Maximum likelihood method quantifies the overall contribution of gene-environment interaction to continuous traits: An application to complex traits in the UK Biobank

As genome-wide association studies (GWAS) increased in size, numerous gene-environment interactions (GxE) have been discovered, many of which however explore only one environment at a time and may suffer from statistical artefacts leading to biased interaction estimates. Here we propose a maximum likelihood method to estimate the contribution of GxE to complex traits taking into account all interacting environmental variables at the same time, without the need to measure any. This is possible because GxE induces fluctuations in the conditional trait variance, the extent of which depends on the strength of GxE. The approach can be applied to continuous outcomes and for single SNPs or genetic risk scores (GRS). Extensive simulations demonstrated that our method yields unbiased interaction estimates and excellent confidence interval coverage. We also offer a strategy to distinguish specific GxE from general heteroscedasticity (scale effects). Applying our method to 32 complex traits in the UK Biobank reveals that for body mass index (BMI) the GRSxE explains an additional 1.9% variance on top of the 5.2% GRS contribution. However, this interaction is not specific to the GRS and holds for any variable similarly correlated with BMI. On the contrary, the GRSxE interaction effect for leg impedance Embedded Image is significantly (P < 10−56) larger than it would be expected for a similarly correlated variable Embedded Image. We showed that our method could robustly detect the global contribution of GxE to complex traits, which turned out to be substantial for certain obesity measures.