Premium
A Penalized Likelihood Approach for Bivariate Conditional Normal Models for Dynamic Co‐expression Analysis
Author(s) -
Chen Jun,
Xie Jichun,
Li Hongzhe
Publication year - 2011
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2010.01413.x
Subject(s) - bivariate analysis , conditional independence , expression (computer science) , coordinate descent , likelihood ratio test , computer science , computational biology , microarray analysis techniques , gene , mathematics , gene expression , biology , data mining , algorithm , genetics , statistics , artificial intelligence , machine learning , programming language
Summary Gene co‐expressions have been widely used in the analysis of microarray gene expression data. However, the co‐expression patterns between two genes can be mediated by cellular states, as reflected by expression of other genes, single nucleotide polymorphisms, and activity of protein kinases. In this article, we introduce a bivariate conditional normal model for identifying the variables that can mediate the co‐expression patterns between two genes. Based on this model, we introduce a likelihood ratio (LR) test and a penalized likelihood procedure for identifying the mediators that affect gene co‐expression patterns. We propose an efficient computational algorithm based on iterative reweighted least squares and cyclic coordinate descent and have shown that when the tuning parameter in the penalized likelihood is appropriately selected, such a procedure has the oracle property in selecting the variables. We present simulation results to compare with existing methods and show that the LR‐based approach can perform similarly or better than the existing method of liquid association and the penalized likelihood procedure can be quite effective in selecting the mediators. We apply the proposed method to yeast gene expression data in order to identify the kinases or single nucleotide polymorphisms that mediate the co‐expression patterns between genes.