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.
KeywordsMaximum Likelihood Estimate Baseline Hazard Partial Likelihood Accelerate Failure Time Model Compact Data
- 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)
- 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)
- 75.Ware, J.H., Demets, D.L.: Reanalysis of some baboon descent data. Biometrics 459–463 (1976)Google Scholar