A model of gene-gene and gene-environment interactions and its implications for targeting environmental interventions by genotype

Table 4 Limits on the gene-environment interaction factor (f_ge) and the proportion of the population in the high-genotypic risk group (γ).

Gene-environment interaction model	Interaction factor f_ge	Risk distribution		Utility U_ge	Fraction of population at high genotypic risk
					Maximum γ_max	Minimum γ_min
Genetic effect in high-exposure group only	1/PAF^E_e	R ₀₀	R _ge	Positive	γ_maxge (where PAF^E_ge = PAF^E_e; PI = 1; and U_ge = 1-γ).	γ_minge (where R_ge = 1).
		R ₀₀	R _0e
Multiplicative	1	R _g0	R _g0 R _0e /R ₀₀		γ_maxge = γ₀ (where PAF^E_ge = PAF^E_e; R₀₀ = 0; and PAF^G_g = 1).
		R ₀₀	R _0e
Additive	0	R _g0	R _g0 +R _0e -R ₀₀	Zero	γ₀ (where R₀₀ = 0).
		R ₀₀	R _0e
Reverse multiplicative	-r_t/(1-r_t)	R _g0	(1-R _g0 ) (1- R _0e )/ (1-R ₀₀ )	Negative		γ_neg = γ_minge (where PAF^E_ge = 0 and R_ge = 1)
		R ₀₀	R _0e
Genetic effect in low-exposure group only	-ε/(1-ε)PAF^E_e	R _g0	R _0e			γ_neg (where PAF^E_ge = 0 and PI = 0).
		R ₀₀	R _0e

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