Unveiling challenges in Mendelian randomization for gene-environment interaction

Gene-environment (GxE) interactions play a crucial role in understanding the complex etiology of various traits, but assessing them using observational data can be challenging due to unmeasured confounders for lifestyle and environmental risk factors. Mendelian randomization (MR) has emerged as a valuable method for assessing causal relationships based on observational data. This approach utilizes genetic variants as instrumental variables (IVs) with the aim of providing a valid statistical test and estimation of causal effects in the presence of unmeasured confounders. MR has gained substantial popularity in recent years largely due to the success of genome-wide association studies. Many methods have been developed for MR; however, limited work has been done on evaluating GxE interaction. In this paper, we focus on two primary IV approaches: the two-stage predictor substitution and the two-stage residual inclusion, and extend them to accommodate GxE interaction under both the linear and logistic regression models for continuous and binary outcomes, respectively. Comprehensive simulation study and analytical derivations reveal that resolving the linear regression model is relatively straightforward. In contrast, the logistic regression model presents a considerably more intricate challenge, which demands additional effort.