While there are papers looking at pleiotropy from a conditional FDR point of view71, we arrive to qualitatively similar conclusions using a somewhat simpler approach of family-wise error rate. Our test attempts to discover shared risk genes between schizophrenia and ND using summary statistics from their respective GWASs. To ensure that such a test is not overly influenced by a strong signal in just one trait, we implemented a “weakest link” approach (i.e., choosing the larger P-value of the pair of trait tests at the SNP under investigation)72. In more detail, let Xj and Pj be the χ2 distributed statistics and their associated (background enrichment adjusted) P-values, j = 1, …, m, for association tests between the m traits and a SNP. As the overlap statistic of all traits we use (or, alternatively,). Under the assumption that the trait tests 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
