Chunk #23 — Methods and results — A reparameterization of the equation to address the problem

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Testing for measured gene-environment interaction: problems with the use of cross-product terms and a regression model reparameterization solution.

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The relationship between Eq. (3) and the coefficients from Eqs. (A1)–(A3) are as follows: γ0=δ00,δ00=γ0,γ1=−1.5δ00+2δ10−0.5δ20,δ01=γ2,γ2=δ01,δ10=γ0+γ1+γ4,γ3=−1.5δ01+2δ11+0.5δ21,δ11=γ2+γ3+γ5,γ4=0.5δ00−δ10+0.5δ20,δ20=γ0+2γ1+4γ4,γ5=0.5δ01−δ11+0.5δ21,δ21=γ2+2γ3+4γ5.