Multiple Testing of Submatrices of a Precision Matrix With Applications to Identification of Between Pathway Interactions

Making accurate inference for gene regulatory networks, including inferring about pathway-by-pathway interactions, is an important and difficult task. Motivated by such genomic applications, we consider multiple testing for conditional dependence between subgroups of variables. Under a Gaussian grap...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2018-01, Vol.113 (521), p.328-339
Main Authors: Xia, Yin, Cai, Tianxi, Cai, T. Tony
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Between pathway interactions
Breast cancer
breast neoplasms
Computer simulation
Conditional dependence
Covariance structure
Dependence
Discovery
False discovery proportion
False discovery rate
Gaussian graphical model
Gene expression
gene regulatory networks
Genomics
model validation
Multiple testing
Power
Precision matrix
Regression analysis
Regularity
simulation models
statistical inference
Statistical methods
statistical models
Statistics
Subgroups
Testing submatrices
Theory and Methods
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Summary:Making accurate inference for gene regulatory networks, including inferring about pathway-by-pathway interactions, is an important and difficult task. Motivated by such genomic applications, we consider multiple testing for conditional dependence between subgroups of variables. Under a Gaussian graphical model framework, the problem is translated into simultaneous testing for a collection of submatrices of a high-dimensional precision matrix with each submatrix summarizing the dependence structure between two subgroups of variables. A novel multiple testing procedure is proposed and both theoretical and numerical properties of the procedure are investigated. Asymptotic null distribution of the test statistic for an individual hypothesis is established and the proposed multiple testing procedure is shown to asymptotically control the false discovery rate (FDR) and false discovery proportion (FDP) at the prespecified level under regularity conditions. Simulations show that the procedure works well in controlling the FDR and has good power in detecting the true interactions. The procedure is applied to a breast cancer gene expression study to identify between pathway interactions. Supplementary materials for this article are available online.
ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2016.1251930