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 FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.
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Allison, D.B., Gadbury, G.L., Heo, M., Fernandez, J.R., Lee, C.-K., Prolla, T.A., Weindruch, R.: A mixture model approach for the analysis of microarray gene expression data. Computational Statistics and Data Analysis 39, 1–20 (2002)
Benjamini, Y., Hochberg, Y.: Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journalof the RoyalStatistical Society B 57, 289–300 (1995)
Broet, P., Richardson, S., Radvanyi, F.: Bayesian hierarchical model for identifying changes in gene expression from microarray experiments. Journal of Computational Biology 9, 671–683 (2002)
Broet, P., Lewin, A., Richardson, S., Dalmasso, C., Magdelenat, H.: A mixture model-based strategy for selecting sets of genes in multiclass response microar-ray experiments. Bioinformatics 20, 2562–2571 (2004)
Efron, B., Tibshirani, R., Storey, J.D., Tusher, V.: Empirical Bayes analysis of a microarray experiment. Journal of the American Statistical Association 96, 1151–1160 (2001)
Efron, B., Tibshirani, R.: Empirical Bayes methods and false discovery rates for microarrays. Genetic Epidemiology 23, 70–86 (2002)
Genovese, C.R., Wasserman, L.: Operating Characteristics and Extensions of the False Discovery Rate Procedure. Journal of the Royal Statistical Society B 64, 499–517 (2002)
Hedenfalk, I., Duggan, D., Chen, Y.D., Radmacher, M., Bittner, M., Simon, R., Meltzer, P., Gusterson, B., Esteller, M., Kallioniemi, O.P., et al.: Gene-expression profiles in hereditary breast cancer. The New England Journal of Medicine 344, 539–548 (2001)
Lee, M.-L.T., Kuo, F.C., Whitmore, G.A., Sklar, J.: Importance of replication in microarray gene expression studies: statistical methods and evidence from repetitive cDNA hybridizations. Proceedings of the National Academy of Sciences USA 97, 9834–9838 (2000)
McLachlan, G.J., Do, K.A., Ambroise, C.: Analyzing Microarray Gene Expression Data. Wiley, New York (2004)
Pan, W.: A comparative review of statistical methods for discovering differentially expressed genes in replicated microarray experiments. Bioinformatics 18, 546–554 (2002)
Pan, W., Lin, J., Le, C.T.: A mixture model approach to detecting diferen-tially expressed genes with microarray data. Functional and Integrative Genomics 3, 117–124 (2003)
Storey, J.D., Tibshirani, R.: Statistical significance for genome-wide studies. Proceedings of the National Academy of Sciences USA 100, 9440–9445 (2003)
Storey, J.: The positive false discovery rate: a Bayesian interpretation and the q-value. Annals of Statistics 31, 2013–2035 (2004)
Tusher, V.G., Tibshirani, R., Chu, G.: Significance analysis of microarrays applied to the ionizing radiation response. Proceedings of the National Academy of Sciences USA 98, 5116–5121 (2001)
Wit, E., McClure, J.: Statistics for Microarrays: Design, Analysis and Inference. Wiley, Chichester (2004)
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Jones, L.BT., Bean, R., McLachlan, G., Zhu, J. (2005). Application of Mixture Models to Detect Differentially Expressed Genes. In: Gallagher, M., Hogan, J.P., Maire, F. (eds) Intelligent Data Engineering and Automated Learning - IDEAL 2005. IDEAL 2005. Lecture Notes in Computer Science, vol 3578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11508069_55
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DOI: https://doi.org/10.1007/11508069_55
Publisher Name: Springer, Berlin, Heidelberg
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