Stratified Enrichment of an Annotation
The stratified enrichment analysis assesses the significance of overlap of an annotation X while controlling for any overlap with a potentially colocalizing annotation Y (see Figure 1). We used a three-step approach: first, we fragmented each locus on the basis of the presence of Y while fixing the relative positions of the SNPs and annotation X. An X annotation site was split if it partially overlapped Y. Second, we concatenated these fragments, which yielded two distinct segments: (1) Y, which consisted of concatenated fragments of annotation Y, and (2) Y¯, which lacked annotation Y (Figure 1C). This preserved the relationships and relative positions among X, Y, and the SNPs in the locus in both segments. Third, to generate the stratified null distribution for SNP overlap with X, we randomly shifted X within the Y and Y¯ regions independently and quantified the proportion of loci that had at least one SNP that overlapped X in either region. To ensure that an annotation could not fall outside the segment boundaries, we circularized each of the Y and Y¯ segments. As in the unstratified test, we defined the p value of the enrichment as the proportion of iterations where the number of loci with SNPs overlapping X exceeded the number of loci overlapping X prior to shifting. We note that, just as any form of stratified statistical analysis, the spatial restrictions on shifting X in a stratified manner might reduce power.