Starting with the mixture-normal setup in the derivation of power and the FDR, we assume that there are C=2T components, corresponding to all possible combinations of the SNP being null for some subset of traits and non-null for the others. Let Ω∼ denote the variance-covariance matrix of true effect sizes for the component in which the SNP is non-null for all the traits. We assume that the variance-covariance matrix of true effect sizes for any component c, denoted Ωc, is equal to Ω∼ but with the rows and columns zeroed out that correspond to null traits in component c. Given our estimate of Ω, for any vector of mixing weights p=(p1,p2,…,pC), we construct an estimate of Ω∼: we set the (t,s)th entry of Ω∼(p) equal to ω∼ts(p)=ωts∑c∈Et,spc, where Et,s is the set of components in which the SNP is non-null for both traits t and s. We call the mixing weights p feasible if the resulting matrix Ω∼(p) is positive semi-definite. We maximize the FDR (given by the formula above) over all feasible mixing weights p. Given that the FDR
