The eigen higher criticism and eigen Berk–Jones tests for multiple trait association studies based on GWAS summary statistics

Abstract In this article, we propose the eigen higher criticism and the eigen Berk–Jones testing procedures to test the association between a single genetic variant and multiple correlated traits based on summary statistics from single‐trait genome‐wide association studies. Since the association pattern between each genetic variant and multiple traits varies across the whole genome, we further develop an omnibus (OMNI) test using the aggregated Cauchy association test to achieve more robust performance. The p values of our proposed tests can be computed analytically, thus, our methods are appealing in large‐scale multiple phenotype association studies. Through extensive simulation studies, we found that all of our proposed tests can maintain the correct type I error rates and our proposed tests have greater power in certain settings. In addition, the OMNI test can always provide robust power performance across a wide range of scenarios. We apply the proposed tests to the Global Lipids Genetics Consortium summary statistics data set and identify additional genetic variants that were missed by the original single‐trait analyses. We also develop an R package EBMMT publicly available at https://github.com/Vivian-Liu-Wei64/EBMMT .