Cauchy Combination Test: a Powerful Test with Analytic P-Value Calculation Under Arbitrary Dependency Structures

• Activity Number: 40 - Recent Advances in Statistical Methods for Genome-Wide Association Studies
• Type: Contributed
• Date/Time: Sunday, July 29, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Genomics and Genetics
• Author(s): Yaowu Liu* and Jun Xie and Xihong Lin
• Companies: Harvard School of Public Health and Purdue University and Harvard University
• Keywords: Cauchy distribution; GWAS; Sparse alternative; Hypothesis testing

Abstract

Combining individual p-values to aggregate multiple small effects has a long-standing interest in statistics, dating back to the classic Fisher's combination test. In modern large-scale data analysis, correlation and sparsity are common features, and efficient computation is a necessary requirement for dealing with massive data. To overcome these challenges, we propose a new test that takes advantage of the Cauchy distribution. We prove a non-asymptotic result that the tail of the null distribution of our proposed test statistic can be well approximated by a Cauchy distribution under arbitrary dependency structures. Based on this theoretical result, the p-value calculation of our proposed test is not only accurate, but also as simple as the classic z-test or t-test, making our test well suited for analyzing massive data. We further show that the power of the proposed test is asymptotically optimal in a strong sparsity setting.The proposed test has also been applied to a genome-wide association study of Crohn's disease and compared with several existing tests.