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APTS module: Survival Analysis

Module leader: I Van Keilegom

Please see the full Module Specifications PDF file document for background information relating to all of the APTS modules, including how to interpret the information below.

Aims: The aim of this module is to familiarize the student with the basic concepts and models in survival analysis. The mechanisms of censoring and truncation, and their impact on the estimation of basic quantities and on the development of tests are discussed. The content will also include parametric and semiparametric models which are very common in survival analysis.


  • Introduction to basic concepts (like the mechanisms of censoring and truncation, some common parametric distributions in survival analysis, ...)
  • Nonparametric estimation of basic quantities (Kaplan-Meier estimator of the survival distribution, Nelson-Aalen estimator of the cumulative hazard function,...), the development of some (asymptotic) properties of these estimators, and hypothesis testing regarding the equality of two or more survival curves
  • Proportional hazards model (estimation of model components, hypothesis testing, selection of explanatory variables, model validation, ...)
  • Accelerated failure time model (estimation of parameters in model, hypothesis testing, model selection, model validation,...)
  • Frailty model (introduction, motivation, estimation of model components, ...) (if time allows)


  • Either the discussion of a research paper, which can be theoretical or applied depending on the interests of the student
  • Either a mini-project involving the analysis of a dataset selected by the student


  • Cox, D.R. and Oakes, D. (1984). Analysis of survival data, Chapman and Hall, New York.
  • Fleming, T.R. and Harrington, D.P. (1981). Counting processes and survival analysis, Wiley, New York.
  • Kalbfleisch, J.D. and Prentice, R.L. (1980). The statistical analysis of failure time data, Wiley, New York.
  • Klein, J.P. and Moeschberger, M.L. (1997). Survival analysis, techniques for censored and truncated data, Springer, New York.
  • Kleinbaum, D.G. et Klein, M. (2005). Survival analysis, a self-learning text, Springer, New York.