Nonparametric analysis of replicated microarray experiments

Statistical Modeling

Volumn 4, Issue 3, 2004, Pages 195-209

  Gannoun, Ali ^a   Saracco, Jérôme ^b   Urfer, Wolfgang ^c   Bonney, George E ^d  

^a UNIV MONTPELLIER   (France)

^b UNIVERSITÉ DE MONTPELLIER   (France)

^c TU DORTMUND UNIVERSITY   (Germany)

^d HOWARD UNIVERSITY COLLEGE OF MEDICINE   (United States)

Author keywords

Kernel estimator; microarray; mixture modelling; regression modelling; t test

Indexed keywords

EID: 84993820504     PISSN: 1471082X     EISSN: None     Source Type: Journal    
DOI: 10.1191/1471082X04st073oa     Document Type: Article

References (38)

1. Allison D.B., Gadbury G.L., Heo M.S., Fernandez J.R., Lee C-K, Prolla T.A. and Weindruch R. (2002) A mixture model approach for the analysis of microarray gene expression data. Computational and Data Analysis 39, 1-20.
2. Alon U., Barkai N., Notterman D.A., Gish K., Ybarra S., Mack D. and Levine A.J. (1999) Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proceedings of the National Academy of Sciences of the United States of America 96, 6745-6750.
3. Baldi P. and Long A.D. (2001) A Bayesian framework for the analysis of microarray expression data: Regularized t-Test and Statistical Inferences of Gene Changes. Bioinformatics 17, 509-519.
4. Bosq D. and Lecoutre J.P. (1987) Théorie de l'estimation fonctionnelle. Paris: Economica.
5. Brown P.O. and Botstein D. (1999) Exploring the New World of the genome with DNA microarrays. Nature Genetics 21, 33-37.
6. Chen Y., Dougherty E.R. and Bittner M. (1997) Ratio-based decisions and the quantitative analysis of cDNA microarray images. Biomedical Optics 2, 364-374.
7. Chilingaryan A., Gevorgyan N., Vardanyan A., Jones D. and Szabo A. (2002) Multivariate approach for selecting sets of differentially expressed genes. Mathematical Biosciences 176, 59-69.
8. Cline D.B.H. and Hart J.D. (1991) Kernel estimation of densities with discontinuities or discontinuous derivatives. Statistics 22, 69-84.
9. Dempster A.P., Laird N.M. and Rubin D.B. (1977) Maximum likelihood estimation from incomplete data, via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B 39, 1-38.
10. Deheuvels P. (1977) Estimation non paramétrique de la densité par histogrammes généralisés. Revue de Statistique Appliquée 25, 35-42.
11. Dudoit S., Yang Y.H., Speed T.P. and Callow M.J. (2002) Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments. Statistica Sinica 12, 111-139.
12. Efron B., Storey J. and Tibshirani R. (2001) Microarrays, empirical Bayes methods, and false discovery rates. Technical Report 213, University of California, Berkeley.
13. Efron B., Tibshirani R., Goss V. and Chu G. (2000) Microarrays and their use in a comparative experiment. Technical Report, Stanford University.
14. Friedman N., Linial M., Nachman I. and Pe'er D. (2000) Using Bayesian networks to analyze expression data. Journal of Computational Biology 7, 601-620.
15. 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.
16. Hall P. and Wehrly T.E. (1991) A geometrical method for removing edge effects from kernel-type nonparametric regression estimators. Journal of the American Statistical Association 86, 665-672.
17. Hedenfalk I., Duggan D., Chen Y., Radmacher M., Bittner M., Simon R., Meltzer P., Gusterson B., Esteller M., Raffeld M., Yakhini Z., Ben-Dor A., Dougherty E., Kononen J., Bubendorf L., Fehrle W., Pittaluga S., Gruvberger S., Loman N., Johannsson O., Olsson H., Wilfond B., Sauter G., Kallioniemi O.P., Borg, Å. and Jeffrey T. (2001) Gene expression profiles in hereditary breast cancer. New England Journal of Medicine 244, 539-548.
18. Hyndman R.J. and Yao Q. (1991) Nonparametric estimation and symetry tests for conditional density function. Journal of Nonparametric Statistics 14, 259-278.
19. Imoto S., Goto T. and Miyano S. (2002) Estimation of genetic networks and functional structures between genes by using Bayesian network and nonparametric regression. Proceedings of Pacific Symposium on Biocomputing 7, 175-186.
20. Kerr M.K., Martin M. and Churchill G.A. (2000) Analysis of variance for gene expression microarray data. Journal of Computational Biology 7, 819-837.
21. Kuruvilla F.G., Park P.J. and Schreiber S.L. (2002) Vector algebra in the analysis of genome-wide expression data. Genome Biology 3, 1-11.
22. Lander E.S. (1999) Array of hope. Nature Genetics 21, 3-4.
23. 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.
24. Li C. and Wong W.H. (2001) Model-based analysis of oligonucleotide arrays: expression index computation and outlier detection. Proceedings of the National Academy of Sciences of the United States of America 98, 31-36.
25. McLachlan G. and Peel D. (1999) The EMMIX algorithm for the fitting of normal and t-Components. Journal of Statistical Software, 4(2) (http://www.jstatsoft.org/).
26. Newton M.A., Kendziorski C.M., Richmond C.S., Blattner F.R. and Tsui K.W. (2001) On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data. Journal of Computational Biology 8, 37-52.
27. Newton M.A., Noueiry A., Sarkar D. and Ahlquist P. (2004) Detecting differential gene expression with a semiparametric hierarchical mixture method. Biostatistics 5, 155-176.
28. Pan W. (2002) A comparative review of statistical methods for discovering differentially expressed genes in replicated microarray experiments. Bioinformatics 12, 546-554.
29. 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, in press.
30. Press W.H., Teukolsky C.M., Vetterling W.T. and Flannery B.P. (1992) Numerical recipies in C, the art of scientific computing. 2nd edition. New York: Combridge.
31. Quackenbush J. (2001) Computational analysis of microarray data. Nature Reviews. Genetics 2, 418-427.
32. Schwarz G. (1978) Estimating the dimension of a model. Annals of Statistics 6, 461-464.
33. Schuster E.F. (1985) Incorporating support constraints into nonparametric estimation of densities. Communications in Statistics, Theory and Methods 14, 1123-1136.
34. Sebastiani P. and Ramoni M. (2002) Statistical challenges in functional genomics. Technical Report, Massachustts University.
35. Silverman B.W. (1986) Density estimation for statistics and data analysis. Monographs on Statistics and Applied Probability. London: Chapman & Hall.
36. Thomas J.G., Olson J.M., Tapscott S.J. and Zhao L.P. (2001) An efficient and robust statistical modeling approach to discover differentially expressed genes using genomic expression profiles. Genome Research 11, 1227-1236.
37. Tusher V.G., Tibshirani R. and Chu G. (2001) Significance analysis of microarrays applied to the ionizing radiation response. Proceedings of the National Academy of Sciences of the United States of America 98, 5116-5121.
38. Zhang L., Zhou W., Velculescu V.E., Kern S.E., Hruban R.H., Hamilton S.R., Vogelstein B. and Kinzler K.W. (1997) Gene expression profiles in normal and cancer cells. Science 276, 1268-1272.