Table of Contents
ISRN Bioinformatics
Volume 2012, Article ID 564715, 18 pages
http://dx.doi.org/10.5402/2012/564715
Research Article

Nonlinear Dependence in the Discovery of Differentially Expressed Genes

1Department of Electrical and Computer Engineering, Michigan State University, 2120 EB, East Lansing, MI 48824, USA
2Carcinogenesis Laboratory, Department of Molecular Biology and Biochemistry, Michigan State University, 341 FST, East Lansing, MI 48824, USA
3College of Computer Science and Information Engineering, Zhejiang Gongshang University, 18 Xuezheng Street, Zhejiang Province Hangzhou, 310018, China

Received 16 September 2011; Accepted 9 November 2011

Academic Editors: T. Can and S. Panni

Copyright © 2012 J. R. Deller et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. National Genome Research Institute, U.S. National Institutes of Health, http://www.genome.gov/.
  2. G. P. Page, S. O. Zakharkin, K. Kim, T. Mehta, L. Chen, and K. Zhang, “Microarray analysis,” Methods in Molecular Biology, vol. 404, pp. 409–430, 2007. View at Google Scholar · View at Scopus
  3. J. Wang, “Computational biology of genome expression and regulation—a review of microarray bioinformatics,” Journal of Environmental Pathology, Toxicology and Oncology, vol. 27, no. 3, pp. 157–179, 2008. View at Google Scholar · View at Scopus
  4. B. Efron, “Size, power and false discovery rates,” Annals of Statistics, vol. 35, no. 4, pp. 1351–1377, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. B. Efron, “Large-scale simultaneous hypothesis testing: the choice of a null hypothesis,” Journal of the American Statistical Association, vol. 99, no. 465, pp. 96–104, 2004. View at Google Scholar · View at Scopus
  6. M. Schena, D. Shalon, R. W. Davis, and P. O. Brown, “Quantitative monitoring of gene expression patterns with a complementary DNA microarray,” Science, vol. 270, no. 5235, pp. 467–470, 1995. View at Google Scholar · View at Scopus
  7. S. Datta and S. Datta, “Evaluation of clustering algorithms for gene expression data,” BMC Bioinformatics, vol. 7, no. 4, article S17, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. F. D. Gibbons and F. P. Roth, “Judging the quality of gene expression-based clustering methods using gene annotation,” Genome Research, vol. 12, no. 10, pp. 1574–1581, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Handl, J. Knowles, and D. B. Kell, “Computational cluster validation in post-genomic data analysis,” Bioinformatics, vol. 21, no. 15, pp. 3201–3212, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Sémon and L. Duret, “Evolutionary origin and maintenance of coexpressed gene clusters in mammals,” Molecular Biology and Evolution, vol. 23, no. 9, pp. 1715–1723, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. K. C. Li, “Genome-wide coexpression dynamics: theory and application,” Proceedings of the National Academy of Sciences of the United States of America, vol. 99, no. 26, pp. 16875–16880, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. Kluger, R. Basri, J. T. Chang, and M. Gerstein, “Spectral biclustering of microarray data: coclustering genes and conditions,” Genome Research, vol. 13, no. 4, pp. 703–716, 2003. View at Publisher · View at Google Scholar · View at Scopus
  13. C. A. Tsai, T. C. Lee, I. C. Ho, U. C. Yang, C. H. Chen, and J. J. Chen, “Multi-class clustering and prediction in the analysis of microarray data,” Mathematical Biosciences, vol. 193, no. 1, pp. 79–100, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. V. G. Tusher, R. Tibshirani, and G. Chu, “Significance analysis of microarrays applied to the ionizing radiation response,” Proceedings of the National Academy of Sciences of the United States of America, vol. 98, no. 9, pp. 5116–5121, 2001. View at Publisher · View at Google Scholar · View at Scopus
  15. Y. Choi and C. Kendziorski, “Statistical methods for gene set co-expression analysis,” Bioinformatics, vol. 25, no. 21, pp. 2780–2786, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Barry, A. Nobel, and F. Wright, “A statistical framework for testing functional categories in microarray data,” Annals of Applied Statistics, vol. 2, pp. 286–315, 2008. View at Google Scholar
  17. T. Peters, D. W. Bulger, T.-H. Loi, J. Y. H. Yang, and D. Ma, “Two-step cross-entropy feature selection for microarrays-power through complementarity,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 4, pp. 1148–1151, 2011. View at Publisher · View at Google Scholar
  18. F. Yang and K. Z. Mao, “Robust feature selection for microarray data based on multicriterion fusion,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 4, pp. 1080–1092, 2011. View at Publisher · View at Google Scholar
  19. G. Tiño, H. Zhao, and H. Yan, “Searching for coexpressed genes in three-color cDNA microarray data using a probabilistic model-based hough transform,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 4, pp. 1093–1107, 2011. View at Publisher · View at Google Scholar
  20. J. Ruan, A. K. Dean, and W. Zhang, “A general co-expression network-based approach to gene expression analysis: comparison and applications,” BMC Systems Biology, vol. 4, article 8, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Dettling, E. Gabrielson, and G. Parmigiani, “Searching for differentially expressed gene combinations,” Genome Biology, vol. 6, no. 10, article R88, 2005. View at Google Scholar · View at Scopus
  22. Y. Lai, B. Wu, L. Chen, and H. Zhao, “A statistical method for identifying differential gene-gene co-expression patterns,” Bioinformatics, vol. 20, no. 17, pp. 3146–3155, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. K. Ng, W. Wu, and L. Zhang, “Positive correlation between gene coexpression and positional clustering in the zebrafish genome,” BMC Genomics, vol. 10, article 42, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. I. Bernthaler, A. Mühlberger, R. Fechete, P. Perco, A. Lukas, and B. Mayer, “Interpreting microarray experiments via Co-expressed Gene Groups Analysis (CGGA),” in Proceedings of the 9th International Conference on Discovery Science, vol. 4265 of Lecture Notes in Computer Science, pp. 316–320, Springer, 2006.
  25. A. Reverter and E. K. F. Chan, “Combining partial correlation and an information theory approach to the reversed engineering of gene co-expression networks,” Bioinformatics, vol. 24, no. 21, pp. 2491–2497, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. A. B. Tchagang and A. H. Tewfik, “DNA microarray data analysis: a novel biclustering algorithm approach,” Eurasip Journal on Applied Signal Processing, vol. 2006, Article ID 59809, 12 pages, 2006. View at Publisher · View at Google Scholar · View at Scopus
  27. R. Martinez, N. Pasquier, C. Pasquier, and L. Lopez-Perez, “A dependency graph approach for the analysis of differential gene expression profiles,” Molecular BioSystems, vol. 5, no. 12, pp. 1720–1731, 2009. View at Publisher · View at Google Scholar
  28. C. A. Tsai and J. J. Chen, “Multivariate analysis of variance test for gene set analysis,” Bioinformatics, vol. 25, no. 7, pp. 897–903, 2009. View at Publisher · View at Google Scholar · View at Scopus
  29. W. Pan, “A comparative review of statistical methods for discovering differentially expressed genes in replicated microarray experiments,” Bioinformatics, vol. 18, no. 4, pp. 546–554, 2002. View at Google Scholar · View at Scopus
  30. A. B. Owen, “Variance of the number of false discoveries,” Journal of the Royal Statistical Society. Series B, vol. 67, no. 3, pp. 411–426, 2005. View at Publisher · View at Google Scholar · View at Scopus
  31. B. Efron, “Correlation and large-scale simultaneous significance testing,” Journal of the American Statistical Association, vol. 102, no. 477, pp. 93–103, 2007. View at Publisher · View at Google Scholar · View at Scopus
  32. Y. Pawitan, K. R. K. Murthy, S. Michiels, and A. Ploner, “Bias in the estimation of false discovery rate in microarray studies,” Bioinformatics, vol. 21, no. 20, pp. 3865–3872, 2005. View at Publisher · View at Google Scholar · View at Scopus
  33. J. T. Leek and J. D. Storey, “Capturing heterogeneity in gene expression studies by surrogate variable analysis,” PLoS Genetics, vol. 3, no. 9, article e161, 2007. View at Publisher · View at Google Scholar · View at Scopus
  34. S. A. Degrelle, C. Hennequet-Antier, H. Chiapello et al., “Amplification biases: possible differences among deviating gene expressions,” BMC Genomics, vol. 9, article 46, 2008. View at Publisher · View at Google Scholar · View at Scopus
  35. X. Qiu, L. Klebanov, and A. Yakovlev, “Correlation between gene expression levels and limitations of the empirical Bayes methodology for finding differentially expressed genes,” Statistical Applications in Genetics and Molecular Biology, vol. 4, no. 1, article 34, 2005. View at Google Scholar · View at Scopus
  36. X. Qiu and A. Yakovlev, “Some comments of instability of false discovery rate estimation,” Journal of Bioinformatics and Computational Biology, vol. 4, no. 5, pp. 1057–1068, 2006. View at Publisher · View at Google Scholar · View at Scopus
  37. J. D. Storey, J. Y. Dai, and J. T. Leek, “The optimal discovery procedure for large-scale significance testing, with applications to comparative microarray experiments,” Biostatistics, vol. 8, no. 2, pp. 414–432, 2007. View at Publisher · View at Google Scholar · View at Scopus
  38. R. Tibshirani and L. Wasserman, “Correlation-sharing for detection of differential gene expression,” preprint, http://arxiv.org/abs/math/0608061.
  39. R. Hu, X. Qiu, and G. Glazko, “A new gene selection procedure based on the covariance distance,” Bioinformatics, vol. 26, no. 3, pp. 348–354, 2010. View at Google Scholar · View at Scopus
  40. Q. Cui, B. Liu, T. Jiang, and S. Ma, “Characterizing the dynamic connectivity between genes by variable parameter regression and Kalman filtering based on temporal gene expression data,” Bioinformatics, vol. 21, no. 8, pp. 1538–1541, 2005. View at Publisher · View at Google Scholar · View at Scopus
  41. V. Martyanov and R. H. Gross, “Identifying functional relationships within sets of co-expressed genes by combining upstream regulatory motif analysis and gene expression information,” BMC Genomics, vol. 11, no. 2, article S8, 2010. View at Publisher · View at Google Scholar · View at Scopus
  42. R. Tewhey, V. Bansal, A. Torkamani, E. J. Topol, and N. J. Schork, “The importance of phase information for human genomics,” Nature Reviews Genetics, vol. 12, no. 3, pp. 215–223, 2011. View at Publisher · View at Google Scholar
  43. Z. Xiang, Z. S. Qin, and Y. He, “CRCView: a web server for analyzing and visualizing microarray gene expression data using model-based clustering,” Bioinformatics, vol. 23, no. 14, pp. 1843–1845, 2007. View at Publisher · View at Google Scholar · View at Scopus
  44. A. K. C. Wong, W. H. Au, and K. C. C. Chan, “Discovering high-order patterns of gene expression levels,” Journal of Computational Biology, vol. 15, no. 6, pp. 625–637, 2008. View at Publisher · View at Google Scholar · View at Scopus
  45. S. Bandyopadhyay and M. Bhattacharyya, “A biologically inspired measure for co-expression analysis,” IEEE Transactions Computational Biology and Bioinformatics, vol. 8, pp. 929–942, 2011. View at Google Scholar
  46. L. Dalton, V. Ballarin, and M. Brun, “Clustering algorithms: on learning, validation, performance, and applications to genomics,” Current Genomics, vol. 10, no. 6, pp. 430–445, 2009. View at Publisher · View at Google Scholar · View at Scopus
  47. N. Ancona, R. Maglietta, A. Piepoli et al., “On the statistical assessment of classifiers using DNA microarray data,” BMC Bioinformatics, vol. 7, article 387, 2006. View at Publisher · View at Google Scholar · View at Scopus
  48. T. Hu, H. Peng, and W. Sun, “Incorporating nonlinear relationships in microarray missing value imputation,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 3, pp. 723–731, 2011. View at Publisher · View at Google Scholar
  49. H. M. Hsueh, C. A. Tsai, and J. J. Chen, “Incorporating the number of true null hypotheses to improve power in multiple testing: application to gene microarray data,” Journal of Statistical Computation and Simulation, vol. 77, no. 9, pp. 757–767, 2007. View at Publisher · View at Google Scholar · View at Scopus
  50. M. Langaas, B. H. Lindqvist, and E. Ferkingstad, “Estimating the proportion of true null hypotheses, with application to DNA microarray data,” Journal of the Royal Statistical Society. Series B, vol. 67, no. 4, pp. 555–572, 2005. View at Publisher · View at Google Scholar · View at Scopus
  51. J. D. Storey, J. E. Taylor, and D. Siegmund, “Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach,” Journal of the Royal Statistical Society. Series B, vol. 66, no. 1, pp. 187–205, 2004. View at Publisher · View at Google Scholar · View at Scopus
  52. M. Waterman and D. Whiteman, “Estimation of probability densities by empirical density functions,” Journal of Mathematical Education in Science and Technology, vol. 9, no. 2, pp. 127–137, 1978. View at Google Scholar
  53. B. M. Bolstad, R. A. Irizarry, M. Åstrand, and T. P. Speed, “A comparison of normalization methods for high density oligonucleotide array data based on variance and bias,” Bioinformatics, vol. 19, no. 2, pp. 185–193, 2003. View at Publisher · View at Google Scholar · View at Scopus
  54. X. Qiu, A. I. Brooks, L. Klebanov, and A. Yakovlev, “The effects of normalization on the correlation structure of microarray data,” BMC Bioinformatics, vol. 6, article 120, 2005. View at Publisher · View at Google Scholar · View at Scopus
  55. H. Hotelling, “New light on the correlation coefficient and its transforms,” Journal of the Royal Statistical Society, vol. 15, no. 2, pp. 193–232, 1953. View at Google Scholar
  56. J. Wishart, “The generalised product moment distribution in samples from a normal multivariate population,” Biometrika, vol. 20, pp. 32–52, 1928. View at Google Scholar
  57. J. Barnard, R. McCulloch, and X. L. Meng, “Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage,” Statistica Sinica, vol. 10, no. 4, pp. 1281–1311, 2000. View at Google Scholar · View at Scopus
  58. I. Olkin, “Note on ‘The Jacobians of certain matrix transformations useful in multivariate analysis’,” Biometrika, vol. 40, no. 1-2, p. 43, 1953. View at Google Scholar
  59. J. Liechty, M. Liechty, and P. Muller, “Bayesian correlation estimation,” Biometrika, vol. 91, no. 1, pp. 1–14, 2004. View at Google Scholar
  60. I. Hedenfalk, D. Duggan, Y. Chen et al., “Gene-expression profiles in hereditary breast cancer,” New England Journal of Medicine, vol. 344, no. 8, pp. 539–548, 2001. View at Publisher · View at Google Scholar · View at Scopus
  61. C. A. Tsai, Y. J. Chen, and J. J. Chen, “Testing for differentially expressed genes with microarray data,” Nucleic Acids Research, vol. 31, no. 9, article e52, 2003. View at Google Scholar · View at Scopus
  62. A. B. Van 't Wout, G. K. Lehrman, S. A. Mikheeva et al., “Cellular gene expression upon human immunodeficiency virus type 1 infection of CD4+-T-cell lines,” Journal of Virology, vol. 77, no. 2, pp. 1392–1402, 2003. View at Publisher · View at Google Scholar · View at Scopus
  63. E. L. Lehmann and J. P. Romano, “Generalizations of the familywise error rate,” Annals of Statistics, vol. 33, no. 3, pp. 1138–1154, 2005. View at Publisher · View at Google Scholar · View at Scopus
  64. M. A. Newton, C. M. Kendziorski, C. S. Richmond, F. R. Blattner, and K. W. Tsui, “On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data,” Journal of Computational Biology, vol. 8, no. 1, pp. 37–52, 2001. View at Publisher · View at Google Scholar · View at Scopus
  65. G. Golub and C. Van Loan, Matrix Computations, Johns-Hopkins University Press, 3rd edition, 1996.
  66. H. Qi and D. Sun, “A quadratically convergent Newton method for computing the nearest correlation matrix,” SIAM Journal on Matrix Analysis and Applications, vol. 28, no. 2, pp. 360–385, 2006. View at Publisher · View at Google Scholar · View at Scopus
  67. E. Jaynes, Probability Theory: The Logic of Science, Cambridge University Press, Cambridge, UK, 2003.
  68. T. Cover and J. Thomas, Elements of Information Theory, Wiley, New York, NY, USA, 1991.
  69. I. Gelfand and S. Fomin, Calculus of Variations [English translation], translated by R. A. Silverman, Dover Press, New York, NY, USA, 2000.
  70. S. Haykin, Adaptive Filter Theory, Prentice-Hall, Upper Saddle River, NJ, USA, 4th edition, 2002.