Table 4

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

Gene-environment interaction model
Interaction factor fge
Risk distribution
Utility Uge
Fraction of population at high genotypic risk











Maximum γmax
Minimum γmin

Genetic effect in high-exposure group only
1/PAFEe
R00
Rge
Positive
γmaxge (where PAFEge = PAFEe; PI = 1; and Uge = 1-γ).
γminge (where Rge = 1).


R00
R0e



Multiplicative
1
Rg0
Rg0R0e/R00

γmaxge = γ0 (where PAFEge = PAFEe; R00 = 0; and PAFGg = 1).



R00
R0e



Additive
0
Rg0
Rg0+R0e-R00
Zero
γ0 (where R00 = 0).



R00
R0e



Reverse multiplicative
-rt/(1-rt)
Rg0
(1-Rg0) (1-R0e)/(1-R00)
Negative

γneg = γminge (where PAFEge = 0 and Rge = 1)


R00
R0e



Genetic effect in low-exposure group only
-ε/(1-ε)PAFEe
Rg0
R0e


γneg (where PAFEge = 0 and PI = 0).


R00
R0e




Wallace Theoretical Biology and Medical Modelling 2006 3:35   doi:10.1186/1742-4682-3-35