In the cross-trait analysis, MiXeR models additive genetic effects as a mixture of four components, representing null SNPs in both traits (π0); SNPs with a specific effect on the first and on the second trait (π1 and π2, respectively); and SNPs with non-zero effect on both traits (π12). In the last component, MiXeR models variance-covariance matrix as Σ12=[σ12ρ12σ1σ2ρ12σ1σ2σ22] where ρ12 indicates correlation of effect sizes within the shared component, and σ12 and σ22 correspond to the discoverability parameter estimated in the univariate analysis of the two traits. These components are then plotted in Venn diagrams. After fitting parameters of the model, the Dice coefficient of polygenic overlap is then calculated as 2π12π1+2π12+π2, and genetic correlation is calculated as rg=ρ12π12(π1+π12)(π2+π12). Fraction of influencing variants with concordant effect direction is calculated as twice the multivariate normal CDF at point (0, 0) for the bivariate normal distribution with zero mean and variance-covariance matrix Σ12. All code is available online (https://github.com/precimed/mixer).
