Course: Analysis of Time-to-Event Data (Ereigniszeitanalyse)

Winter term 2019/20

Course description

Time-to-event data, also often referred to as survival data, arise when interest is focused on the time elapsing before an event is experienced. By events we mean occurrences that are of interest in scientific studies from various disciplines such as medicine, epidemiology, demography, biology, sociology, economics, engineering, et cetera. Examples of such events are: death, onset of infection, divorce, unemployment, and failure of a mechanical device. All of these may be subject to scientific interest where one tries to understand their cause or establish risk factors. The purpose of this course is to provide a gentle, yet intense, introduction of the most commonly used statistical methods for analyzing time-to-event data. This course covers the following topics:

  • Basic concepts and quantities of interest
  • Counting processes
  • Nonparametric estimation and comparison of survival curves
  • Parametric regression models
  • Semiparametric proportional hazards regression
  • Refinements of the semiparametric proportional hazards model
  • Competing risks and multistate models
  • Analysis of recurrent events
  • Frailty models for related observations
The lectures will be accompanied by tutorials covering both theoretical aspects and the practice of solving applied exercises using the software package R.

This course comprises 4 contact hours per week (2 hours lectures, 2 hours tutorials) and is intended for students enrolled in the Master of Applied Statistics programme at the Georg August University Göttingen.

Lecturer: PD Dr. Steffen Unkel

Class teacher: Burak Kürsad Günhan


  • Please use Stud.IP to sign up for this module so that we can send e-mails to all participants from there.


Lecture Thursday 08:30 - 10:00 Lecture room MED 23, Humboldtallee 32
Tutorial Tuesday 08:30 - 10:00 Lecture room MED 23, Humboldtallee 32


Date Lecture/Tutorial TopicMaterial
October 22nd (Tuesday) Lecture Basic quantities and concepts Lecture slides
October 24th (Thursday) Lecture Nonparametric estimation of functions of survival time Lecture slides, HTML file, RMD file
November 5th (Tuesday) Tutorial Study Sheet 1 Study sheet 1, R code
November 7th (Thursday) Lecture Nonparametric estimation of functions of survival time (continuation) HTML file, RMD file
November 12th (Tuesday) Tutorial Study Sheet 2 Study sheet 2, R code
November 14th (Thursday) Lecture Nonparametric methods for comparing survival distributions Lecture slides, HTML file, RMD file
November 19th (Tuesday) Tutorial Study sheet 3 Study sheet 3, melanoma.dat, Description of the melanoma data, R code
November 21st (Thursday) Lecture Parametric regression models Lecture slides, HTML file, RMD file
November 26th (Tuesday) Lecture Parametric regression models (continuation)
November 28th (Thursday) Tutorial Study sheet 4 Study sheet 4, R code
December 3rd (Tuesday) Tutorial Study sheet 5 Study sheet 5, R code
December 5th (Thursday) Tutorial Study sheet 5 (continuation)
December 10th (Tuesday) Lecture Semiparametric proportional hazards regression Lecture slides, HTML file, RMD file
Reminder on shrinkage regression and cross-validation
December 12th (Thursday) Tutorial Study sheet 6 Study sheet 6
December 17th (Tuesday) Lecture Semiparametric proportional hazards regression (continuation)
January 7th (Tuesday) Tutorial Study sheet 7 Study sheet 7

Supplemental resources

Topic Material
Lexis diagrams Plummer, M. and Carstensen, B. (2011): Lexis: An R class for epidemiological studies with long-term follow-up,
Journal of Statistical Software, Vol. 38, Issue 5.
Survival Analysis in R Diez, D. M. (2013): Survival Analysis in R.
Multistate models de Wreede, L. C., Fiocco, M. and Putter, H. (2011): mstate: An R Package for the Analysis of Competing Risks and Multi-State Models,
Journal of Statistical Software, Vol. 38, Issue 7.
Frailty models Rondeau, V., Mazroui, Y. and Gonzalez, J. R. (2012): frailtypack: An R Package for the Analysis of Correlated Survival Data with Frailty Models Using Penalized Likelihood Estimation or Parametrical Estimation, Journal of Statistical Software, Vol. 47, Issue 3.

R packages

Package Citation info
survival Therneau, T (2015): A Package for Survival Analysis in S, R package version 2.41-3
Epi Carstensen, B., Plummer, M., Laara, E. and Hills, M. (2017): Epi: A Package for Statistical Analysis in Epidemiology, R package version 2.19
KMsurv Data sets from Klein and Moeschberger (1997), Survival Analysis, R package version 0.1-5
OIsurv Survival analysis supplement to OpenIntro guide, R package version 0.2
URL: Confidence intervals for the Kaplan-Meier estimator, R package version 0.5-2
flexsurv Flexible Parametric Survival and Multi-State Models, R package version 1.1
muhaz Hazard Function Estimation in Survival Analysis, R package version 1.2.6
eha Event History Analysis, R package version 2.5.0
penalized L1 (Lasso and Fused Lasso) and L2 (Ridge) Penalized Estimation in GLMs and in the Cox Model, R package version 0.9-50
timereg Flexible regression models for survival data, R package version 1.9.1
cmprsk Subdistribution Analysis of Competing Risks, R package version 2.2-7.
mvna Nelson-Aalen Estimator of the Cumulative Hazard in Multistate Models, R package version 2.0.1
mstate Data preparation, estimation and prediction in multi-state models, R package version 0.2.10
etm Empirical Transition Matrix, R package version 0.6-2
compeir Event-specific incidence rates for competing risks data, R package version 1.0
survrec Survival analysis for recurrent event data, R package version 1.2-2
frailtypack General Frailty Models: Shared, Joint and Nested Frailty Models with Prediction, R package version 2.12.6



  • Aalen, O. O., Borgan, O. and Gjessing, H. K. (2008): Survival and Event History Analysis: A Process Point of View, Springer.
  • Beyersmann, J., Schumacher, M. and Allignol, A. (2012): Competing Risks and Multistate Models with R, Springer.
  • Collett, D. (2015): Modelling Survival Data in Medical Research, 3rd edition, Chapman & Hall/CRC.
  • Hosmer Jr., D. W., Lemeshow, S. and May, S. (2008): Applied Survival Analysis: Regression Modelling of Time to Event Data, 2nd edition, Wiley.
  • Hougaard, P. (2000): Analysis of Multivariate Survival Data, Springer.
  • Klein, J. P. and Moeschberger, M. L. (2003): Survival Analysis: Techniques for Censored and Truncated Data, 2nd edition, Springer.
  • Lee, E. T. and Wang, J. W. (2013): Statistical Methods for Survival Data Analysis, 4th edition, Wiley.
  • Moore, D. F. (2016): Applied Survival Analysis Using R, Springer.


Written exam (duration: 90 minutes). The exam will take place on Friday, February 14th 2020, between 10:15 a.m. and 11:45 a.m. in the departmental library, Department of Medical Statistics, Humboldtallee 32. The permitted examination aids are:

  • Unannotated lecture slides;
  • One handwritten DIN A4 sheet (one-sided);
  • Pocket calculator;
  • English dictionary (without personal comments).