Figure 3.

The relative power of detecting the gene-environment interaction effect δ. The frequency of binary exposure is 0.6; the exposure status is fixed for the Families scenario such that two parents are unexposed and three offspring are exposed. (A) The ESS multiplier ${\gamma }_{\delta }$ is greater than one for both Families and Unrelated+Grouping scenarios compared to the baseline Unrelated scenario. The amount of variance explained by the random effects (${\sigma }_a^2+{\sigma }_{ai}^2$ or ${\sigma }_f^2$) varies from 0 to 100%. (B) The power of detecting δ increases with the sample size at different rates for the Unrelated, Families and Unrelated+Grouping scenarios. The random effects (jointly) and the interaction variable explain 50% and 1% of trait variance, respectively. (C) The covariance matrices of the trait and interaction variable Σ_y and Σ_v (used to compute ${\gamma }_{\delta }$) are depicted when 50% of trait variance is explained by random effects (denoted by * on panel A). The colored gradients in entries of matrices denote quantitative differences for positive values, while gray-colored entries correspond to negative values. The ratio between ${\sigma }_{ai}^2$ and ${\sigma }_a^2$ is fixed to 0.1; both genetic and environmental variables also explain 1% of the trait variance in addition to 1% of the interaction variable.