# 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 and additive hazards regression; goodness-of-fit tools based on martingale residuals; analysis of clustered survival data using frailty models and/or marginal models; competing risk models; statistical computing in R.

Education

MSc Programme in Statistics

Learning outcome

Knowledge:

* 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.

* Understand and establish etimating equations in the context of
event history data. Derive asymptotic properties based on estimating
equations.

Comptences: Ability to

* explain and understand when survival analyses methods are needed.

* derive asymptotic distributions for simple estimating equations.

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

4 hours of lectures and 2 hours of exercises per week for 7 weeks.

VidSand1 + VidSand2

ECTS
7,5 ECTS
Type of assessment
Written assignment, 3 days
A takehome exam combining theoretical and practical work.
Aid
All aids allowed
Marking scale
passed/not passed
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
• Exercises
• 14
• Preparation
• 132
• Exam
• 32
• English
• 206