A Kernel Method Used for the Analysis of Replicated Micro-array Experiments
Microarrays are part of a new class of biotechnologies which allow the monitoring of expression levels of thousands of genes simultaneously. In microarray data analysis, the comparison of gene expression profiles with respect to different conditions and the selection of biologically interesting genes are crucial tasks. Multivariate statistical methods have been applied to analyze these large data sets. To identify genes with altered expression under two experimental conditions, we describe in this chapter a new nonparametric statistical approach. Specifically, we propose estimating the distributions of a t-type statistic and its null statistic, using kernel methods. A comparison of these two distributions by means of a likelihood ratio test can identify genes with significantly changed expressions. A method for the calculation of the cut-off point and the acceptance region is also derived. This methodology is applied to a leukemia data set containing expression levels of 7129 genes. The corresponding results are compared to the traditional t-test and the normal mixture model.
KeywordsMicroarray Experiment Kernel Method Kernel Estimator Normal Mixture Null Statistic
Unable to display preview. Download preview PDF.
- Bosq, D. and Lecoutre, J. P. (1987). Théorie de l’estimation fonctionnelle. Economica: Paris.Google Scholar
- Efron, B., Tibshirani, R., Goss, V. and Chu, G. (2000). Microarrays and their use in a comparative experiment. Technical report: Stanford University.Google Scholar
- Efron, B., Storey, J. and Tibshirani, R. (2001). Microarrays, empirical Bayes methods, and false discovery rates. Technical report:Univ. California, Berkeley.Google Scholar
- Golub, T. R., Slonim, D. K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J. P., Coller, H., Loh, M. L., Downing, J. R., Caligiuri, M. A., Bloomfield, C. D., and Lander, E. S. (1999). Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science, 286, 531–537.CrossRefGoogle Scholar
- Hall, P. and Yao, Q. (1991). Nonparametric estimation and symetry tests for conditional density function. Journal of Nonparametric Statistics, 14, 259–278.Google Scholar
- Lee, M. L. T., Kuo, F. C., Whitmore, G. A. and Sklar, J. (2000). Importance of microarray gene expression studies: Statistical methods and evidence from repetitive cDNA hybridizations. Proceedings of the National Academy of Sciences of the United States of America, 97, 9834–9839.zbMATHCrossRefGoogle Scholar
- McLachlan, G. and Peel, D. (1999). The EMMIX Algorithm for the Fitting of Normal and t-Components. Journal of Statistical Software, 4 (http://www.jstatsoft.org/).Google Scholar
- Pan, W., Lin, J. and Le, C. T. (2004). A mixture model approach to detecting differentially expressed genes with microarray data. Functional and Integrative Genomics, (To appear).Google Scholar
- Silverman, B. W. (1986). Density estimation for statistics and data analysis. Monographs on Statistics and Applied Probability. Chapman & Hall, London.Google Scholar