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The Deep Survival Forest and Elastic-Net-Cox Cascade Models as Extensions of the Deep Forest

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Proceedings of International Scientific Conference on Telecommunications, Computing and Control

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 220))

Abstract

Two new survival models, the deep survival forest and the Elastic-Net-Cox Cascade, are presented in the paper. They can be regarded as a combination of random survival forests and the Elastic-Net-Cox models with the deep forest (DF) proposed by Zhou and Feng. The main ideas to construct the models are to replace the original random forests incorporated into the DF with the corresponding survival analysis models. A stacking algorithm implemented in the deep survival forest and the Elastic-Net-Cox Cascade, which can be regarded as a link between the DF levels, uses quantiles of the random time-to-event and the mean time-to-event computed from the estimated survival functions at every level of the DF. Numerical examples with real data illustrate the proposed models.

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References

  1. Hosmer, D., Lemeshow, S., May, S.: Applied Survival Analysis: Regression Modeling of Time to Event Data. Wiley, New Jersey (2008)

    Book  Google Scholar 

  2. Cox, D.: Regression models and life-tables. J. R. Stat. Soc., Ser. B (Methodological) 34, 187–220 (1972)

    Google Scholar 

  3. Lee, E., Wang, J.: Statistical Methods for Survival Data Analysis. Wiley, New Jersey (2003)

    Book  Google Scholar 

  4. Kumar, D., Klefsjo, B.: Proportional hazards model: a review. Reliab. Eng. Syst. Saf. 44, 177–188 (1994)

    Article  Google Scholar 

  5. Scheike, T., Zhang, M.: Extensions and applications of the Cox-Aalen survival model. Biometrics 59, 1036–1045 (2003)

    Article  MathSciNet  Google Scholar 

  6. Wang, P., Li, Y., Reddy, C.: Machine learning for survival analysis: a survey. arXiv:1708.04649 (2017)

  7. Zhou, D., Mital, D., Srinivasan, S., Shibata, M.: PenalisedCox regression models for survival data. Int. J. Med. Eng. Inf. 9, 1–19 (2017)

    Google Scholar 

  8. Kim, J., Sohn, I., Jung, S.H., Kim, S., Park, C.: Analysis of survival data with group lasso. Commun. Stat.—Simul. Comput. 41, 1593–1605 (2012)

    Article  MathSciNet  Google Scholar 

  9. Tibshirani, R.: The lasso method for variable selection in the cox model. Stat. Med. 16, 385–395 (1997)

    Article  Google Scholar 

  10. Zhang, H., Lu, W.: Adaptive Lasso for Cox’s proportional hazards model. Biometrika 94, 691–703 (2007)

    Article  MathSciNet  Google Scholar 

  11. Witten, D., Tibshirani, R.: Survival analysis with high-dimensional covariates. Stat. Methods Med. Res. 19, 29–51 (2010)

    Article  MathSciNet  Google Scholar 

  12. Simon, N., Friedman, J., Hastie, T., Tibshirani, R.: Regularization paths for Cox’s proportional hazards model via coordinate descent. J. Stat. Softw. 39, 1–13 (2011)

    Article  Google Scholar 

  13. Biganzoli, E., Boracchi, P., Marubini, E.: A general framework for neural network models on censored survival data. Neural Netw. 15, 209–218 (2002)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Faraggi, D., Simon, R.: A neural network model for survival data. Stat. Med. 14, 73–82 (1995)

    Article  Google Scholar 

  16. Luck, M., Sylvain, T., Cardinal, H., Lodi, A., Bengio, Y.: Deep learning for patient-specific kidney graft survival analysis. arXiv:1705.10245 (2017)

  17. Nezhad, M., Sadati, N., Yang, K., Zhu, D.: A deep active survival analysis approach for precision treatment recommendations: application of prostate cancer. arXiv:1804.03280v1 (2018)

  18. Belle, V.V., Pelckmans, K., Suykens, J., Huffel, S.V.: Survival SVM: a practical scalable algorithm. In: ESANN, pp. 89–94 (2008)

    Google Scholar 

  19. Khan, F., Zubek, V.: Support vector regression for censored data (SVRc): A novel tool for survival analysis. In: 2008 Eighth IEEE International Conference on Data Mining, pp. 863–868. IEEE (2008)

    Google Scholar 

  20. Polsterl, S., Navab, N., Katouzian, A.: An efficient training algorithm for kernel survival support vector machines. arXiv:1611.07054v (2016)

  21. Kiaee, F., Sheikhzadeh, H., Mahabadi, S.: Relevance vector machine for survival analysis. IEEE Trans. Neural Netw. Learn. Syst. 27, 648–660 (2015)

    Article  MathSciNet  Google Scholar 

  22. Breiman, L.: Random Forests. Mach. Learn. 45, 5–32 (2001)

    Article  Google Scholar 

  23. Bou-Hamad, I., Larocque, D., Ben-Ameur, H.: Discrete-time survival trees and forests with time-varying covariates: application to bankruptcy data. Stat. Model. 11, 429–446 (2011)

    Google Scholar 

  24. Hu, C., Steingrimsson, J.: Personalized risk prediction in clinical oncology research: applications and practical issues using survival trees and random forests. J. Biopharm. Stat. 28, 333–349 (2018)

    Article  Google Scholar 

  25. Ishwaran, H., Blackstone, E., Pothier, C., Lauer, M.: Relative risk forests for exercise heart rate recovery as a predictor of mortality. J. Am. Stat. Assoc. 99, 591–600 (2004)

    Article  MathSciNet  Google Scholar 

  26. Wright, M., Dankowski, T., Ziegler, A.: Unbiased split variable selection for random survival forests using maximally selected rank statistics. Stat. Med. 36, 1272–1284 (2017)

    Article  MathSciNet  Google Scholar 

  27. Harrell, F., Califf, R., Pryor, D., Lee, K., Rosati, R.: Evaluating the yield of medical tests. J. Am. Med. Assoc. 247, 2543–2546 (1982)

    Article  Google Scholar 

  28. Zhou, Z.H., Feng, J.: Deep forest: towards an alternative to deep neural networks. arXiv:1702.08835v2 (2017)

  29. Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Ser. B (Methodological) 58, 267–288 (1996)

    Google Scholar 

  30. Ishwaran, H., Kogalur, U., Blackstone, E., Lauer, M.: Random survival forests. Ann. Appl. Stat. 2, 841–860 (2008)

    Article  MathSciNet  Google Scholar 

  31. Utkin, L., Konstantinov, A., Meldo, A., Ryabinin, M., Chukanov, V.: A deep forest improvement by using weighted schemes. In: Proceedings of the 24th Conference of Open Innovations Association FRUCT, Moscow, Russia, pp. 451–456. IEEE (2019).

    Google Scholar 

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Acknowledgements

The reported study was funded by RFBR, project number 18-29-03250.

Author information

Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Lev Utkin & Andrei Konstantinov

  2. Clinical Research Center of Specialized Types of Medical Care (Oncological), St. Petersburg, Russia

    Anna Meldo

  3. St. Petersburg State Forest Technical University, St. Petersburg, Russia

    Victoria Sokolova

  4. Durham University, Durham, UK

    Frank Coolen

Authors
  1. Lev Utkin
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  2. Andrei Konstantinov
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  3. Anna Meldo
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  4. Victoria Sokolova
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  5. Frank Coolen
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Corresponding author

Correspondence to Lev Utkin .

Editor information

Editors and Affiliations

  1. Higher School of Software Engineering, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Nikita Voinov

  2. Department of Computer Science and Biomedical Engineering, Graz University of Technology, Graz, Austria

    Tobias Schreck

  3. School of Maths, Computer Science and Engineering, City, University of London, London, UK

    Sanowar Khan

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Utkin, L., Konstantinov, A., Meldo, A., Sokolova, V., Coolen, F. (2021). The Deep Survival Forest and Elastic-Net-Cox Cascade Models as Extensions of the Deep Forest. In: Voinov, N., Schreck, T., Khan, S. (eds) Proceedings of International Scientific Conference on Telecommunications, Computing and Control. Smart Innovation, Systems and Technologies, vol 220. Springer, Singapore. https://doi.org/10.1007/978-981-33-6632-9_18

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  • DOI: https://doi.org/10.1007/978-981-33-6632-9_18

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-33-6631-2

  • Online ISBN: 978-981-33-6632-9

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