Distinguishing between interaction and dispersion effects in the analysis of gene-environment interaction

Genotype-by-environment interaction (GxE) occurs when the size of a genetic effect varies systematically across levels of the environment and when the size of an environmental effect varies systematically across levels of the genotype. However, total variance in the phenotype may shift as a function of the moderator irrespective of its etiology such that the proportional effect of the predictor is constant. We expand the traditional GxE regression model to directly account for heteroscedasticity associated with both the genotype and the measured environment. We then derive a test statistic,{xi} , for inferring whether GxE can be attributed to an effect of the moderator on the dispersion of the phenotype. We apply this method to identify genotype-by-birth year interactions for Body Mass Index (BMI) that are distinguishable from general secular increases in the variance of BMI or associations of the genetic predictors (both PGS and individual loci) with BMI variance. We provide software for analyzing such models.