An easy-to-implement approach for analyzing case-control and case-only studies assuming gene-environment independence and Hardy-Weinberg equilibrium

The case-control study is a simple and an useful method to characterize the effect of a gene, the effect of an exposure, as well as the interaction between the two. The control-free case-only study is yet an even simpler design, if interest is centered on gene-environment interaction only. It requires the sometimes plausible assumption that the gene under study is independent of exposures among the non-diseased in the study populations. The Hardy-Weinberg equilibrium is also sometimes reasonable to assume. This paper presents an easy-to-implement approach for analyzing case-control and case-only studies under the above dual assumptions. The proposed approach, the 'conditional logistic regression with counterfactuals', offers the flexibility for complex modeling yet remains well within the reach to the practicing epidemiologists. When the dual assumptions are met, the conditional logistic regression with counterfactuals is unbiased and has the correct type I error rates. It also results in smaller variances and achieves higher powers as compared with using the conventional analysis (unconditional logistic regression).