A Geometric Perspective on the Powers of Principal Component Association Tests for Multiple Phenotypes in Genetic Association Studies

• Activity Number: 359
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Zhonghua Liu* and Xihong Lin
• Companies: Harvard University and Harvard School of Public Health
• Keywords: Eigen-analysis ; Multiple Phenotypes ; Principal components ; Principal angles ; Power ; Summary statistics

Abstract

Principal component analysis (PCA) has been commonly used for analyzing multiple phenotypes in genetic association studies. However, little work is done regarding when PCA is powerful and when it is not. In this paper, we propose several principal component association testing (PCAT) procedures using summary statistics with the advantage that raw data are not necessarily needed and information integration from continuous and binary phenoyptes become easier and coherent. In contrast to the univaraite case, we find that the angles (principal angles) between the effect size vector and the eigenvectors, the overall effect magnitudes as well as the eigenvalues of the correlation matrix all contribute to the statistical powers of PCAT methods. Utilizing eigen-analysis of the correlation matrix and asymptotic power analysis, we provide a novel geometric perspective on when PCA is powerful and when it is not to detect the genetic signals. The results from extensive simulation studies support our theoretical analysis. We apply PCAT to a large global lipids level genome-wide association study with about 2.6 millions markers and identify hundreds of novel genetic variants.