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Chunk #26 — 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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In Fig. 2a, the simulated data has equivalent slope differences between adjacent lines and the lines all cross at the same point; however, the data does not show ordered genotypic groups. As illustrated in Fig. 2a, the four-parameter model does not fit the data points and yields slopes in increasing order for G levels 0, 1 and 2, despite the fact that this is not the nature of the simulated lines (which are ordered 0, 2, 1). The interaction term in the four-parameter model is highly significant with p < 10−16, which misleadingly indicates the existence of an additive interaction. This result is spuriously generated by the gene dose effects, which are not additive. The six parameter model accurately represents the data and captures the true nature of the regression lines.