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Liu Z, Lin X. A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies. J Am Stat Assoc. 2019;114(527):975-990doi: 10.1080/01621459.2018.1513363.
Liu, Z., & Lin, X. (2019). A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies. Journal of the American Statistical Association, 114(527), 975-990. https://doi.org/10.1080/01621459.2018.1513363
Liu, Zhonghua, and Lin, Xihong. "A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies." Journal of the American Statistical Association vol. 114,527 (2019): 975-990. doi: https://doi.org/10.1080/01621459.2018.1513363
Liu Z, Lin X. A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies. J Am Stat Assoc. 2019;114(527):975-990. doi: 10.1080/01621459.2018.1513363. Epub 2019 Feb 26. PMID: 31564761; PMCID: PMC6764517.
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J Am Stat Assoc. 2019;114(527):975-990. doi: 10.1080/01621459.2018.1513363. Epub 2019 Feb 26.

A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies.

Journal of the American Statistical Association

Zhonghua Liu, Xihong Lin

Affiliations

  1. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, China ([email protected]).
  2. Chair and Henry Pickering Walcott Professor of Biostatistics, Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA 02115 ([email protected]).

PMID: 31564761 PMCID: PMC6764517 DOI: 10.1080/01621459.2018.1513363

Abstract

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has been proposed to analyze multiple correlated phenotypes. It has been empirically observed that the first PC, which summarizes the largest amount of variance, can be less powerful than higher order PCs and other commonly used methods in detecting genetic association signals. In this paper, we investigate the properties of PCA-based multiple phenotype analysis from a geometric perspective by introducing a novel concept called principal angle. A particular PC is powerful if its principal angle is 0° and is powerless if its principal angle is 90°. Without prior knowledge about the true principal angle, each PC can be powerless. We propose linear, non-linear and data-adaptive omnibus tests by combining PCs. We demonstrate that the Wald test is a special quadratic PC-based test. We show that the omnibus PC test is robust and powerful in a wide range of scenarios. We study the properties of the proposed methods using power analysis and eigen-analysis. The subtle differences and close connections between these combined PC methods are illustrated graphically in terms of their rejection boundaries. Our proposed tests have convex acceptance regions and hence are admissible. The

Keywords: Dimension reduction; Eigen-analysis; Genome-wide Association Studies (GWAS); Omnibus test; Power analysis; Principal angle; Summary statistics

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