The problem has to do with the approach to testing interactions (111): If the product term (i.e., the interaction term in multiple regression) is calculated from two normally distributed symmetrical variables, it has restricted variance but is uncorrelated with the first-order predictors (Figure 3, top row). However, a product term of two categorical variables (e.g., minor allele frequency [MAF] of 25% and rate of exposure [Pexp] of 25%) is significantly correlated with the first-order predictors (Figure 3, middle row). Such is the case in practically all observational G×E studies of psychiatric phenotypes. As a result, the residual variance of the product term after factoring out first-order predictors—and the corresponding power to detect interactions—declines rapidly with minor allele frequencies and rates of exposure departing from 50%. The full power for testing interactions between categorical variables is only preserved in the optimal case where minor allele frequency and exposure rate equal 50% (bottom of Figure 3). An implication of this insight is that hypothesis-driven G×E studies that recruit participants on the basis of their genotype and their environmental exposure (e.g., experimental G×E
