Advertisement

Additional Topics

  • Dirk F. Moore
Chapter
Part of the Use R! book series (USE R)

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.

Keywords

Maximum Likelihood Estimate Baseline Hazard Partial Likelihood Accelerate Failure Time Model Compact Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 7.
    Betensky, R.A., Finkelstein, D.M.: A non-parametric maximum likelihood estimator for bivariate interval censored data. Stat. Med. 18(22), 3089–3100 (1999)CrossRefGoogle Scholar
  2. 15.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 17.
    Fay, M.P.: Comparing several score tests for interval censored data. Stat. Med. 18(3), 273–285 (1999)CrossRefGoogle Scholar
  4. 18.
    Finkelstein, D.M.: A proportional hazards model for interval-censored failure time data. Biometrics 42(4), 845–854 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 23.
    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. 24.
    Goeman, J.J.: L1 penalized estimation in the Cox proportional hazards model. Biom. J. 52(1), 70–84 (2010)MathSciNetzbMATHGoogle Scholar
  7. 29.
    Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer, New York (2009)CrossRefzbMATHGoogle Scholar
  8. 31.
    Holford, T.R.: The analysis of rates and of survivorship using log-linear models. Biometrics 36, 299–305 (1980)CrossRefzbMATHGoogle Scholar
  9. 38.
    Kuhn, M., Johnson, K.: Applied Predictive Modeling. Springer, New York (2013)CrossRefzbMATHGoogle Scholar
  10. 40.
    Laird, N., Olivier, D.: Covariance analysis of censored survival data using log-linear analysis techniques. J. Am. Stat. Assoc. 76(374), 231–240 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 42.
    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)CrossRefGoogle Scholar
  12. 43.
    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. 71.
    Tibshirani, R.: Regression Shrinkage and Selection via the Lasso. J. R. Stat. Soc. Ser. B Methodol. 58, 267–288 (1996)MathSciNetzbMATHGoogle Scholar
  14. 72.
    Tibshirani, R.: The lasso method for variable selection in the Cox model. Stat. Med. 16, 385–395 (1997)CrossRefGoogle Scholar
  15. 73.
    Turnbull, B.W.: The empirical distribution function with arbitrarily grouped, censored and truncated data. J. R. Stat. Soc. Ser. B 38, 290–295 (1976)MathSciNetzbMATHGoogle Scholar
  16. 75.
    Ware, J.H., Demets, D.L.: Reanalysis of some baboon descent data. Biometrics 459–463 (1976)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Dirk F. Moore
    • 1
  1. 1.Department of BiostatisticsRutgers School of Public HealthPiscatawayUSA

Personalised recommendations