Chunk #54 — Materials and Methods — Statistical inference — Hypothesis testing of annotation enrichment and pleiotropy

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GPA: a statistical approach to prioritizing GWAS results by integrating pleiotropy and annotation.

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Now we consider testing pleiotropy between two GWAS. When there is no pleiotropy, i.e., the signals from the two GWAS are independent of each other, testing pleiotropy can be formulated by testing the following hypothesis: (15)where and . The LRT statistic is constructed as follows: where represents the parameter estimates obtained under , and the superscript P indicates the Pleiotropy test. The test statistic () asymptotically follows distribution with under the null.