Abstract:
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We consider the problem of exploiting the gene-environment independence (GEI) assumption in a case-control study inferring the joint effect of genotype and environmental exposure on disease risk, specifically focused on the special case of both genotype and exposure being binary. Despite the fact that the GEI-constrained estimator is asymptotically equivalent to it unconstrained counterpart, we study the potential benefit of employing the GEI assumption with finite sample size. We note that the prospective intercept can sometimes be identified as a pair of `twin' values. Also, the GEI and general maximum-likelihood estimators of the gene-environment interaction coincide if the data cell proportions are directly compatible with the GEI assumption. Further, we approach the problem in a Bayesian framework by reweighing the general posterior subject to the prior specified over the subset of parameter space that is consistent with the GEI assumption. Our simulation study shows that there are situations where exploiting the GEI assumption can be beneficial. Finally, we have also extended the proposed method to address the concern that the GEI assumption may sometimes be violated.
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