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Chunk #29 — 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 the above examples, a significant interaction would be detected by the four parameter model, but the implied nature of the interaction is erroneously indicated by the regression lines of the four parameter model. We consider a final example (indicated in the last columns of Table 1 and corresponding to Appendix C), illustrating a case where the four parameter model is not significant; however, an interaction exists in the data, and is accurately captured by the six parameter model. In this case the six parameter model accurately shows interaction with p < 4.9 × 10−12 but the four parameter model shows no interaction (p = 0.239) and corresponds to Type II error.