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Chunk #5 — Quantification of bias when improperly controlling for covariates in G×E studies

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Gene × environment interaction studies have not properly controlled for potential confounders: the problem and the (simple) solution.
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When the signs of the βC1×EσC1,GσG2 or the βG×C1σC1,EσE2 terms are opposite the sign of the βG×E term, properly controlling for covariates can increase power to detect true G×E interactions. However, when those terms are of the same sign as the βG×E term, properly controlling for covariates will weaken evidence for apparent G×E interactions.