Testing for measured gene-environment interaction: problems with the use of cross-product terms and a regression model reparameterization solution.
- Authors
- Aliev, Fazil; Latendresse, Shawn J; Bacanu, Silviu-Alin; Neale, Michael C; Dick, Danielle M
- Year
- 2014
- Journal
- Behavior genetics
- PMID
- 24531874
- DOI
- 10.1007/s10519-014-9642-1
- PMCID
- PMC4004105
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.
Regression lines as illustrated for a three category genotype
LLM interpretation
This figure consists of a 3D scatter plot and a corresponding 2D projection showing the relationship between genotype, environment, and phenotype. The x-axis represents environment, the y-axis represents phenotype, and the z-axis (in the 3D plot) represents three distinct genotype categories. Three separate regression lines (blue, red, and green) indicate that different genotypes exhibit varying phenotypic responses to environmental changes, with the blue genotype showing the steepest slope.
a Simulated data violates the constraint of ordered genotypes. Parameters are the same as in Appendix B and Table 1. b Simulated data violates the constraint of equivalent slope differences between adjacent genotypic groups. Parameters are the same as in Table 1. c Simulated data violates the constraint of all lines crossing at a single point. Parameters are the same as in Table 1
LLM interpretation
This figure consists of six scatter plots with overlaid regression lines, organized into three rows (A, B, C) comparing a "Four Parameter Model" (left) and a "Six Parameter Model" (right). Each plot maps "Phenotype" against "Environment" for three genotypic groups (Gene=0, 1, and 2), showing how the two models fit simulated data that violates specific constraints. The Six Parameter Model consistently shows a closer fit to the data points across all three scenarios compared to the Four Parameter Model.
Possible outcomes for slope differences and corresponding conclusions about interactions
LLM interpretation
This figure consists of six conceptual line graphs (labeled A–F) illustrating how different slope patterns between genotypes (Gene=0, 1, 2) across an environmental gradient relate to gene-environment interactions. Each plot maps "Phenotype" on the y-axis against "Environment" on the x-axis, with lines representing different genetic groups. Accompanying text for each panel defines the specific conditions (significance of slopes A and B) that lead to conclusions of additive, dominant, recessive, or overdominance interactions.
| Name | Type |
|---|---|
| E local | drug |
| Environmental variable local | drug |
| G local | variant |
| G=0 local | variant |
| G=1 local | variant |
| G=2 local | variant |
| G2 local | variant |
| G2E local | variant |
| gene-environment interaction | phenotype |
| genetic variants | cohort |
| G variable local | gene |
| p-factor | phenotype |
| phenotype | phenotype |
| Simulated cohort (n=10,000) local | cohort |
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