Hybrid Algorithms for Multiple Change-Point Detection in Biological Sequences

  • Madawa Priyadarshana
  • Tatiana Polushina
  • Georgy Sofronov
Chapter
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 823)

Abstract

Array comparative genomic hybridization (aCGH) is one of the techniques that can be used to detect copy number variations in DNA sequences in high resolution. It has been identified that abrupt changes in the human genome play a vital role in the progression and development of many complex diseases. In this study we propose two distinct hybrid algorithms that combine efficient sequential change-point detection procedures (the Shiryaev-Roberts procedure and the cumulative sum control chart (CUSUM) procedure) with the Cross-Entropy method, which is an evolutionary stochastic optimization technique to estimate both the number of change-points and their corresponding locations in aCGH data. The proposed hybrid algorithms are applied to both artificially generated data and real aCGH experimental data to illustrate their usefulness. Our results show that the proposed methodologies are effective in detecting multiple change-points in biological sequences of continuous measurements.

Keywords

Cross-entropy method Change-point modelling aCGH data DNA sequences Copy number variation Sequential change-point analysis Shiryaev-Roberts procedure Cumulative sum procedure Combinatorial optimization Stochastic optimization 

Notes

Acknowledgements

W. J. R. M. Priyadarshana acknowledges the funding received towards his PhD from the International Macquarie University Research Excellence (iMQRES) scholarship. The authors acknowledge the anonymous referees for their useful comments.

References

  1. 1.
    D. Barry, J.A. Hartigan, A Bayesian analysis for change point problems. J. Am. Stat. Assoc. 88, 309–319 (1993)MATHMathSciNetGoogle Scholar
  2. 2.
    J.V. Braun, H.G. Müller, Statistical methods for DNA sequence segmentation. Stat. Sci. 13, 142–162 (1998)CrossRefMATHGoogle Scholar
  3. 3.
    N.P. Carter, Methods and strategies for analyzing copy number variation using DNA microarrays. Nat. Genet. 39, S16–S21 (2007)CrossRefGoogle Scholar
  4. 4.
    A, Costa, O.D. Jones, D. Kroese, Convergence properties of the cross-entropy method for discrete optimization. Oper. Res. Lett. 35, 573–580 (2007)Google Scholar
  5. 5.
    B. Efron, T. Hastie, I. Johnstone, R. Tibshirani. Least angle regression. Ann. Stat. 32, 407–451 (2004)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    C. Erdman, J.W. Emerson, bcp: an R package for performing a Bayesian analysis of change point problems. J. Stat. Softw. 23, 1–13 (2007)Google Scholar
  7. 7.
    C. Erdman, J.W. Emerson, A fast Bayesian change point analysis for the segmentation of microarray data. Bioinformatics 24(19), 2143–2148 (2008)CrossRefGoogle Scholar
  8. 8.
    G.E. Evans, G.Y. Sofronov, J.M. Keith, D.P. Kroese, Identifying change-points in biological sequences via the cross-entropy method. Ann. Oper. Res. 189, 155–165 (2011)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    L. Feuk, A.R. Carson, S.W. Scherer, Structural variation in the human genome. Nat. Rev. Genet. 7(2), 85–97 (2006)CrossRefGoogle Scholar
  10. 10.
    D.C. Hoaglin, F. Mosteller, J.W. Tukey, Understanding Robust and Exploratory Data Analysis (Wiley, New York, 1983)MATHGoogle Scholar
  11. 11.
    G. Hodgson, J.H. Hager, S. Volik, S. Hariono, M. Wernick, D. Moore, N. Nowak, D.G. Albertson, D. Pinkel, C. Collins, D. Hanahan, J.W. Gray, Genome scanning with array CGH delineates regional alterations in mouse islet carcinomas. Nat. Genet. 29, 459–464 (2001)CrossRefGoogle Scholar
  12. 12.
    S. Ivakhno, T. Royce, A.J. Cox, D.J. Evers, R.K. Cheetham, S. Tavare, CNAseg-a novel framework for identification of copy number changes in cancer from second-generation sequencing data. Bioinformatics. 26, 3051–3058 (2010)CrossRefGoogle Scholar
  13. 13.
    V.E. Johnson, Revised standards for statistical evidence. Proc. Natl. Acad. Sci. (2013). doi:10.1073/pnas.1313476110Google Scholar
  14. 14.
    A. Kallioniemi, O.P. Kallioniemi, D. Sudar, D. Rutovitz, J.W. Gray, F. Waldman, D. Pinkel, Comparative genomic hybridization for molecular cytogenetic analysis of solid tumors. Science 258, 818–821 (1992)CrossRefGoogle Scholar
  15. 15.
    J.M. Keith, Segmenting eukaryotic genomes with the generalized Gibbs sampler. J. Comput. Biol. 13, 1369–1383 (2006)CrossRefMathSciNetGoogle Scholar
  16. 16.
    R. Killick, I. Eckley, changepoint: an R package for changepoint analysis. R package version 1.1. (2013). http://CRAN.R-project.org/package=changepoint
  17. 17.
    R. Killick, P. Fearnhead, I. Eckley, Optimal detection of changepoints with a linear computational cost. J. Am. Stat. Assoc. 107, 590–598 (2012)CrossRefMathSciNetGoogle Scholar
  18. 18.
    S. Kullback, R.A. Leibler, On information and sufficiency. Ann. Math. Stat. 22, 79–86 (1951)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    W.R. Lai, M.D. Johnson, R. Kucherlapati, P.J. Park, Comparative analysis of algorithms for identifying amplifications and deletions in array CGH data. Bioinformatics 21, 3763–3770 (2005)CrossRefGoogle Scholar
  20. 20.
    R. Lucito, J. Healy, J. Alexander, A. Reiner, D. Esposito, M. Chi, L. Rodgers, A. Brady, J. Sebat, J. Troge, J.A. West, S. Rostan, K.C.Q. Nguyen, S. Powers, K.Q. Ye, A. Olshen, E. Venkatraman, L. Norton, M. Wigler, Representational oligonucleotide microarray analysis: a high-resolution method to detect genome copy number variation. Genome Res. 13, 2291–2305 (2003)CrossRefGoogle Scholar
  21. 21.
    V.M.R. Muggeo, cumSeg: change point detection in genomic sequences. R package version 1.1. (2012). http://CRAN.R-project.org/package=cumSeg
  22. 22.
    M.R.V. Muggeo, G. Adelfio, Efficient change point detection for genomic sequences of continuous measurements. Bioinformatics 27, 161–166 (2011)CrossRefGoogle Scholar
  23. 23.
    J. Oliver, P. Bernaola-Galvan, P. Carpena, R. Roman-Roldan, Isochore chromosome maps of eukaryotic genomes. Gene 276(1–2), 47–56 (2001)CrossRefGoogle Scholar
  24. 24.
    A.B. Olshen, E.S. Venkatraman, R. Lucito, M. Wigler, Circular binary segmentation for the analysis of array-based DNA copy number data. Biostatistics, 5, 557–572 (2004)CrossRefMATHGoogle Scholar
  25. 25.
    E.S. Page, Continuous inspection schemes. Biometrika 41, 100–115 (1954)CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    J.R. Pollack, C.M. Perou, A.A. Alizadeh, M.B. Eisen, A. Pergamenschikov, C.F. Williams, S.S. Jeffrey, D. Botstein, P.O. Brown, Genome-wide analysis of DNA copy-number changes using cDNA microarrays. Nat. Genet. 23(1), 41–46 (1999)CrossRefGoogle Scholar
  27. 27.
    J.R. Pollack, T. Sørlie, C.M. Perou, C.A. Rees, S.S. Jeffrey, P.E. Lonning, R. Tibshirani, D. Bo, D. Botstein, A.L. Børresen-Dale, P.O. Brown, Microarray analysis reveals a major direct role of DNA copy number alteration in the transcriptional program of human breast tumors. Proc. Natl. Acad. Sci. U.S.A. 99, 12963–12968 (2002)CrossRefGoogle Scholar
  28. 28.
    M. Pollak, A.G. Tartakovsky, Exact optimality of the Shiryaev-Roberts procedure for detecting changes in distributions, in Information Theory and its Applications, ISITA 2008 International Symposium, Auckland (2008), pp. 1–6Google Scholar
  29. 29.
    M. Pollak, A.G. Tartakovsky, Optimality properties of the Shiryaev-Roberts procedure. Statistica Sinica 19, 1729–1739 (2009)MATHMathSciNetGoogle Scholar
  30. 30.
    A. Polunchenko, G. Sokolov, W. Du, Quickest change-point detection: a bird’s eye view, in Joint Statistical Meeting (JSM), Montreal (2013)Google Scholar
  31. 31.
    T. Polushina, G. Sofronov, Change-point detection in biological sequences via genetic algorithm, in Proceedings IEEE Congress on Evolutionary Computation (CEC), New Orleans (2011), pp. 1966–1971Google Scholar
  32. 32.
    T.V. Polushina, G.Y. Sofronov, A hybrid genetic algorithm for change-point detection in binary biomolecular sequences, in Proceedings of the IASTED International Conference on Artificial Intelligence and Applications (AIA 2013), Innsbruck (2013), pp. 1–8Google Scholar
  33. 33.
    W.J.R.M. Priyadarshana, G. Sofronov, A modified cross entropy method for detecting multiple change points in DNA Count Data, in WCCI 2012 IEEE World Congress on Computational Intelligence (CEC), Brisbane (2012), pp. 1020–1027Google Scholar
  34. 34.
    W.J.R.M. Priyadarshana, G. Sofronov, GAMLSS and extended cross-entropy method to detect multiple change-points in DNA read count data, in Proceedings of the 28th International Workshop on Statistical Modelling, Palermo, vol. 1, ed. by V.M.R. Muggeo, V. Capursi, G. Boscaino, G. Lovison (2013), pp. 453–457Google Scholar
  35. 35.
    W.J.R.M. Priyadarshana, T. Polushina, G. Sofronov, A hybrid algorithm for multiple change-point detection in continuous measurements, in International Symposium on Computational Models for Life Sciences, Sydney, ed. by C. Sun, T. Bednarz, T.D. Pham, P. Vallotton, D. Wang. AIP Conference Proceedings (2013), pp. 108–117Google Scholar
  36. 36.
    R Core Team:R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing (2013), http://www.R-project.org/
  37. 37.
    S.W. Roberts, A comparison of some control chart procedures. Technometrics 8, 411–430 (1966)CrossRefMathSciNetGoogle Scholar
  38. 38.
    R. Rubinstein, D.P. Kroese, The Cross-Entropy Method: a Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning (Springer, New York, 2004)CrossRefGoogle Scholar
  39. 39.
    G. Schwarz, Estimating the dimension of a model. Ann. Stat. 6, 461–464 (1978)CrossRefMATHGoogle Scholar
  40. 40.
    J. Sebat, B. Lakshmi, J. Troge, J. Alexander, J. Young, P. Lundin, S. Maner, H. Massa, M. Walker, M. Chi, N. Navin, R. Lucito, J. Healy, J. Hicks, K. Ye, A. Reiner, T.C. Gilliam, B. Trask, N. Patterson, A. Zetterberg, M. Wigler. Large-scale copy number polymorphism in the human genome. Science 305, 525–528 (2004)CrossRefGoogle Scholar
  41. 41.
    A. Sen, M. Srivastava, On tests for detecting a change in mean. Ann. Stat. 3, 98–108 (1975)CrossRefMATHMathSciNetGoogle Scholar
  42. 42.
    A.N. Shiryaev, The problem of the most rapid detection of a disturbance in a stationary process. Soviet Mathmatics. Dokl. 2, 795–799 (1961)MATHGoogle Scholar
  43. 43.
    A.N. Shiryaev, On optimum methods in quickest detection problems. Theory Probab. Appl. 8, 22–46 (1963)CrossRefMATHGoogle Scholar
  44. 44.
    A.N. Shiryaev, Optimal Stopping Rules (Springer, New York, 1978)MATHGoogle Scholar
  45. 45.
    R.J. Simes, An improved Bonferroni procedure for multiple tests of significance. Biometrika 73, 751–754 (1986)CrossRefMATHMathSciNetGoogle Scholar
  46. 46.
    A.M. Snijders, N. Nowak, R. Segraves, S. Blackwood, N. Brown, J. Conroy, G. Hamilton, A.K. Hindle, B. Huey, K. Kimura, S. Law, K. Myamboo, J. Palmer, B. Ylstra, J.P. Yue, J.W. Gray, A.N. Jain, D. Pinkel, D.G. Albertson, Assembly of microarrays for genome-wide measurement of DNA copy number. Nat. Genet. 29, 263–264 (2001)CrossRefGoogle Scholar
  47. 47.
    G. Sofronov, Change-point modelling in biological sequences via the Bayesian adaptive independent sampler. Int. Proc. Comput. Sci. Inf. Technol. 5, 122–126 (2011)Google Scholar
  48. 48.
    G.Y. Sofronov, G.E. Evans, J.M. Keith, D.P. Kroese, Identifying change-points in biological sequences via sequential importance sampling. Environ. Model. Assess. 14, 577–584 (2009)CrossRefGoogle Scholar
  49. 49.
    G. Sofronov, T. Polushina, W.J.R.M. Priyadarshana, Sequential change-point detection via the cross-entropy method, in The 11th Symposium on Neural Network Applications in Electrical Engineering (NEUREL’12), Belgrade (2012), pp. 185–188Google Scholar
  50. 50.
    A. Subramanian, H. Kuehn, J. Gould, P. Tamayo, J.P. Mesirov, GSEA-P: a desktop application for Gene set enrichment analysis. Bioinformatics 23, 3251–3253 (2007)CrossRefGoogle Scholar
  51. 51.
    A. Theisen, Microarray-based comparative genomic hybridization (aCGH). Nat. Educ. 1(1), 45 (2008)Google Scholar
  52. 52.
    R. Tibshirani, P. Wang, Spatial smoothing and hot spot detection for CGH data using the fused lasso. Biostatistics 9, 18–29 (2008)CrossRefMATHGoogle Scholar
  53. 53.
    E.S. Venkatraman, A. Olshen, DNAcopy: DNA copy number data analysis. R package version 1.34.0 (2013)Google Scholar
  54. 54.
    H. Wang, B. Li, C. Leng, Shrinkage tuning parameter selection with a diverging number of parameters. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 71, 671–683 (2009)CrossRefMATHMathSciNetGoogle Scholar
  55. 55.
    C. Xie, M.T. Tammi, CNV-seq, a new method to detect copy number variation using high-throughput sequencing. BMC Bioinformatics 10, 80 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Madawa Priyadarshana
    • 1
  • Tatiana Polushina
    • 2
  • Georgy Sofronov
    • 1
  1. 1.Faculty of Science, Department of StatisticsMacquarie UniversitySydneyAustralia
  2. 2.Faculty of Medicine and Dentistry, Department of Clinical ScienceUniversity of BergenBergenNorway

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