Skip to main content

Competing Risks Models

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

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

  • 3578 Accesses

Abstract

In the previous chapters we considered various statistical techniques that model the time to a particular event of interest. In this chapter, we consider competing risks models, which extend the previously described models to survival data with several distinct types of target events. Competing risks models are often used in survival analysis to model several causes of death. Similarly, competing risks models are useful to model the duration of unemployment, where one often wants to distinguish between full-time and part-time jobs that end the unemployment spell. We will first consider parametric competing risks models for discrete time-to-event data (Sect. 8.1). These include the popular multinomial model and the cumulative model for ordered responses, which can both be embedded into the binary-response framework. Parameter estimation and variable selection methods for discrete-time competing risks models are described in Sects. 8.2 and 8.3, respectively.

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

  • Agresti, A. (2013). Categorical data analysis (3rd ed.). New York: Wiley.

    MATH  Google Scholar 

  • Beyersmann, J., Allignol, A., & Schumacher, M. (2011). Competing risks and multistate models with R. New York: Springer.

    MATH  Google Scholar 

  • Bojesen Christensen, R. H. (2015). Ordinal: Regression models for ordinal data. R package version 2015.6-28. http://cran.r-project.org/web/packages/ordinal/

    Google Scholar 

  • Enberg, J., Gottschalk, P., & Wolf, D. (1990). A random-effects logit model of work-welfare transitions. Journal of Econometrics, 43, 63–75.

    Article  Google Scholar 

  • Fahrmeir, L., & Wagenpfeil, S. (1996). Smoothing hazard functions and time-varying effects in discrete duration and competing risks models. Journal of the American Statistical Association, 91, 1584–1594.

    Article  MathSciNet  MATH  Google Scholar 

  • Han, A., & Hausman, J. A. (1990). Flexible parametric estimation of duration and competing risk models. Journal of Applied Econometrics, 5, 1–28.

    Article  Google Scholar 

  • Kalbfleisch, J. D., & Prentice, R. L. (2002). The statistical analysis of failure time data (2nd ed.). New York: Wiley.

    Book  MATH  Google Scholar 

  • Klein, J. P., & Moeschberger, M. L. (2003). Survival analysis: Statistical methods for censored and truncated data (2nd ed.). New York: Springer.

    MATH  Google Scholar 

  • Kleinbaum, D. G., & Klein, M. (2013). Survival analysis: A self-learning text (3rd ed.). New York: Springer.

    MATH  Google Scholar 

  • Kruskal, W. H. (1958). Ordinal measures of association. Journal of the American Statistical Association, 53, 814–861.

    Article  MathSciNet  MATH  Google Scholar 

  • McCullagh, P. (1980). Regression model for ordinal data (with discussion). Journal of the Royal Statistical Society, Series B, 42, 109–127.

    MathSciNet  MATH  Google Scholar 

  • Möst, S. (2014). Regularization in Discrete Survival Models. Ph.D. Thesis, Department of Statistics, University of Munich.

    Google Scholar 

  • Möst, S., Pößnecker, W., & Tutz, G. (2015). Variable selection for discrete competing risks models. Quality & Quantity. doi:10.1007/s11135-015-0222-0.

    Google Scholar 

  • Narendranathan, W., & Stewart, M. B. (1993). Modelling the probability of leaving unemployment: Competing risks models with flexible base-line hazards. Applied Statistics, 42, 63–83.

    Article  MATH  Google Scholar 

  • Steele, F., Goldstein, H., & Browne, W. (2004). A general multilevel multistate competing risks model for event history data, with an application to a study of contraceptive use dynamics. Statistical Modelling, 4, 145–159.

    Article  MathSciNet  MATH  Google Scholar 

  • Tutz, G. (1995). Competing risks models in discrete time with nominal or ordinal categories of response. Quality & Quantity, 29, 405–420.

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Tutz, G., Pößnecker, W., & Uhlmann, L. (2015). Variable selection in general multinomial logit models. Computational Statistics & Data Analysis, 82, 207–222.

    Article  MathSciNet  Google Scholar 

  • Yee, T. (2010). The VGAM package for categorical data analysis. Journal of Statistical Software, 32(10), 1–34.

    Article  MathSciNet  Google Scholar 

  • Yuan, M., & Lin, Y. (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B, 68, 49–67.

    Article  MathSciNet  MATH  Google Scholar 

  • Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association, 101, 1418–1429.

    Article  MathSciNet  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). Competing Risks Models. In: Modeling Discrete Time-to-Event Data. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-28158-2_8

Download citation

Publish with us

Policies and ethics