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A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies (303706)

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a 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 other methods in detecting genetic association signals. In this paper, we will 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 0o and is powerless if its principal angle is 90o. Without prior knowledge about the true principal angle, each PC can be powerless. Hence, we propose linear, nonlinear and adaptive omnibus tests by combining PCs. We show the Wald test is a special case of these tests. We discuss when each method should be used using power analysis and eigen-analysis. The subtle differences and close connections between those 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 calculated analytically. We conduct extensive simulation studies in both low and high dimensional settings with various signal vectors and correlation structures. We apply the proposed tests to analyze the Global lipids Genome-Wide Association Study (GWAS) data set to demonstrate the effectiveness of the proposed combined PC testing procedures.