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Bayesian hierarchical graph-structured model for pathway analysis using gene expression data

  • Hui Zhou and Tian Zheng EMAIL logo
Published/Copyright: May 15, 2013
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Statistical Applications in Genetics and Molecular Biology
From the journal Statistical Applications in Genetics and Molecular Biology Volume 12 Issue 3

Abstract

In genomic analysis, there is growing interest in network structures that represent biochemistry interactions. Graph structured or constrained inference takes advantage of a known relational structure among variables to introduce smoothness and reduce complexity in modeling, especially for high-dimensional genomic data. There has been a lot of interest in its application in model regularization and selection. However, prior knowledge on the graphical structure among the variables can be limited and partial. Empirical data may suggest variations and modifications to such a graph, which could lead to new and interesting biological findings. In this paper, we propose a Bayesian random graph-constrained model, rGrace, an extension from the Grace model, to combine a priori network information with empirical evidence, for applications such as pathway analysis. Using both simulations and real data examples, we show that the new method, while leading to improved predictive performance, can identify discrepancy between data and a prior known graph structure and suggest modifications and updates.

Keywords: gene expression; network analysis; Bayesian anslysis
Corresponding author: Tian Zheng, Department of Statistics, Columbia University, New York, NY 10027, USA

Appendix A Derivation of Sampling Scheme for β|σ2

According to Andrews and Mallows (1947), for a>0, a scale mixture of normal distributions representation of the Laplace distribution is

Let and Z=||βj||2. Then

or

Therefore,

Hence

where Ds is a block diagonal matrix with J blocks in the diagonal, and the j th block Dsj is Note that, assuming a block structure for

where each Oj is an orthogonal matrix and is a diagonal matrix, that is With the block diagonal structure assumption of (2) can be written as:

As a result, we can treat β|σ2 alternatively as:

This research is, in parts, supported by NSF grants DMS-0714669 and SES-1023176, NIH grant R01 GM070789, and a 2010 Google research award. We would like to thank two anonymous reviewers for their constructive comments.

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Published Online: 2013-05-15
Published in Print: 2013-06-01

©2013 by Walter de Gruyter Berlin Boston

Articles in the same Issue

  1. Masthead
  2. Masthead
  3. Review
  4. Genetic model selection in genome-wide association studies: robust methods and the use of meta-analysis
  5. Research Articles
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https://doi.org/10.1515/sagmb-2013-0011
Keywords for this article
gene expression; network analysis; Bayesian anslysis

Articles in the same Issue

  1. Masthead
  2. Masthead
  3. Review
  4. Genetic model selection in genome-wide association studies: robust methods and the use of meta-analysis
  5. Research Articles
  6. Hierarchical Bayesian mixture modelling for antigen-specific T-cell subtyping in combinatorially encoded flow cytometry studies
  7. An extension of the Wilcoxon-Mann-Whitney test for analyzing RT-qPCR data
  8. Block-diagonal discriminant analysis and its bias-corrected rules
  9. Statistical issues associated with modeling of synonymous mutation data
  10. Sensitivity to prior specification in Bayesian genome-based prediction models
  11. Bayesian hierarchical graph-structured model for pathway analysis using gene expression data
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