The main potential problem arises for SNPs that are truly null for one trait but non-null for another trait. For such SNPs, MTAG’s effect-size estimates for the first trait are biased away from zero, leading to an increased rate of false positives (and inflated type I error rate). We derive an analytic formula for the resulting false discovery rate (FDR), given any specified mixture-normal distribution of effect sizes (including multivariate spike-and-slab distributions), and we illustrate how the formula can be used to probe the credibility of MTAG-identified loci.
