Samples of trios were directly simulated via Monte Carlo simulation. First mother and father polygenic risk, family environmental risk, and individual protective environment were simulated from a standard normal distribution. A single resistance SNP was simulated in parents. Genetic variables were simulated in the offspring conditional on parental SNPs using gene-dropping simulation and on parental polygenic risk as the mean of parental polygenic risk. Given a set of correlations and residual variance, a random normal (0,1) underlying risk was directly simulated per individual. Risk was dichotomized to disease status via the logit model with a constant added to simulate a specified population prevalence of disorder. In all simulations, we assumed a population prevalence of 5%. For the case-control and high-risk design samples we over-simulated to generate 500 case or high-risk families from the stated environmental quantiles, respectively. In the low-risk design, we over-simulated to generate 500 subjects with liability at or below the 10th percentile and 500 subjects above the 60th percentile. In the random design, we simulated 1000 trios irrespective of outcome and environmental stratum. We selected parameter values
