Kernel-based gene–environment interaction tests for rare variants with multiple quantitative phenotypes

Previous studies have suggested that gene–environment interactions (GEIs) between a common variant and an environmental factor can influence multiple correlated phenotypes simultaneously, that is, GEI pleiotropy, and that analyzing multiple phenotypes jointly is more powerful than analyzing phenotypes separately by using single-phenotype GEI tests. Methods to test the GEI for rare variants with multiple phenotypes are, however, lacking. In our work, we model the correlation among the GEI effects of a variant on multiple quantitative phenotypes through four kernels and propose four multiphenotype GEI tests for rare variants, which are a test with a homogeneous kernel (Hom-GEI), a test with a heterogeneous kernel (Het-GEI), a test with a projection phenotype kernel (PPK-GEI) and a test with a linear phenotype kernel (LPK-GEI). Through numerical simulations, we show that correlation among phenotypes can enhance the statistical power except for LPK-GEI, which simply combines statistics from single-phenotype GEI tests and ignores the phenotypic correlations. Among almost all considered scenarios, Het-GEI and PPK-GEI are more powerful than Hom-GEI and LPK-GEI. We apply Het-GEI and PPK-GEI in the genome-wide GEI analysis of systolic blood pressure (SBP) and diastolic blood pressure (DBP) in the UK Biobank. We analyze 18,101 genes and find that LEUTX is associated with SBP and DBP (p = 2.20×10−6) through its interaction with hemoglobin. The single-phenotype GEI test and our multiphenotype GEI tests Het-GEI and PPK-GEI are also used to evaluate the gene–hemoglobin interactions for 22 genes that were previously reported to be associated with SBP or DBP in a meta-analysis of genetic main effects. MYO1C shows nominal significance (p