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Survival Analysis a counting process approach


Admission requirements

Prerequisites are introduction to probability theory and statistics (first and second year bachelor courses).


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). This type of data 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. As a result 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 data will be introduced and techniques for estimating the survival function by employing parametric and non-parametric methods will be illustrated. Multiplicative hazards regression models, testing and inference techniques will be studied in great details. Special aspects as time-dependent covariates effects and stratification will be introduced. Techniques to be used to assess the validity of the hazard regression model will be discussed. The last part of the course focus on more advanced models: frailty, competing risks and multi-states models.
Frailty models are employed in survival analysis to account for unobserved heterogeneity in a population. These models are used to model the dependence among individuals in a cluster, such as families or hospitals, where subjects may be more similar to each other than to individuals in other clusters. A random effect is incorporated in a frailty model (the frailty term) which acts multiplicatively on the hazard.
A competing risks model is concerned with failure time data where each subject may experience one of the K different type of terminal events. Multi-states are employed when some intermediate events may occur before the final event of interest and one is interested in the effects of the occurrence of those intermediate events on the final events. Also for these more complex models estimation and prediction techniques will be discussed.

Course Objectives

At the end of this course, the student will be familiar with different types of censoring and truncation mechanism; will be able to write down the likelihood for different types of censored and truncated data and can maximize it for given parametric models. The student will be able to: estimate the survival in a parametric and non-parametric setting, estimate a Cox model, test its assumptions, interpret a hazard ratio, and derive model-based survival curves; fit frailty, competing risks and multi-state models and interpret the results from the analysis.


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Mode of instruction

Weekly lectures, and exercise classes

Assessment method

The final grade consists of a group presentation based on an article provided during the course (20%, no retake) and a written (retake) exam (80%).

Reading list

Odd O. Aalen • Ørnulf Borgan • Håkon K. Gjessing: Survival and Event History Analysis. A Process Point of View. Springer 2008
Slides and relevant material will be distributed to students during the course.


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