Likelihood ratio test for detecting Gene (G)-environment (E) interactions under an additive risk model exploiting G-E independence for case-control data

There has been a long-standing controversy in epidemiology with regard to an appropriate risk scale for testing interactions between genes (G) and environmental exposure (E). Although interaction tests based on the logistic model-which approximates the multiplicative risk for rare diseases-have been more widely applied because of its convenience in statistical modeling, interactions under additive risk models have been regarded as closer to true biologic interactions and more useful in intervention-related decision-making processes in public health. It has been well known that exploiting a natural assumption of G-E independence for the underlying population can dramatically increase statistical power for detecting multiplicative interactions in case-control studies. However, the implication of the independence assumption for tests for additive interaction has not been previously investigated. In this article, the authors develop a likelihood ratio test for detecting additive interactions for case-control studies that incorporates the G-E independence assumption. Numerical investigation of power suggests that incorporation of the independence assumption can enhance the efficiency of the test for additive interaction by 2-to 2.5-fold. The authors illustrate their method by applying it to data from a bladder cancer study.