Testing for measured gene-environment interaction: problems with the use of cross-product terms and a regression model reparameterization solution

The study of gene-environment interaction (G × E) has garnered widespread attention. The most common way to assess interaction effects is in a regression model with a G × E interaction term that is a product of the values specified for the genotypic (G) and environmental (E) variables. In this paper we discuss the circumstances under which interaction can be modeled as a product term and cases in which use of a product term is inappropriate and may lead to erroneous conclusions about the presence and nature of interaction effects. In the case of a binary coded genetic variant (as used in dominant and recessive models, or where the minor allele occurs so infrequently that it is not observed in the homozygous state), the regression coefficient corresponding to a significant interaction term reflects a slope difference between the two genotype categories and appropriately characterizes the statistical interaction between the genetic and environmental variables. However, when using a three-category polymorphic genotype, as is commonly done when modeling an additive effect, both false positive and false negative results can occur, and the nature of the interaction can be misrepresented. We present a reparameterized regression equation that accurately captures interaction effects without the constraints imposed by modeling interactions using a single cross-product term. In addition, we provide a series of recommendations for making conclusions about the presence of meaningful G × E interactions, which take into account the nature of the observed interactions and whether they map onto sensible genotypic models.