Figure 3.

Estimation of G and GxE heritability in six simulated scenarios

We investigated the performance of GENIE in estimating G and GxE heritability under six simulated scenarios. (1) Correlated Y: the phenotypes were correlated with the continuous environment exposure, with Pearson’s correlation $r=0.5$; (2) heritable E: the environment exposure E was simulated from the same set of genotype data as in the phenotype simulation, with an additive genetic heritability of 0.1; (3) same causal SNPs: additive genetic causal SNPs completely overlap with GxE causal SNPs; (4) same causal SNPs for additive and heritable E: additive genetic causal SNPs completely overlap with the causal SNPs explaining heritability in E, where E is the same as in scenario (2); (5) collider bias: the phenotype Y and environment exposure E are correlated through an unobserved confounder; we simulated a heritable environment variable with a genetic heritability of 0.1. The phenotypes were then generated to have a Pearson’s correlation $r=0.2$ with the heritable E. We assumed that the correlation was due to an unobserved confounder.¹⁷ (6) Heavy-tailed noise: we drew the environment noise component from the Student’s t-distribution with degrees of freedom = 4. In all scenarios, we simulated 100 replicates of phenotypes with NxE and varying magnitude of GxE effects across $N=291,273$ individuals genotyped at $454,207$ SNPs. The ground truth GxE heritability was 0, 0.04, and 0.1, with corresponding NxE variance of 0.04, 0.04, and 0.1. The additive genetic heritability was fixed at 0.25. The x and y axes denote the true GxE heritability and the estimated G and GxE heritability. Points and error bars represent the mean and estimated $95\%$ CI, respectively. Across all simulations where there is no GxE, the mean of P(rejection at $p<t$) are $5.5\%$ and $0\%$ for $t=0.05$ and $t=0.05/200$, respectively ($5.5\%$ is not significantly different from the nominal rate of $5\%$).