Course syllabus

# Analys av överlevnadsdata Survival Analysis

## FMSN10, 7,5 credits, A (Second Cycle)

Valid for: 2013/14
Decided by: Education Board B
Date of Decision: 2013-04-10

## General Information

Elective for: F4, F4-bm, Pi4, Pi4-bm, Pi4-mrk
Language of instruction: The course will be given in English on demand

## 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.

## Learning outcomes

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.

Competences and skills
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

• 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.

## Examination details

Assessment: Oral exam and written project reports. The course grade is av weighting of the results of the exam and the project reports.

• FMS012 Mathematical Statistics, Basic Course or FMS032 Mathematical Statistics, Basic Course or FMS035 Mathematical Statistics, Basic Course or FMS086 Mathematical Statistics or FMS140 Mathematical Statistics, Basic Course

Required prior knowledge: Inference, e.g. Monte Carlo and Empirical Methods for Stochastic Inference helps.
The number of participants is limited to: No
The course overlaps following course/s: MAS213, MASM21