Survival analysis is the study of the distribution of life times, i.e. the times from an initiating event (birth, diagnosis, start of treatment) to some terminal event (relapse, death). Survival analysis is most prominently (but not only) used in the biomedical sciences. A special feature of survival data is that it takes time to observe the event of interest. A result of this seemingly innocent observation is that for a number of subjects the event is not observed, but instead it is known that it has not taken place yet. This phenomenon is called censoring and it requires special statistical methods. During the course different types of censored and truncated data will be introduced and techniques for estimating the survival function by employing both parametric and non-parametric methods will be illustrated. Also techniques for testing equality of survival functions (the log-rank test and alternatives) are discussed. Finally regression models for survival analysis, based on the hazard function (most notably the Cox proportional hazards model), will be studied in great detail. Special aspects such as time-dependent covariates and stratification will be introduced. Techniques to be used to assess the validity of the proportional hazards regression model will be discussed. The last part of the course focuses on models for multivariate survival analysis, including competing risks and multi-state models and frailty models.
- Has knowledge about censoring and truncation, can distinguish different types of (left-, right-, interval-) censoring and is aware of its implications
- Can write down the likelihood for different types of censored and truncated data, and can maximize it for given parametric models
- Can calculate the Kaplan-Meier and Nelson-Aalen estimate and its variances under right censoring and/or left truncation, is aware of its assumptions and can argue its validity
- Can formulate the Cox models, is aware of and can test its assumptions, can interpret a hazard ration, and can derive model-based survival curves
- Is aware of issues with time-dependent covariates and can formulate and understand a time-dependent Cox model
- Is aware of competing risks, has knowledge about cause-specific and subdistribution hazards and cumulative incidence functions, can calculate cumulative incidence estimators, and can distinguish between different regression models for competing risks (Cox models for cause-specific hazards vs Fine-Gray models)
- Is able to analyze standard survival data, interpret the results from the analysis and explain their findings to substantive researchers
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Mode of Instruction
Weekly 2 × 45 min of class based on the reading material, and 2 × 45 min of practical sessions with exercises. For many of these exercises we expect you to bring a laptop with the statistical package R (http://www.r-project.org) already installed.
Written exam (75%), a written report (10%), and a presentation (15%).
The report should describe the student’s results and the analysis of the survival data. The report should include feedback received during the 15 min presentation of the student’s results and data analysis.
Survival Analysis: Techniques for Censored and Truncated Data. John P. Klein, & Melvin L. Moeschberger, Springer-Verlag (2nd edition. 2003).
Lecture material provided in class.
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Hein Putter: h.putter [at] lumc [dot] nl