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

Cai, Tianxi; Cai, T. Tony; Liao, Katherine P.; Liu, Weidong

doi:10.5705/ss.202017.0189

Cited by 9 publications

(19 citation statements)

References 41 publications

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“…In some applications, the cross-covariance matrix, not the overall covariance matrix, is of particular interest. (Cai et al, 2015a) considered multiple testing of cross-covariances in the context of the phenome-wide association studies (PheWAS). Suppose X ∈ R p 1 and Y ∈ R p 2 are jointly distributed with covariance matrix Σ.…”

Section: Discussionmentioning

confidence: 99%

Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics

Cai¹,

Zhang²

2018

Ann. Statist.

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135

172

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Perturbation bounds for singular spaces, in particular Wedin's sin Θ theorem, are a fundamental tool in many fields including highdimensional statistics, machine learning, and applied mathematics. In this paper, we establish separate perturbation bounds, measured in both spectral and Frobenius sin Θ distances, for the left and right singular subspaces. Lower bounds, which show that the individual perturbation bounds are rate-optimal, are also given.The new perturbation bounds are applicable to a wide range of problems. In this paper, we consider in detail applications to low-rank matrix denoising and singular space estimation, high-dimensional clustering, and canonical correlation analysis (CCA). In particular, separate matching upper and lower bounds are obtained for estimating the left and right singular spaces. To the best of our knowledge, this is the first result that gives different optimal rates for the left and right singular spaces under the same perturbation.

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Section: Discussionmentioning

confidence: 99%

Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics

Cai¹,

Zhang²

2018

Ann. Statist.

Self Cite

135

172

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“…We then obtain the p-value of the CLC test statistic for each phenotypic category. In the third step, we propose an FDR control approach based on the method proposed by Cai et al [12]. FDR is widely used to claim significance for high-dimensional correlated data.…”

Section: Methodsmentioning

confidence: 99%

“…The key to empirically controlling the FDP is to find a good estimate of the numerator ∑ m ∈ H 0 I ( p m ≤ t ). Using the idea in Cai et al [12], we estimate the numerator by ∑ m ∈ H 0 I ( p m ≤ t ) ≈ m 0 G ( t ), where m 0 is the number of categories under the null hypothesis and we can use M to estimate m 0 due to the sparsity in the number of alternative hypotheses in many real data applications, and G ( t ) = P ( U (0,1) ≤ t ) = t .…”

Section: Methodsmentioning

confidence: 99%

“…In the second step, we apply the CLC method to combine test statistics within each phenotypic category based on the phenotypic clusters and obtain p-values from each phenotypic category. In the third step, we develop a false discovery rate (FDR) control approach based on a large-scale association testing procedure with theoretical guarantees for FDR control under flexible correlation structures [12]. Using extensive simulation studies, we evaluate the performance of the proposed method and compare the power of the proposed method with the powers of three commonly used methods in association studies using multiple phenotypes.…”

Section: Introductionmentioning

confidence: 99%

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HCLC-FC: a novel statistical method for phenome-wide association studies

Liang

Cao

Sha

et al. 2022

Preprint

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The emergence of genetic data coupled to longitudinal electronic medical records (EMRs) offers the possibility of phenome-wide association studies (PheWAS). In PheWAS, the whole phenome can be divided into numerous phenotypic categories according to the genetic architecture across phenotypes. Currently, statistical analyses for PheWAS are mainly univariate analyses, which test the association between one genetic variant and one phenotype at a time. In this article, we derived a novel and powerful multivariate method for PheWAS. The proposed method involves three steps. In the first step, we apply the bottom-up hierarchical clustering method to partition a large number of phenotypes into disjoint clusters within each phenotypic category. In the second step, the clustering linear combination method is used to combine test statistics within each category based on the phenotypic clusters and obtain p-values from each phenotypic category. In the third step, we propose a new false discovery rate (FDR) control approach. We perform extensive simulation studies to compare the performance of our method with that of other existing methods. The results show that our proposed method controls FDR very well and outperforms other methods we compared with. We also apply the proposed approach to a set of EMR-based phenotypes across more than 300,000 samples from UK Biobank. We find that the proposed approach not only can well-control FDR at a nominal level but also successfully identify 1,244 significant SNPs that are reported to be associated with some phenotypes in the GWAS catalog. Our open-access tools and instructions on how to implement HCLC-FC are available at https://github.com/XiaoyuLiang/HCLCFC .

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“…The standard FDR controlling method that accounts for the correlation tends to be overly conservative(17, 18). Thus, to account for the high degree of correlation without requiring strong assumptions on the correlation structure, we applied a modified Benjamini-Hochberg procedure method that efficiently performs simultaneous testing of associations between a large number of PheWAS codes with multiple autoantibodies (19). …”

Section: Methodsmentioning

confidence: 99%

Phenome‐Wide Association Study of Autoantibodies to Citrullinated and Noncitrullinated Epitopes in Rheumatoid Arthritis

Liao

Hejblum

Kuo

et al. 2017

Arthritis & Rheumatology

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ObjectivePatients with rheumatoid arthritis (RA) develop autoantibodies against a spectrum of antigens, but the clinical significance of these autoantibodies is unclear. Using a phenome‐wide association study (PheWAS) approach, we examined the association between autoantibodies and clinical subphenotypes of RA.MethodsThis study was conducted in a cohort of RA patients identified from the electronic medical records (EMRs) of 2 tertiary care centers. Using a published multiplex bead assay, we measured 36 autoantibodies targeting epitopes implicated in RA. We extracted all International Classification of Diseases, Ninth Revision (ICD‐9) codes for each subject and grouped them into disease categories (PheWAS codes), using a published method. We tested for the association of each autoantibody (grouped by the targeted protein) with PheWAS codes. To determine significant associations (at a false discovery rate [FDR] of ≤0.1), we reviewed the medical records of 50 patients with each PheWAS code to determine positive predictive values (PPVs).ResultsWe studied 1,006 RA patients; the mean ± SD age of the patients was 61.0 ± 12.9 years, and 79.0% were female. A total of 3,568 unique ICD‐9 codes were grouped into 625 PheWAS codes; the 206 PheWAS codes with a prevalence of ≥3% were studied. Using the PheWAS method, we identified 24 significant associations of autoantibodies to epitopes at an FDR of ≤0.1. The associations that were strongest and had the highest PPV for the PheWAS code were autoantibodies against fibronectin and obesity (P = 6.1 × 10−4, PPV 100%), and that between fibrinogen and pneumonopathy (P = 2.7 × 10−4, PPV 96%). Pneumonopathy codes included diagnoses for cryptogenic organizing pneumonia and obliterative bronchiolitis.ConclusionWe demonstrated application of a bioinformatics method, the PheWAS, to screen for the clinical significance of RA‐related autoantibodies. Using the PheWAS approach, we identified potentially significant links between variations in the levels of autoantibodies and comorbidities of interest in RA.

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

Cited by 9 publications

References 41 publications

Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics

Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics

HCLC-FC: a novel statistical method for phenome-wide association studies

Phenome‐Wide Association Study of Autoantibodies to Citrullinated and Noncitrullinated Epitopes in Rheumatoid Arthritis

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