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.
| # | Section | Preview |
|---|---|---|
| 20 | Methods and results — A reparameterization of the equation to address the problem | One approach is to recode the genotype data into three orthogonal components, taking the values:… |
| 21 | Methods and results — A reparameterization of the equation to address the problem | The first coefficient in Eq. (2), (G − 1)(G − 2)/2 is zero if G = 1 or G = 2 and is 1 if G = 0.… |
| 22 | Methods and results — A reparameterization of the equation to address the problem | Substituting terms for H0, H1, and H2 into Eq. (2), it is easy to see that the model involves G2 and… |
| 23 | Methods and results — A reparameterization of the equation to address the problem | The relationship between Eq. (3) and the coefficients from Eqs. (A1)–(A3) are as follows:… |
| 24 | Methods and results — A reparameterization of the equation to address the problem | In order to illustrate why this method is more appropriate for modeling G × E with three category… |
| 25 | Methods and results — A reparameterization of the equation to address the problem | respectively. Then for each G level we assumed that the Phenotypes were linearly dependent on the… |
| 26 | Methods and results — A reparameterization of the equation to address the problem | In Fig. 2a, the simulated data has equivalent slope differences between adjacent lines and the lines… |
| 27 | Methods and results — A reparameterization of the equation to address the problem | Figure 2b illustrates the case when differences between slopes are different in the simulated data,… |
| 28 | Methods and results — A reparameterization of the equation to address the problem | In Fig. 2c the simulated data for each genotypic group do not cross at the same point (note that… |
| 29 | Methods and results — A reparameterization of the equation to address the problem | In the above examples, a significant interaction would be detected by the four parameter model, but… |
| 30 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | In the previous section we demonstrated that the six parameter model more accurately captures… |
| 31 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | First we rewrite Eq. (3) for each of the three genotype groups:… |
| 32 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | Recall that the significance of the interaction is determined by the slope difference between the… |
| 33 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | The slope difference A between G = 1 and G = 0 is A≡(γ2+γ3+γ5)−γ2=γ3+γ5. |
| 34 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | Similarly, slope differences between G = 2 and G = 1, and between G = 2 and G = 0 are, respectively,… |
| 35 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | Note also that C = A + B. Accordingly, we have three hypotheses and corresponding p-values… |
| 36 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | Generally, to test for any interaction effect means that one of the coefficients A, B or C is… |
| 37 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | However, in the context of studying gene-environment interaction, the assumed genetic model should… |
| 38 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | a likely biological model suggests an increased probability that the interaction is a false positive… |
| 39 | Methods and results — Testing for significance of gene-environment interaction effects using the reparameterized equation | a classic genetic model (additive, dominant, or recessive) should be viewed skeptically without a… |
| 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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