To determine the circumstances in which TATES outperforms the original Simes procedure, we conducted six additional simulations. While the original Simes procedure corrects for the observed number of p-values, TATES corrects for the effective number of p-values, by taking the correlations between the p-values into account. The difference in terms of power between Simes and TATES is thus expected to be larger as the correlations between the p-values (phenotypes) are stronger (i.e., the effective number becomes smaller).
