Skip to main content

Tree-Based Approaches

  • Chapter
  • First Online:
Modeling Discrete Time-to-Event Data

Part of the book series: Springer Series in Statistics ((SSS))

  • 3539 Accesses

Abstract

In previous chapters we considered modeling techniques that assume the predictor of the model to be an additive function of the covariates. Although this assumption is intuitive and facilitates interpretation of the models, it may happen that additive predictors do not capture the true data structure. This is, for example, the case when interactions between categorical covariates are present. In this chapter we consider recursive partitioning techniques (also termed “tree-based methods”), which are a popular approach to estimate non-additive predictors. Starting with an introduction to recursive partitioning, we consider two strategies to adapt tree-based methods to discrete survival data. The two strategies, which are described in detail in Sects. 6.2 and 6.3, are characterized by different choices for the split criterion to form the nodes of the trees. Section 6.4 contains an overview of tree ensembles for discrete survival data, which are designed to reduce the variance and to increase the prediction accuracy of single-tree methods.

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 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  • Bou-Hamad, I., Larocque, D., & Ben-Ameur, H. (2011a). Discrete-time survival trees and forests with time-varying covariates: Application to bankruptcy data. Statistical Modelling, 11, 429–446.

    Article  MathSciNet  Google Scholar 

  • Bou-Hamad, I., Larocque, D., & Ben-Ameur, H. (2011b). A review of survival trees. Statistics Surveys, 5, 44–71.

    Article  MathSciNet  MATH  Google Scholar 

  • Bou-Hamad, I., Larocque, D., Ben-Ameur, H., Masse, L., Vitaro, F., & Tremblay, R. (2009). Discrete-time survival trees. Canadian Journal of Statistics, 37, 17–32.

    Article  MathSciNet  MATH  Google Scholar 

  • Breiman, L. (1996). Bagging predictors. Machine Learning, 24, 123–140.

    MathSciNet  MATH  Google Scholar 

  • Breiman, L. (2001). Random forests. Machine Learning, 45, 5–32.

    Article  MATH  Google Scholar 

  • Breiman, L., Cutler, A., Liaw, A., & Wiener, M. (2015). randomForest: Breiman and Cutler’s random forests for classification and regression. R package version 4.6-12. http://cran.r-project.org/web/packages/randomForest

    Google Scholar 

  • Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, J. C. (1984). Classification and regression trees. Monterey, CA: Wadsworth.

    MATH  Google Scholar 

  • Broström, H. (2007). Estimating class probabilities in random forests. In ICMLA ’07: Proceedings of the 6th International Conference on Machine Learning and Applications (pp. 211–216). Washington, DC: IEEE Computer Society.

    Google Scholar 

  • Ferri, C., Flach, P. A., & Hernandez-Orallo, J. (2003). Improving the AUC of probabilistic estimation trees. In Proceedings of the 14th European Conference on Artifical Intelligence (Vol. 2837, pp. 121–132). Berlin: Springer.

    Google Scholar 

  • Gneiting, T., & Raftery, A. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102, 359–376.

    Article  MathSciNet  MATH  Google Scholar 

  • Hastie, T., Tibshirani, R., & Friedman, J. H. (2009). The elements of statistical learning (2nd ed.). New York: Springer.

    Book  MATH  Google Scholar 

  • Hothorn, T., Hornik, K., & Zeileis, A. (2006). Unbiased recursive partitioning: A conditional inference framework. Journal of Computational and Graphical Statistics, 15, 651–674.

    Article  MathSciNet  Google Scholar 

  • Hothorn, T., Lausen, B., Benner, A., & Radespiel-Tröger, M. (2004). Bagging survival trees. Statistics in Medicine, 23, 77–91.

    Article  Google Scholar 

  • Ishwaran, H., Kogalur, U. B., Blackstone, E. H., & Lauer, M. S. (2008). Random survival forests. Annals of Applied Statistics, 2, 841–860.

    Article  MathSciNet  MATH  Google Scholar 

  • Ishwaran, H., Kogalur, U. B., Chen, X., & Minn, A. J. (2011). Random survival forests for high-dimensional data. Statistical Analysis and Data Mining, 4, 115–132.

    Article  MathSciNet  Google Scholar 

  • Klein, J. P., Moeschberger, M. L., & J. Yan (2012). KMsurv: Data sets from Klein and Moeschberger (1997), survival analysis. R package version 0.1-5. http://cran.r-project.org/web/packages/KMsurv

  • LeBlanc, M., & Crowley, J. (1993). Survival trees by goodness of split. Journal of the American Statistical Association, 88, 457–467.

    Article  MathSciNet  MATH  Google Scholar 

  • LeBlanc, M., & Crowley, J. (1995). A review of tree-based prognostic models. Journal of Cancer Treatment and Research, 75, 113–124.

    Article  Google Scholar 

  • Mayer, P., Larocque, D., & Schmid, M. (2014). DStree: Recursive partitioning for discrete-time survival trees. R package version 1.0. http://cran.r-project.org/web/packages/DStree/index.html

  • Morgan, J. N., & Sonquist, J. A. (1963). Problems in the analysis of survey data, and a proposal. Journal of the American Statistical Association, 58, 415–435.

    Article  MATH  Google Scholar 

  • Provost, F., & Domingos, P. (2003). Tree induction for probability-based ranking. Machine Learning, 52, 199–215.

    Article  MATH  Google Scholar 

  • Quinlan, J. R. (1993). C4.5: Programs for machine learning. San Francisco, CA: Morgan Kaufmann.

    Google Scholar 

  • Schmid, M., Küchenhoff, H., Hoerauf, A., & Tutz, G. (2016). A survival tree method for the analysis of discrete event times in clinical and epidemiological studies. Statistics in Medicine, 35, 734–751.

    Article  Google Scholar 

  • Strobl, C., Malley, J., & Tutz, G. (2009). An introduction to recursive partitioning: Rationale, application and characteristics of classification and regression trees, bagging and random forests. Psychological Methods, 14, 323–348.

    Article  Google Scholar 

  • Therneau, T., Atkinson, B., & Ripley, B. (2015). rpart: Recursive partitioning. R package version 4.1-9. http://cran.r-project.org/web/packages/rpart

    Google Scholar 

  • Tutz, G. (2012). Regression for categorical data. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Tutz, G., Schmid, M. (2016). Tree-Based Approaches. In: Modeling Discrete Time-to-Event Data. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-28158-2_6

Download citation

Publish with us

Policies and ethics