Abstract : Background: It is generally acknowledged that most complex diseases are affected in part by interactions between genes and genes and/or between genes and environmental factors. Taking into account environmental exposures and their interactions with genetic factors in genome-wide association studies (GWAS) can help to identify high-risk subgroups in the population and provide a better understanding of the disease. For this reason, many methods have been developed to detect gene-environment (G×E) interactions. Despite this, few loci that interact with environmental exposures have been identified so far. Indeed, the modest effect of G×E interactions as well as confounding factors entail low statistical power to detect such interactions. Another potential obstacle to detect G×E interaction is the fact that true exposure is seldom observed: Indeed, only proxy effects are measured in general. Furthermore, power studies used to evaluate a new method often are done through simulations that give an advantage to the new approach over the other methods. Methods: In this work, we compare the relative performance of popular methods such as PLINK, random forests and linear mixed models to detect G×E interactions in the particular scenario where the causal exposure (E) is unknown and only proxy covariates are observed. For this purpose, we provide an adapted simulated dataset and apply a recently introduced method for H1 simulations called waffect. Results: When the causal environmental exposure is unobserved but only a proxy of this exposure is observed, all the methods considered fail to detect G×E interaction. Conclusions: The hidden causal exposure is an obstacle to detect G×E interaction in GWAS and the approaches considered in our power study all have insufficient power to detect the strong simulated interaction.