Distinct explanations underlie gene-environment interactions in the UK Biobank.

The role of gene-environment (GxE) interaction in disease and complex trait architectures is widely hypothesized, but currently unknown. Here, we apply three statistical approaches to quantify and distinguish three different types of GxE interaction for a given trait and E variable. First, we detect locus-specific GxE interaction by testing for genetic correlation $\left(r_g\right)<1$ across E bins. Second, we detect genome-wide effects of the E variable on genetic variance by leveraging polygenic risk scores (PRS) to test for significant PRSxE in a regression of phenotypes on PRS, E, and PRSxE, together with differences in SNP-heritability across E bins. Third, we detect genome-wide proportional amplification of genetic and environmental effects as a function of the E variable by testing for significant PRSxE with no differences in SNP-heritability across E bins. Simulations show that these approaches achieve high sensitivity and specificity in distinguishing these three GxE scenarios. We applied our framework to 33 UK Biobank traits (25 quantitative traits and 8 diseases; average $N=325\text{K}$) and 10 E variables spanning lifestyle, diet, and other environmental exposures. First, we identified 19 trait-E pairs with $r_g$ significantly < 1 (FDR<5%) (average $r_g=0.95$); for example, white blood cell count had $r_g=0.95$ (s.e. 0.01) between smokers and non-smokers. Second, we identified 28 trait-E pairs with significant PRSxE and significant SNP-heritability differences across E bins; for example, BMI had a significant PRSxE for physical activity (P=4.6e-5) with 5% larger SNP-heritability in the largest versus smallest quintiles of physical activity (P=7e-4). Third, we identified 15 trait-E pairs with significant PRSxE with no SNP-heritability differences across E bins; for example, waist-hip ratio adjusted for BMI had a significant PRSxE effect for time spent watching television (P=5e-3) with no SNP-heritability differences. Across the three scenarios, 8 of the trait-E pairs involved disease traits, whose interpretation is complicated by scale effects. Analyses using biological sex as the E variable produced additional significant findings in each of the three scenarios. Overall, we infer a significant contribution of GxE and GxSex effects to complex trait and disease variance.