In the Yale–Penn cohort, we conducted a multivariate GEWIS considering unrelated participants with complete genotype information (4,044 African-Americans and 3,407 European-Americans). The analysis was conducted using the recently-developed StructLMM, a linear mixed-model approach to identify and characterize loci that interact with one or more environments efficiently27. This method extends the conventional linear mixed models used to test persistent genetic effects (i.e., associations with constant genetic effect sizes across individuals in the population), permitting the investigator to model the heterogeneity in effect sizes due to gene-by-environment interactions. The multi-environment StructLMM model can be used to conduct an interaction test and an association test27. The interaction test is defined where persistent genetic and additive environment effects are accounted for in the null model. Conversely, the StructLMM association test analyzes the main effects while accounting for the possibility of heterogeneous genetic effects due to G × E.
