are independent, the P-value (also denoted as overlap P-value) for a given overlap statistic, r, at a SNP is . If we further assume that (under the null hypothesis - H0) none of the traits is associated with the genetic variant, the overlap P-value simplifies to P(R ≤ r) = rm (1). Otherwise, P(Pj ≤ r) can be computed based on the distribution of the j-th trait P-values. For instance, for two phenotype configuration and a putative threshold of 5 × 10−8, the parametric version of our method requires that, for a significant pleiotropic signal, the p-values for both phenotypes to be <2.2 × 10−4 (). This substantially less than 5 × 10−8 p-value threshold is similar in spirit to the one from Andeassen et al.71 While the overlap p-value (1) does eliminate most of the influence of an extreme signal for one phenotype, it does not eliminate it completely. However, for a putative threshold of 5 × 10−8 in (1), under the worst case scenario of an extreme signal in one phenotype, the false positive rate per SNP is still rather small, i.e. 2.2 × 10−4. Even more, as seen in Andreassen et al., the false positive rate is
