To incorporate information from functional annotation data, we extend the basic model as follows. Suppose we have collected information from functional annotation sources in the annotation matrix: , where indicates whether the j-th SNP is annotated in the d-th functional annotation source. For example, when there are two annotation sources – eQTL data and DNase I hypersensitivity sites (DHS) data – then is an matrix. If the j-th SNP is an eQTL, then , otherwise ; if it is located in a DHS, then , otherwise . Now we model the relationship between and as (5)Clearly, can be interpreted as the proportion of null SNPs being annotated in the d-th annotation, and corresponds to the proportion of non-null SNPs being annotated in the d-th annotation. Therefore, implies that there exists enrichment for the d-th annotation. The statistical inference about enrichment of annotation data will be discussed in details in Section “Hypothesis testing of annotation enrichment and pleiotropy”.
