Chunk #22 — 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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Substituting terms for H0, H1, and H2 into Eq. (2), it is easy to see that the model involves G2 and G2E terms and corresponds to the full model with trichotomous G and continuous E variables with interaction (see, Kleinbaum et al. 2002, Chapters 6 & 7), which can be rewritten as: (3)P=γ0+γ1G+γ2E+γ3G×E+γ4G2+γ5G2×E.