Analysis of time-to-event for observational studies: Guidance to the use of intensity models

Per Kragh Andersen, Maja Pohar Perme, Hans C. van Houwelingen, Richard J. Cook, Pierre Joly, Torben Martinussen, Jeremy M.G. Taylor, Michal Abrahamowicz, Terry M. Therneau

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper provides guidance for researchers with some mathematical background on the conduct of time-to-event analysis in observational studies based on intensity (hazard) models. Discussions of basic concepts like time axis, event definition and censoring are given. Hazard models are introduced, with special emphasis on the Cox proportional hazards regression model. We provide check lists that may be useful both when fitting the model and assessing its goodness of fit and when interpreting the results. Special attention is paid to how to avoid problems with immortal time bias by introducing time-dependent covariates. We discuss prediction based on hazard models and difficulties when attempting to draw proper causal conclusions from such models. Finally, we present a series of examples where the methods and check lists are exemplified. Computational details and implementation using the freely available R software are documented in Supplementary Material. The paper was prepared as part of the STRATOS initiative.

Original languageEnglish (US)
Pages (from-to)185-211
Number of pages27
JournalStatistics in Medicine
Issue number1
StatePublished - Jan 15 2021


  • Cox regression model
  • STRATOS initiative
  • censoring
  • hazard function
  • immortal time bias
  • multistate model
  • prediction
  • survival analysis
  • time-dependent covariates

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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