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To detect gene-environment interactions, a logistic regression model is typically fitted to a set of case-control data, and the focus is on testing of the cross-product terms (gene × environment) in the model. A significant result is indicative of a gene-environment interaction under a multiplicative model for disease odds. Based on the sufficient-cause model for rates, in this paper we put forward a general approach to testing for sufficient-cause gene-environment interactions in case-control studies. The proposed tests can be tailored to detect a particular type of sufficient-cause gene-environment interaction with greater sensitivity. These tests include testing for autosomal dominant, autosomal recessive, and gene-dosage interactions. The tests can also detect trend interactions (e.g., a larger gene-environment interaction with a higher level of environmental exposure) and threshold interactions (e.g., gene-environment interaction occurs only when environmental exposure reaches a certain threshold level). Two assumptions are necessary for the validity of the tests: 1) the rare-disease assumption and 2) the no-redundancy assumption. Another 2 assumptions are optional but, if imposed correctly, can boost the statistical powers of the tests: 3) the gene-environment independence assumption and 4) the Hardy-Weinberg equilibrium assumption. SAS code (SAS Institute, Inc., Cary, North Carolina) for implementing the methods is provided.

Testing for Sufficient-Cause Gene-Environment Interactions Under the Assumptions of Independence and Hardy-Weinberg Equilibrium