Skip to main content
SpringerLink
Log in

Additional Topics

  • Chapter
  • First Online:
Applied Survival Analysis Using R

Part of the book series: Use R! ((USE R))

  • 16k Accesses

Abstract

The exponential distribution, with its constant hazard assumption, is too inflexible to be useful in most lifetime data applications. The piecewise exponential model, by contrast, is a generalization of the exponential which can offer considerable flexibility for modeling. In Chap. 2 (Exercise 2.5) we saw a simple piecewise exponential model with two “pieces”. That is, the survival time axis was divided into two intervals, with a constant hazard on each interval. Here we show how to generalize this model to accommodate multiple intervals on which the hazard is constant. An important feature of the piecewise exponential is that the likelihood is equivalent to a Poisson likelihood. Thus, we can use a Poisson model-fitting function in R to find maximum likelihood estimates of the hazard function and of parameters of a proportional hazards model.

The original version of this chapter was revised. An erratum to this chapter can be found at DOI 10.1007/978-3-319-31245-3_13

An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-319-31245-3_13

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
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

Notes

  1. 1.

    The “icfit” function in the “interval” package does not require times to have values greater than zero, but the “survreg” function does.

  2. 2.

    The “Icens” package is on bioconductor,http:www.bioconductor.org. In the R graphical interface window, be sure to select the drop down menu items “Packages”, then “Repositories”, and then include “BioC software” in addition to the default repository “CRAN”.

References

  1. Betensky, R.A., Finkelstein, D.M.: A non-parametric maximum likelihood estimator for bivariate interval censored data. Stat. Med. 18(22), 3089–3100 (1999)

    Article  Google Scholar 

  2. Demarqui, F.N., Loschi, R.H., Colosimo, E.A.: Estimating the grid of time-points for the piecewise exponential model. Lifetime Data Anal. 14(3), 333–356 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fay, M.P.: Comparing several score tests for interval censored data. Stat. Med. 18(3), 273–285 (1999)

    Article  Google Scholar 

  4. Finkelstein, D.M.: A proportional hazards model for interval-censored failure time data. Biometrics 42(4), 845–854 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goeman, J., Meijer, R., Chaturvedi, N.: L1 and L2 penalized regression models, R package Version 0.9-45, http://cran.r-project.org (2014)

  6. Goeman, J.J.: L1 penalized estimation in the Cox proportional hazards model. Biom. J. 52(1), 70–84 (2010)

    MathSciNet  MATH  Google Scholar 

  7. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer, New York (2009)

    Book  MATH  Google Scholar 

  8. Holford, T.R.: The analysis of rates and of survivorship using log-linear models. Biometrics 36, 299–305 (1980)

    Article  MATH  Google Scholar 

  9. Kuhn, M., Johnson, K.: Applied Predictive Modeling. Springer, New York (2013)

    Book  MATH  Google Scholar 

  10. Laird, N., Olivier, D.: Covariance analysis of censored survival data using log-linear analysis techniques. J. Am. Stat. Assoc. 76(374), 231–240 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, L., Yan, J., Xu, J., Liu, C.-Q., Zhen, Z.-J., Chen, H.-W., Ji, Y., Wu, Z.-P., Hu, J.-Y., Zheng, L., et al.: CXCL17 expression predicts poor prognosis and correlates with adverse immune infiltration in hepatocellular carcinoma. PloS One 9(10), e110064 (2014)

    Article  Google Scholar 

  12. Li, L., Yan, J., Xu, J., Liu, C.-Q., Zhen, Z.-J., Chen, H.-W., Ji, Y., Wu, Z.-P., Hu, J.-Y., Zheng, L., et al.: Data from: CXCL17 expression predicts poor prognosis and correlates with adverse immune infiltration in hepatocellular carcidata. Dryad Digital Repository, http://datadryad.org (2014)

  13. Tibshirani, R.: Regression Shrinkage and Selection via the Lasso. J. R. Stat. Soc. Ser. B Methodol. 58, 267–288 (1996)

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  15. Turnbull, B.W.: The empirical distribution function with arbitrarily grouped, censored and truncated data. J. R. Stat. Soc. Ser. B 38, 290–295 (1976)

    MathSciNet  MATH  Google Scholar 

  16. Ware, J.H., Demets, D.L.: Reanalysis of some baboon descent data. Biometrics 459–463 (1976)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biostatistics, Rutgers School of Public Health, Piscataway, NJ, USA

    Dirk F. Moore

Authors
  1. Dirk F. Moore
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Moore, D.F. (2016). Additional Topics. In: Applied Survival Analysis Using R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-31245-3_12

Download citation

Publish with us

Policies and ethics

Search

Navigation