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Interpretable Survival Gradient Boosting Models with Bagged Trees Base Learners

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New Frontiers in Mining Complex Patterns (NFMCP 2019)

Abstract

In this paper we present a novel survival analysis modeling approach based on gradient boosting using bagged trees as base learners. The resulting models consist of additive components of single variable models and their pairwise interactions, which makes them visually interpretable. We show that our method produces competitive results often having the predictive power higher than full-complexity models. This is achieved while maintaining full interpretability of the model, which makes our method useful in medical applications.

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References

  1. Cox, D.R.: Regression models and life-tables. J. Roy. Stat. Soc. Ser. B 34, 187–202 (1972). https://doi.org/10.1111/j.2517-6161.1972.tb00899.x

    Article  MathSciNet  MATH  Google Scholar 

  2. Ishwaran, H., Kogalur, U.B., Blackstone, E.H., Lauer, M.S.: Random survival forests. Ann. Appl. Stat. 2, 841–860 (2008). https://doi.org/10.1214/08-AOAS169

    Article  MathSciNet  MATH  Google Scholar 

  3. Ridgeway, G.: The state of boosting. Comput. Sci. Stat. 31, 172–181 (1999)

    Google Scholar 

  4. Katzman, J., Shaham, U., Bates, J., Cloninger, A., Jiang, T., Kluger, Y.: DeepSurv: personalized treatment recommender system using a cox proportional hazards deep neural network (2016). https://doi.org/10.1186/s12874-018-0482-1

  5. Klein, J.P., Moeschberger, M.L.: Survival Analysis: Techniques for Censored and Truncated Data. Springer, New York (1997). https://doi.org/10.1007/978-1-4757-2728-9

    Book  MATH  Google Scholar 

  6. Rajkomar, A., Dean, J., Kohane, I.: Machine learning in medicine. N. Engl. J. Med. 380, 1347–1358 (2019). https://doi.org/10.1056/NEJMra1814259

    Article  Google Scholar 

  7. Vock, D.M., Wolfson, J., Bandyopadhyay, S., Adomavicius, G., Johnson, P.E., Vazquez-Benitez, G., et al.: Adapting machine learning techniques to censored time-to-event health record data: a general-purpose approach using inverse probability of censoring weighting. J. Biomed. Inform. 61, 119–131 (2016). https://doi.org/10.1016/j.jbi.2016.03.009

    Article  Google Scholar 

  8. Hothorn, T., Bühlmann, P., Dudoit, S., Molinaro, A., Van Der Laan, M.J.: Survival ensembles. Biostatistics 7, 355–373 (2006). https://doi.org/10.1093/biostatistics/kxj011

  9. LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. Nature 521, 436–444 (2015). https://doi.org/10.1038/nature14539

    Article  Google Scholar 

  10. Chen, T., Guestrin, C.: XGBoost: A Scalable Tree Boosting System (2016). https://doi.org/10.1145/2939672.2939785

  11. Friedman, J.H.: Greedy function approximation: a gradient boosting machine. Ann. Stat. 29, 1189–1232 (2001)

    Article  MathSciNet  Google Scholar 

  12. Hastie, T.J., Tibshirani, R.J.: Generalized Additive Models, vol. 43. CRC Press, Boca Raton (1990)

    MATH  Google Scholar 

  13. Wood, S.: Generalized Additive Models: An Introduction with R. CRC Press, Boca Raton (2006)

    Book  Google Scholar 

  14. Lou, Y., Caruana, R., Gehrke, J., Hooker, G.: Accurate intelligible models with pairwise interactions. In: Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining; Part F1288, pp. 623–631 (2013). https://doi.org/10.1145/2487575.2487579

  15. Buehlmann, P., Hothorn, T.: Boosting algorithms: regularization, prediction and model fitting (with discussion). Stat. Sci. 22, 477–505 (2007)

    Article  Google Scholar 

  16. Lou, Y., Caruana, R., Gehrke, J.: Intelligible models for classification and regression. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD 2012, p. 150. ACM Press, New York (2012). https://doi.org/10.1145/2339530.2339556

  17. Chen, Y., Jia, Z., Mercola, D., Xie, X.: A gradient boosting algorithm for survival analysis via direct optimization of concordance index. Comput. Math. 2013, 8 (2013)

    MATH  Google Scholar 

  18. Huster, W.J., Brookmeyer, R., Self, S.G.: Modelling paired survival data with covariates. Biometrics 45, 145–156 (1989)

    Article  MathSciNet  Google Scholar 

  19. Blair, A.L., Hadden, D.R., Weaver, J.A., Archer, D.B., Johnston, P.B., Maguire, C.J.: The 5-year prognosis for vision in diabetes. Am. J. Ophthalmol. 81, 383–396 (1976)

    Article  Google Scholar 

  20. Curtis, C., Shah, S.P., Chin, S.-F., Turashvili, G., Rueda, O.M., Dunning, M.J., et al.: The genomic and transcriptomic architecture of 2,000 breast tumours reveals novel subgroups. Nature 486, 346–352 (2012). https://doi.org/10.1038/nature10983

    Article  Google Scholar 

  21. Schumacher, M., Bastert, G., Bojar, H., Hübner, K., Olschewski, M., Sauerbrei, W., et al.: Randomized 2 × 2 trial evaluating hormonal treatment and the duration of chemotherapy in node-positive breast cancer patients. German Breast Cancer Study Group. J. Clin. Oncol. 12, 2086–2093 (1994). https://doi.org/10.1200/JCO.1994.12.10.2086

    Article  Google Scholar 

  22. Foekens, J.A., Peters, H.A., Look, M.P., Portengen, H., Schmitt, M., Kramer, M.D., et al.: The urokinase system of plasminogen activation and prognosis in 2780 breast cancer patients. Cancer Res. 60, 636–643 (2000)

    Google Scholar 

  23. Hothorn, T., Buehlmann, P., Kneib, T., Schmid, M., Hofner, B.: {mboost}: Model-Based Boosting (2018)

    Google Scholar 

  24. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer, New York (2009). https://doi.org/10.1007/978-0-387-84858-7

    Book  MATH  Google Scholar 

  25. Harrell Jr., F.E., Califf, R.M., Pryor, D.B., Lee, K.L., Rosati, R.A.: Evaluating the yield of medical tests. J. Am. Med. Assoc. 247, 2543–2546 (1982). https://doi.org/10.1001/jama.1982.03320430047030

    Article  Google Scholar 

  26. Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. CRC Press, Boca Raton (1994)

    Book  Google Scholar 

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Correspondence to Wojciech Jarmulski .

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Jarmulski, W., Wieczorkowska, A. (2020). Interpretable Survival Gradient Boosting Models with Bagged Trees Base Learners. In: Ceci, M., Loglisci, C., Manco, G., Masciari, E., Ras, Z. (eds) New Frontiers in Mining Complex Patterns. NFMCP 2019. Lecture Notes in Computer Science(), vol 11948. Springer, Cham. https://doi.org/10.1007/978-3-030-48861-1_3

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  • DOI: https://doi.org/10.1007/978-3-030-48861-1_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-48860-4

  • Online ISBN: 978-3-030-48861-1

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