A geometric perspective on the power of principal component association tests in multiple phenotype studies
Open accessAbstract
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 article, 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, nonlinear, 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 p-values for the proposed tests can be efficiently calculated analytically and the proposed tests have been implemented in a publicly available R package MPAT. We conduct simulation studies in both low- and high-dimensional settings with various signal vectors and correlation structures. We apply the proposed tests to the joint analysis of metabolic syndrome-related phenotypes with datasets collected from four international consortia to demonstrate the effectiveness of the proposed combined PC testing procedures. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
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These PC-based statistics do not apply to our settings with multiple covariates.
“In particular, SiMMR-PC resembles PC-based test statistics in the multiple phenotype setting with multiple outcome variables and a single covariate (Liu and Lin 2019); but these statistics do not apply to our settings with multiple covariates.”
From Similarity-based multimodal regression (2024) · cites this paper as Liu and Lin 2019
The Principal Component Association Tests section describes testing one SNP at a time across multiple phenotypes, which supports the distinction from a test of multiple predictors jointly. But it also explicitly says the Z-scores account for other covariates included in the single-phenotype analyses. Thus the paper does not support the unqualified claim that its statistics cannot apply when multiple covariates are present; no page number is available in our copy. (LLM, conf=0.84)
Experimental — accuracy not yet measuredSiMMR-PC resembles PC-based test statistics in the multiple phenotype setting with multiple outcome variables and a single covariate.
“In particular, SiMMR-PC resembles PC-based test statistics in the multiple phenotype setting with multiple outcome variables and a single covariate (Liu and Lin 2019); but these statistics do not apply to our settings with multiple covariates.”
From Similarity-based multimodal regression (2024) · cites this paper as Liu and Lin 2019
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Self-citationSimilarity-based multimodal regression
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- Authors
- Liu, Z., & Lin, X.
- Affiliations
- University of Hong Kong (HK)
- Harvard University (US)
- Corresponding author
- Liu, Zhonghua
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2019-02-26
- Volume
- 114
- Issue
- 527
- Pages
- 975-990
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- PMC
- PMC6764517
- OpenAlex
- W2963607751
- Cited by
- 36
- References
- 51
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 5 · 2023: 6 · 2022: 8 · 2021: 6 · 2020: 4 · 2019: 2 · 2017: 1
- FWCI
- 1.84
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Journal of the American Statistical Association (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Institutes of Health (CA R35-CA197449, P01-CA134294, U01-HG009088, U19-CA203654)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Mapping and Diversity in Plants and Animals
- Keywords
- principal component analysis, genetic association testing, statistical power, principal angles, omnibus test, Wald test, critical region, dimensionality reduction
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