum Scores and IRT Scores for the Phenotype in Tests of GxE

“…We based our analyses on the Purcellian GxM interaction (where the 'M' stands for measured environment) framework initially introduced by Purcell (2002) and subsequently extended and evaluated by others (Rathouz et al 2008;van Hulle et al 2013;Van Hulle and Rathouz 2015;. This framework is arguably the foremost in assessing theoretical hypotheses which predict moderation of genetic influences on a specific phenotype by a specific moderator because in addition to accommodating both gene-environment interaction and gene-environment correlation, it can also be used to evaluate a range of other forms of phenotypemoderator transactions (see Zheng and Rathouz 2013).…”

“…In terms of theoretically important processes, GxE is also difficult to distinguish statistically from non-linear main effects of a moderator on a phenotype or from non-linear genetic or environmental influences on a phenotype (e.g. Rathouz et al 2008;. However, there are good reasons to begin by attempting to rule out scaling as the alternative explanation for GxE effects.…”

Editorial Policy for Candidate Gene Studies

“…This is especially pertinent for psychopathology research because highly skewed and kurtotic distributions of dimensions of psychopathology almost never meet the assumption of multivariate normality. In addition, tests of geneenvironment can be difficult to interpret in the presence of gene-environment correlation (Eaves et al 2003;Rathouz et al 2008). Thus, tests of interaction must take this phenomenon into account.…”