Given an annotation file, we may be interested in whether there is statistical evidence for enrichment of GWAS signals in this annotation file. We propose to use the likelihood ratio test (LRT) to assess the statistical significance. To keep the notation simple, we drop the index of annotation files. Specifically, the significance of enrichment of an annotation for single-GWAS data analysis can be assessed by the following test: (13)The LRT statistic is: where collects the parameter estimates obtained under , and the superscript A indicates the Annotation enrichment test. Note that can be easily obtained by running the GPA algorithm without incorporating the annotation data. Under the null, the test statistic asymptotically follows the distribution with 1 degree of freedom [52]. We reject if , where is the -th quantile of distribution with .
