Chunk #21 — 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 first coefficient in Eq. (2), (G − 1)(G − 2)/2 is zero if G = 1 or G = 2 and is 1 if G = 0. Accordingly, the second (−G(G − 2)/2) and third (−G(G − 1)/2) coefficients also are 0 or 1 depending on the corresponding value of G. So, Eq. (2) is equivalent to Eqs. (A1), (A2) and (A3) in Appendix A when G = 0, 1 and 2, respectively. Thus, the regression equation in (2) yields the correct equations for (A1)–(A3).