Survival Analysis

Course content

Survival analysis or failure time data analysis means the statistical analysis of data, where the response of interest is the time T from a well-defined time origin to the occurrence of some given event (end-point). In biomedicine the key example is the time from randomization to a given treatment for some patients until death occurs leading to the observation of survival times for these patients. The objective may be to compare different treatment effects on the survival time possibly correcting for information available on each patient such as age and disease progression indicators. This leaves us with a statistical regression analysis problem. Standard methods will, however, often be inappropriate because survival times are frequently incompletely observed with the most common example being right censoring. The survival time T is said to be right censored if it is only known that T is larger than an observed right censoring value. This may be because the patient is still alive at the point in time where the study is closed and the data are to be analyzed, or because the subject is lost for follow-up due to other reasons. 

The course gives a broad introduction to concepts and methods in survival and event history analysis. Topics covered include counting processes and martingales; the Nelson-Aalen and Kaplan-Meier estimators; the log-rank test; hazard regression models including Cox proportional hazards regression,  goodness-of-fit tools  and marginal models; competing risk models; statistical computing in R.


MSc Programme in Mathematics-Economics
MSc Programme in Statistics

Learning outcome


   * A basic understanding of survival analysis techniques and when they need to be applied.

Skills: Ability to

   * Perform practical analyses of event type outcomes. Using regression
     models and non-parametric methods.  Validate the used models.

   * Use basic counting process calculus to derive properties of estimators  and   relationships between key model quantitites.

Comptences: Ability to

   * explain and understand when survival analyses methods are needed.

   * Identify, justify, analyse and report  failure time models in practical settings.

   * to engage in collaborative work with other researchers in the context of
     survival analysis.

4 hours of lectures and 3 hours of exercises per week for 7 weeks.

The exercises will consider both theoretical problems as well as practical
analyses of data. Here the students will have to participate actively, that is
take active part in working on the problems in class, and take turns
demonstrating the solutions to the different problems.

VidSand1 + VidSand2

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Written assignment, 3 days
A takehome exam combining theoretical and practical work.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 125
  • Exercises
  • 21
  • Exam
  • 32
  • English
  • 206