Using mixture models to detect differentially expressed genes
G. J. McLachlan A B C D , R. W. Bean B , L. Ben-Tovim Jones B and J. X. Zhu BA Department of Mathematics, University of Queensland, Qld 4072, Australia.
B ARC Centre in Bioinformatics, Institute for Molecular Bioscience, University of Queensland, Qld 4072, Australia.
C ARC Special Research Centre for Functional and Applied Genomics, University of Queensland, Qld 4072, Australia.
D Corresponding author. Email: gjm@maths.uq.edu.au
Australian Journal of Experimental Agriculture 45(8) 859-866 https://doi.org/10.1071/EA05051
Submitted: 14 February 2005 Accepted: 6 May 2005 Published: 26 August 2005
Abstract
An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local false discovery rate is provided for each gene, and it can be implemented so that the implied global false discovery rate is bounded as with the Benjamini-Hochberg methodology based on tail areas. The latter procedure is too conservative, unless it is modified according to the prior probability that a gene is not differentially expressed. An attractive feature of the mixture model approach is that it provides a framework for the estimation of this probability and its subsequent use in forming a decision rule. The rule can also be formed to take the false negative rate into account.
Additional keywords: multiple hypothesis testing, false discovery rate, Bayes formula, Bayes rule.
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