On the robustness of tests of genetic associations incorporating gene-environment interaction when the environmental exposure is misspecified.

We consider the robustness of tests of genetic associations that incorporate gene-environment interactions when the environmental exposure is misspecified, which is likely the case when the exposure is continuous. We formally prove that, under the null hypothesis of no genetic association, misspecified ordinary logistic regression and profile likelihood (Chatterjee and Carroll, Biometrika. 2005;92:399-418) analyses of case-control data both consistently estimate the null parameters of no genetic main effect and interaction, provided that genetic and environmental factors are unrelated in the underlying population. However, we argue that the associated likelihood ratio test, score test, and Wald test statistics obtained using the estimated information matrix have incorrect type-1 error rates due to model mis-specification. Based on these observations, we propose the use of the sandwich estimator of variance in conjunction with the consistent maximum (profile) likelihood estimates to construct Wald-type test statistics with correct type-1 error rate for the null of no genetic association.