Once gene clusters were assigned, for creQTL association testing, we computed a modified version of ZE(j), called Z2E(j), to describe how tightly regulated the gene cluster was within a given sample. The modified version replaces the numerator of ZE(j) with the mean of all genes' contributions to the cluster and adds a small positive constant, s0, to the denominator in order to moderate variance and avoid extremely large values of Z2E(j). s0 was chosen by minimizing the coefficient of variation of the denominator of ZE(j) across moving windows of data, akin to the strategy of Tusher et al. [29] for the moderation of t statistics. The modified statistic for association testing is
