Alternatively, we can recast the observed improvement in causal variant localization when incorporating functional annotations as a decrease in size of the set of SNPs to account for a fixed amount of posterior probability mass. We extend existing work for single-locus fine-mapping [5], [8], [9], [7] to define an ρ-level causal set as the set of top SNPs (rank-ordered based on probabilities) across all fine-mapping loci that consume an fraction of the total posterior probability mass. We observe a reduction in the number of SNPs within the 90%, 95% and 99% confidence sets when using functional annotations as compared to no functional data (see Table 2). In addition, although PAINTOR with annotation yields fewer SNPs with high probability than the PAINTOR with no annotation (232.8 vs 265.2 at a threshold of ), having access to annotation yields more simulated causals with high posterior probability (78.6 vs 73.8 at a threshold of ) (see Table S3).
