For case-control studies, the proportion of variance in case-control status (0 or 1) that is explained by all SNPs on the observed scale () can be estimated using a linear model [4]. Therefore, the same approximations to the sampling variance of genetic variance and genetic correlation for quantitative traits can be applied directly to case-control studies. As shown in equation (5), in a univariate analysis, the sampling variance of SNP-based heritability depends only on sample size and variance in genetic relatedness, independent of the properties of the phenotype, so that var() is also approximately in a case-control study with N being the total number of cases and controls. We show in Table 2 that the observed standard errors of the estimates of from published studies are highly consistent with those predicted from our approximation theory.
