On the interpretation, robustness, and power of varieties of case-only tests of gene-environment interaction

The author addresses issues related to interpretation of the parameters in the proposed case-only linear regression approach to testing for gene-environment interaction recently considered by Clarke and Morris (Am J Epidemiol. 2010;171(4):498-505). He also considers the robustness of their likelihood ratio test to violation of the assumption of Gaussian regression residuals under the null hypothesis of no interaction; shows how their approach can be extended to a more general class of regression models; and derives the optimal interaction test statistic for this class of regression models. Finally, the author briefly discusses case-only doubly robust methods recently proposed by Tchetgen Tchetgen and Robins (Biometrics. 2010;Mar 11).