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

• understand survival data and the problems that arise in medical, technical, and econometrical studies using such data,

• describe the basic consepts used in survival analysis, such as hazard function and survival function,

• be familiar with basic non-parametric methods for estimation of the sutvival function and the cumulative hazard function, as well as density estimates of the hazard function,

• describe semi-parametric regression model, such as the Cox regression model and Aalen's regression model, and understand how to estimate parameters and function in these models,

• understand and be able to use kigustic regression,

• understand how to use residual analysis in order to check the model requirements for survival data,

• understand how to use counting processes as models for survival data, and statistical functionals for acquiring the distribution properties of estimates in survival analysis.

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

• be able to distinguish between reality, observations from reality, a mathematical model of reality, and estimates of the parameters of this model,

• understand the limitations of the model's ability to describe reality.

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