Time-varying covariates and coefficients in Cox regression models

Zhongheng Zhang (Corresponding Author), Jaakko Reinikainen, Kazeem Adedayo Adeleke, Marcel E. Pieterse, Catharina G. M. Groothuis-Oudshoorn

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Time-varying covariance occurs when a covariate changes over time during the follow-up period. Such variable can be analyzed with the Cox regression model to estimate its effect on survival time. For this it is essential to organize the data in a counting process style. In situations when the proportional hazards assumption of the Cox regression model does not hold, we say that the effect of the covariate is time-varying. The proportional hazards assumption can be tested by examining the residuals of the model. The rejection of the null hypothesis induces the use of time varying coefficient to describe the data. The time varying coefficient can be described with a step function or a parametric time function. This article aims to illustrate how to carry out statistical analyses in the presence of time-varying covariates or coefficients with R.
Original languageEnglish
Article number121
Number of pages10
JournalAnnals of Translational Medicine
Issue number7
Publication statusPublished - Apr 2018


  • Cox proportional hazards
  • time dependent
  • time varying
  • Schoenfeld residuals
  • time-to-event


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