To simulate case-control GWAS data for two genetically correlated diseases, we followed the classical liability threshold model [13]. For each disease, we first simulated a large cohort of individuals with genotypes of independent SNPs. The MAFs of these SNPs were drawn uniformly from [0.05, 0.5]. Then we randomly designated SNPs as risk SNPs. The per-minor-allele effect of each risk SNP was drawn from a normal distribution with zero-mean and variance of , where is the desired level of variance explained by all SNPs on the liability scale and is the MAF of the corresponding risk SNP. We also simulated the environmental effect on the liability scale for each individual from a standard normal distribution (zero mean and unit variance). The total liability for each individual was then obtained by adding up all the genetic effects and the environmental effect. Given a desired disease prevalence , individuals with liabilities greater than the quantile were classified as cases and others were classified as controls. Then equal numbers of cases and controls were drawn from the cohort as a GWAS data set. When
