Chunk #45 — Reasons to be Concerned about the Published cGxE Literature — Problems with the Recipe: Statistical Concerns in cGxE Research — The use of cross-product terms
The use of a cross-product term can be particularly problematic for modeling three-level, categorical genotypes. In the standard practice of assuming an additive genetic model, the use of a cross-product term will force the slope difference to be the same between all genotypic groups (e.g., the difference in slope between people carrying 0 versus 1 copies of the risk allele is constrained to be the same as the slope difference between individuals who carry 1 versus 2 copies of the risk allele). It also forces the lines for the three genotypic groups to all cross at the same point when an interaction exists. Accordingly, an interaction will only be accurately represented by the cross-product term when these conditions are met, and there is no a priori reason to assume that these constraints are sensible. This means that the regression lines implied by the use of a cross-product term may not accurately reflect the interaction present in the data. Figure 3 illustrates the problem, and demonstrates how a reparameterization of the regression equation using parameters additional to the single cross-product term can correct it (as further delineated in Aliev, Latendresse, Bacanu, Neale, & Dick, 2014).
