Detecting latent exposure in genome-wide association studies using a breakpoint model for logistic regression

Detecting gene-environment (G × E) interactions in the context of genome-wide association studies (GWAS) is a challenging problem since standard methods generally present a lack of power. An additional difficulty arises from the fact that the causal exposure is seldom observed and only a proxy of this exposure is observed. This leads to an additional drop in terms of power and it explains the failure of standard methods in detecting interactions, even very strong ones. In this article, we consider the latent exposure as a source of heterogeneity and we propose a new powerful method, named "Breakpoint Model for Logistic Regression" (BMLR), based on a breakpoint model, in order to detect G × E interactions when causal exposure is unobserved. First, the BMLR method is compared to the ordered-subset analysis for case-control method, which has been developed for the same purpose, through simulations. This highlights the ability of BMLR to detect the heterogeneity, and therefore, to detect interaction with latent exposure. Finally, the BMLR method is compared to standard methods, such as Plink, to perform a GWAS on a published realistic benchmark.