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. 2019 Apr;29(2):983-1005.
doi: 10.5705/ss.202017.0189.

Large-Scale Simultaneous Testing of Cross-Covariance Matrices with Applications to PheWAS

Tianxi Cai  1 , T Tony Cai  2 , Katherine Liao  3 , Weidong Liu  4
Affiliations

Large-Scale Simultaneous Testing of Cross-Covariance Matrices with Applications to PheWAS

Tianxi Cai et al. Stat Sin. 2019 Apr.

Abstract

Motivated by applications in phenome-wide association studies (PheWAS), we consider in this paper simultaneous testing of columns of high-dimensional cross-covariance matrices and develop a multiple testing procedure with theoretical guarantees. It is shown that the proposed testing procedure maintains a desired false discovery rate (FDR) and false discovery proportion (FDP) under mild regularity conditions. We also provide results on the magnitudes of the signals that can be detected with high power. Simulation studies demonstrate that the proposed procedure can be substantially more powerful than existing FDR controlling procedures in the presence of correlation of unknown structure. The proposed multiple testing procedure is applied to a PheWAS of two auto-immune genetic markers using a rheumatoid arthritis patient cohort constructed from the electronic medical records of Partners Healthcare System.

Keywords: Covariance; PheWAS; false discovery rate; multiple responses; multiple testing.

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Figures

Figure 1:
Figure 1:
The frequency that t^ exists when n = 100, p = 1000 with normal error.
Figure 2:
Figure 2:
Empirical FDR of various procedures, including the proposed, BH, BY, Storey et al. (2004) (JS), Guo and Rao (2008) (GR), the Romano and Shaikh (2006b) step-up procedure controlling FDP at 50% with probability at least 1 - α (RSuFDP), the Romano and Shaikh (2006a) step-down procedure controlling FDP at 50% with probability at least 1−α (RSdFDP) as well as the Romano and Shaikh (2006a) step-down FDR controlling procedure (RSdFDR), under the very sparse setting with p1 = 10.
Figure 3:
Figure 3:
Empirical FDR of various procedures, including the proposed, BH, BY, Storey et al. (2004) (JS), Guo and Rao (2008) (GR), the Romano and Shaikh (2006b) step-up procedure controlling FDP at 50% with probability at least 1 - α (RSuFDP), the Romano and Shaikh (2006a) step-down procedure controlling FDP at 50% with probability at least 1− α (RSdFDP) as well as the Romano and Shaikh (2006a) step-down FDR controlling procedure (RSdFDR), under the moderately sparse setting with p1 = 30.
Figure 4:
Figure 4:
Empirical survival distribution of the FDP under different models with p1 = 30 or 10 when n = 100, p = 1000, α = 0.1 and the error is normal.
Figure 5:
Figure 5:
Comparing power of different procedures under different models with p1 = 30 or 10 when n = 100, p = 2000, α = 0.1 and the error is normal.
See this image and copyright information in PMC

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