into account that the m phenotypes, and thus the m p-values, are correlated. In an iterative procedure, TATES weighs the j th p-value in the 1 to m sorted p-values with m e/m ej, where m e is the effective number of independent p-values among all m variables, and m ej the effective number of p-values among the top j p-values. The weight m e is a function of m, and the sum of those eigenvalues larger than 1 of the m×m correlation matrix of the p-values. Similarly, m ej is a function of j and the sum of the eigenvalues larger than 1 based on the j×j correlation matrix of the top j p-values . The correlation matrix of the m p-values is approximated from the observed correlation matrix between the m phenotypes using a 6th order polynomial (coefficient of determination R2 = .992, see Materials and Methods and Figure S1). For each of the n GVs, the trait-based TATES p-value PT equals the smallest weighted p-value, with the null-hypothesis that none of the phenotypes is associated with the GV, and the alternative hypothesis that at least one of the phenotypes is associated with the GV. The TATES procedure
