As shown in equation (10), in a bivariate analysis where traits are measured on different sets of samples, the sampling variance of genetic correlation depends on sample sizes, trait heritabilities and the genetic correlation parameter, which is also independent of the properties of the phenotypes. Therefore, in a bivariate analysis of two independent case-control disease studies,(12)where N 1 and N 2 are the total numbers of cases and controls of the two case-control studies, respectively. This also applies to a bivariate analysis of a quantitative trait and a cases-control disease study on different sets of samples, i.e.(13)These two equations can also be expressed with respect to , given (see above). We show in Table 3 that the reported SEs of from bivariate analyses of psychiatric diseases are also highly in line with the predicted SEs from the approximation theory.
