A competing risks analysis is performed when we want to quantify the occurrence of mutually exclusive event types over time. The classical example is mortality: in the end we all die, but not all at the same age and from the same cause. Competing risks immediately generalize to multi-state models that assume the Markov property. There is still a lot of confusion with respect to the quantities that can be estimated and their interpretation. This books explains when and how to use models and techniques for the analysis of competing risks and intermediate states. It covers the most recent insights on estimation techniques and discusses in detail how to interpret the obtained results.

Table of contents

1)      Basic concepts. The role of time. Data structure. Basic quantities: rate and risk. (Non)-informative information schemes. Summary of basic techniques from survival analysis.

2)      Competing Risks; Nonparametric Estimation. Theoretical relations. The multi-state approach and the subdistribution approach. The competing risks equivalents of the Kaplan-Meier and log-rank test.

3)      Intermediate Events; Nonparametric Estimation. Basic structure and terminology in multi-state models. The Aalen-Johansen estimator.

4)      Regression; Cause-Specific/Transition Hazard. Correspondence with standard Cox model. Combined analysis: techniques and added value.

5)      Regression; Translation to Cumulative Scale. Three ways to quantify the risk based on covariables.

6)      Epilogue. Which type of quantity to choose? Etiology and prediction.

Additional materials

Files that directly relate to the book.

  • ExampleCode.R: script file with all R code that is used and explained in the book;
  • ComputerPracticalsHints.pdf: Some suggestions that may help when making the computer practicals;
  • ComputerPracticalsAnswers.pdf: detailed answers to the computer practicals. Code, output and explanatory text;
  • ComputerPracticalsCode.R: suggested R code;
  • Errata.pdf: file with errors in the book (version May 2016).


  • Competing risks, interpretation and ignorance: presentation given at the dept. of Clinical Epidemiology, Biostatistics and Bioinformatics of the Academic Medical Center, June 2015

Courses and presentations

  • Presentations;
  • Extra comments.