Semiparametric odds ratio model for case-control and matched case-control designs.

We propose a semiparametric odds ratio model that extends Umbach and Weinberg's approach to exploiting gene-environment association model for efficiency gains in case-control designs to both discrete and continuous data. We directly model the gene-environment association in the control population to avoid estimating the intercept in the disease risk model, which is inherently difficult because of the scarcity of information on the parameter with the sampling designs. We propose a novel permutation-based approach to eliminate the high-dimensional nuisance parameters in the matched case-control design. The proposed approach reduces to the conditional logistic regression when the model for the gene-environment association is unrestricted. Simulation studies demonstrate good performance of the proposed approach. We apply the proposed approach to a study of gene-environment interaction on coronary artery disease.