A Multi‐Phenotype Approach to Joint Testing of Main Genetic and Gene‐Environment Interaction Effects

Gene-environment (GxE) interactions crucially contribute to complex phenotypes. The statistical power of a GxE interaction study is limited mainly due to weak GxE interaction effect sizes. Joint tests of the main genetic and GxE effects for a univariate phenotype were proposed to utilize the individually weak GxE effects to improve the discovery of associated genetic loci. We develop a testing procedure to evaluate combined genetic and GxE effects on multiple related phenotypes to enhance the power by merging pleiotropy in the main genetic and GxE effects. We base the approach on a general linear hypothesis testing framework for multivariate regression of continuous phenotypes. We implement the generalized estimating equations (GEE) technique under the seemingly unrelated regressions (SUR) setup for binary or mixed phenotypes. We use extensive simulations to show that the test for joint multi-phenotype genetic and GxE effects outperforms the univariate joint test of genetic and GxE effects and the test for multi-phenotype GxE effect concerning power when there is pleiotropy. The test produces a higher power than the test for the multi-phenotype marginal genetic effect for a weak genetic and substantial GxE effect. For more prominent genetic effects, the latter performs better with a limited increase in power. Overall, the multi-phenotype joint approach offers robust, high power across diverse simulation scenarios. We apply the methods to lipid phenotypes with sleep duration as an environmental factor in the UK Biobank. The proposed approach identified ten independent associated genetic loci missed by other competing methods. In a multi-phenotype analysis of apolipoproteins, ApoA1, and ApoB, our approach discovered two distinct loci considering sleep duration as the environmental factor.