Syllabus academic year 2011/2012
(Created 2011-09-01.)
SURVIVAL ANALYSISFMSN10
Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course will be given in English on demand. FMSN10 overlaps following cours/es: MAS213 and MASM21. Optional for: F4, F4bm, Pi4, Pi4bm, Pi4mrk. Course coordinator: Dragi Anevski, dragi@maths.lth.se, Mathematical Statistics. Prerequisites: FMS012/FMS032/FMS035/FMS086/FMS140 Mathematical statistics. Recommended prerequisits: Inference, e.g. Monte Carlo and Empirical Methods for Stochastic Inference helps. The course might be cancelled if the number of applicants is less than 16. Assessment: Oral exam and written project reports. The course grade is av weighting of the results of the exam and the project reports. Further information: The course is also given at the faculty of science with the code MASM21. Home page: http://www.maths.lth.se/matstat/kurser/fmsn10/.

Aim
Survival data is common in medical, technical, and economical applications. Data usually consists of the time to some event(s) together with other factors that may influence this time. Often the data are censored (i.e. one can only observe whether the time lies in some interval) and/or truncated (i.e. one can only observe those times that lie in some interval). Therefore, modeling and analysis of such data require special methods. These methods are indispencible in, e.g., the pharmaceutical industry and in clinical and pre-clinical research.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

be able to use a statistical programme package for basic studies of survival data in medical statistics, and interpret the result of such studies.

Judgement and approach
For a passing grade the student must

Contents
Survival data; censored and truncated data. Covariates.

Distributions and models for survival data. Counting processes and martingale theory.

Estimation of the survival function and cumulative hazard function (Kaplan-Meier and Nelson-Aalen estimators). Non-parametric one- and multiple sample tests. Kernel estimates of the hazard function.

Semi-parametric regression models for data with covariates. The Cox model. Aalen's model. Likelihood-theory for estimation of the Cox model. Projection methods in counting processes for Aalen's model.

Competing risk methods for analysis with several different endpoints.

Bootstrap methods for survival data.

Statistiscal functionals for limiting distributions in survival analysis.

Literature
Aalen, O., Borgan, Ö., Gjessing, H.K.: Survival and Event History Analysis: A Process Point of View. Springer 2006. ISBN: 978-0387202877