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Xia Y, Cai T, Cai TT. Multiple Testing of Submatrices of a Precision Matrix with Applications to Identification of Between Pathway Interactions. J Am Stat Assoc. 2017;113(521):328-339doi: 10.1080/01621459.2016.1251930.
Xia, Y., Cai, T., & Cai, T. T. (2018). Multiple Testing of Submatrices of a Precision Matrix with Applications to Identification of Between Pathway Interactions. Journal of the American Statistical Association, 113(521), 328-339. https://doi.org/10.1080/01621459.2016.1251930
Xia, Yin, et al. "Multiple Testing of Submatrices of a Precision Matrix with Applications to Identification of Between Pathway Interactions." Journal of the American Statistical Association vol. 113,521 (2018): 328-339. doi: https://doi.org/10.1080/01621459.2016.1251930
Xia Y, Cai T, Cai TT. Multiple Testing of Submatrices of a Precision Matrix with Applications to Identification of Between Pathway Interactions. J Am Stat Assoc. 2018;113(521):328-339. doi: 10.1080/01621459.2016.1251930. Epub 2017 Sep 26. PMID: 29881130; PMCID: PMC5988269.
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J Am Stat Assoc. 2018;113(521):328-339. doi: 10.1080/01621459.2016.1251930. Epub 2017 Sep 26.

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

Journal of the American Statistical Association

Yin Xia, Tianxi Cai, T Tony Cai

Affiliations

  1. Department of Statistics, Fudan University and Department of Statistics & Operations Research, University of North Carolina at Chapel Hill.
  2. Department of Biostatistics, Harvard School of Public Health, Harvard University.
  3. Department of Statistics, The Wharton School, University of Pennsylvania.

PMID: 29881130 PMCID: PMC5988269 DOI: 10.1080/01621459.2016.1251930

Abstract

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 pre-specified 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.

Keywords: Between pathway interactions; Gaussian graphical model; conditional dependence; covariance structure; false discovery proportion; false discovery rate; multiple testing; precision matrix; testing submatrices

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