We can examine whether the proportional contribution of an annotation to a given genome-wide parameter in Stratified Genomic SEM is different than would be expected on the basis of the relative size of that annotation, so long as the parameter is scaled comparably across all annotations considered56. This is formalized by testing the null hypothesis, (θcθ)=(McM), where θc is the parameter estimate in annotation c, as estimated from a Genomic SEM model applied to S0,c; θ is the genome-wide parameter estimate, as estimated from a Genomic SEM model applied to the genome-wide S matrix derived via aggregating the conditional contributions of all annotations included in the multivariate S-LDSC model; Mc is the number of SNPs in annotation c; and M is the total number of SNPs used to computed the LD-scores. This formula can be rearranged to produce a ratio of ratios (the so-called enrichment ratio) that indexes the magnitude of enrichment: (θcθ)(McM), with a value of 1.0 corresponding to the null of no enrichment, values greater than 1.0 corresponding to enrichment (overrepresentation of signal in the annotation relative to its size), and values below 1.0 corresponding to depletion (underrepresentation of signal in the annotation relative to its size).
