Skip to main content

Abstract

In this paper we show how the survival analysis problem can be formulated in terms of support vector regression, starting from a quantile regression perspective. We define an appropriate weighted loss function which takes into account possibly censored observations, and we prove bounds on the estimation error and on the quantile property. We deduce that censoring is a limiting factor in the accuracy of solutions, though the overall rate of convergence is O(n − 1/2). Finally we show some applications of the model to synthetic data, and to the German Breast Cancer Study Group 2 data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 72.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cox, D.R., Oakes, D.: Analysis of Survival Data. Chapman and Hall, London (1984)

    Google Scholar 

  2. Bishop, C.M.: Neural networks for pattern recognition. Oxford University Press, Oxford (1995)

    Google Scholar 

  3. Eleuteri, A., Tagliaferri, R., Milano, L., De Placido, S., De Laurentiis, M.: A novel neural network-based survival analysis model. Neural Networks 16, 855–864 (2003)

    Article  Google Scholar 

  4. Biganzoli, E., Boracchi, P., Mariani, L., Marubini, E.: Feed forward neural networks for the analysis of censored survival data: a partial logistic regression approach. Statistics in Medicine 17, 1169–1186 (1998)

    Article  Google Scholar 

  5. Ripley, B.D., Ripley, R.M.: Neural Networks as Statistical Methods in Survival Analysis. In: Dybowsky, R., Gant, V. (eds.) Artificial Neural Networks: Prospects for Medicine. Landes Biosciences Publishers (1998)

    Google Scholar 

  6. Watanabe, S.: Algebraic Analysis for Non-identifiable Learning Machines. Neural Computation 13, 899–933 (2001)

    Article  MATH  Google Scholar 

  7. Koenker, R.: Censored Quantile Regression Redux. Journal of Statistical Software 27 (2008)

    Google Scholar 

  8. Bottai, M., Zhang, J.: Laplace regression with censored data. Biometrical Journal 52, 487–503 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Vapnik, V.N.: Statistical Learning Theory. John Wiley & Sons, New York (1998)

    MATH  Google Scholar 

  10. Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  11. Van Belle, V., Pelckmans, K., Suykens, J.A.K., Van Huffel, S.: Survival SVM: a Practical Scalable Algorithm. In: Proceedings of the 16th European Symposium on Artifical Neural Networks, ESANN 2008 (2008)

    Google Scholar 

  12. Shivaswamy, P.K., Chu, W., Jansche, M.: A Support Vector Approach to Censored Targets. In: Proceedings of the 7th International Conference on Data Mining (2007)

    Google Scholar 

  13. Harrell Jr., F.E.: Regression Modelling Strategies. Springer, Heidelberg (2005)

    Google Scholar 

  14. Van Belle, V., Pelckmans, K., Suykens, J.A.K., Van Huffel, S.: Additive survival least-squares support vector machines. Statistics in Medicine 29, 296–308 (2010)

    MathSciNet  Google Scholar 

  15. Lama, N., Boracchi, P., Biganzoli, E.: Partial logistic relevance vector machines in survival analysis. Journal of Applied Statistics 38(11) (2011)

    Google Scholar 

  16. Williams, C.K.I., Rasmussen, C.E.: Gaussian Processes for Machine Learning. The MIT Press (2006)

    Google Scholar 

  17. Eleuteri, A., Taktak, A.F.G.: Survival time prediction by support vector regression. Proceedings of Royal Liverpool University Hospital Research Open Day (2007)

    Google Scholar 

  18. Eleuteri, A.: Support vector survival regression. In: 4th IET Conference on Advances in Medical, Signal and Information Processing (2008)

    Google Scholar 

  19. Koenker, R.: Quantile Regression. Cambridge University Press (2005)

    Google Scholar 

  20. Takeuchi, I., Le, Q.V., Sears, T.D., Smola, A.J.: Nonparametric Quantile Estimation. Journal of Machine Learning Research 7, 1231–1264 (2006)

    MathSciNet  MATH  Google Scholar 

  21. Carbonez, A., Györfi, G., van der Meulin, E.C.: Partition-estimate of a regression function under random censoring. Statist. Decis. 13, 21–27 (1995)

    MATH  Google Scholar 

  22. Bartlett, P.L., Mendelson, S.: Rademacher and Gaussian complexities: Risk bounds and structural results. Journal of Machine Learning Research 3, 463–482 (2002)

    MathSciNet  Google Scholar 

  23. Wang, J.L., Stute, W.: The strong law under random censorship. Annals of Statistics 21, 14–44 (1993)

    Article  MathSciNet  Google Scholar 

  24. Bartlett, P.L., Bousquet, O., Mendelson, S.: Localized Rademacher Complexities. In: Kivinen, J., Sloan, R.H. (eds.) COLT 2002. LNCS (LNAI), vol. 2375, pp. 44–58. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  25. Christmann, A., Steinwart, I.: Consistency of kernel-based quantile regression. Journal of Applied Stochastic Models in Business and Industry 24, 171–183 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  26. Chernozukov, V., Fernandez-Val, I., Galichon, A.: Improving point and interval estimators of monotone functions by rearrangement. Biometrika 96, 559–575 (2009)

    Article  MathSciNet  Google Scholar 

  27. Schumacher, M., Basert, G., Bojar, H., Huebner, K., Olschewski, M., Sauerbrei, W., Schmoor, C., Beyerle, C., Neumann, R.L.A., Rauschecker, H.F.: For the German Breast Cancer Study Group: Randomized 2x2 trial evaluating hormonal treatment and the duration of chemotherapy in node-positive breast cancer patients. Journal of Clinical Oncology 12, 2086–2093 (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Eleuteri, A., Taktak, A.F.G. (2012). Support Vector Machines for Survival Regression. In: Biganzoli, E., Vellido, A., Ambrogi, F., Tagliaferri, R. (eds) Computational Intelligence Methods for Bioinformatics and Biostatistics. CIBB 2011. Lecture Notes in Computer Science(), vol 7548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35686-5_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35686-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35685-8

  • Online ISBN: 978-3-642-35686-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics