Several statistical methods have been proposed for testing G-E interactions under additive risk models using genome-wide association study data. However, these approaches have strong assumptions on the underlying genetic model such as dominant or recessive effects that are known to be less robust when the true genetic model is unknown. Our goal is to develop a robust trend test employing a likelihood ratio test for detecting G-E interaction under an additive risk model, also incorporating the G-E independence assumption to increase power. We used a constrained likelihood approach to impose two sets of constraints: (i) the linear trend effect of a genotype and (ii) the additive joint effects of G and E, exploiting a saturated logit model. To incorporate the G-E independence assumption, a retrospective likelihood was used. Numerical investigation of power suggests that the proposed trend test is more powerful compared to those assuming a dominant, recessive, or general model under various parameter settings. Incorporation of the independence assumption enhances the efficiency of the test by 2.5- to 3-fold. We illustrate this method by applying it to Alzheimer disease GWAS data.