The sampling variance of for a complex trait is inversely proportional to sample size (N) and the variance in SNP-based genetic relatedness (), and independent of . The sampling variance of between two complex traits is a function of , N of the two samples, of the two traits and when the traits are measured on different samples, and further depends on the phenotypic correlation () when traits are measured on the same samples. All the approximation theories apply to case-control studies of diseases since the case-control data can be analysed using a linear model on the observed 0–1 scale. The sampling variance for the estimate on the observed scale can then be transformed to that on the underlying liability scale using well-established theory. The standard errors (square root of sampling variance) of either or observed in published studies were all highly consistently with those predicted from our approximation theories, which were also confirmed by simulations based on real genotype data.
