The University of Southampton
Courses

# MATH3085 Survival Models

## Module Overview

This module introduces some of the fundamental ideas and issues of lifetime and time-to-event data analysis, as used in actuarial practice, biomedical research and demography.

### Aims and Objectives

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Understand the key features of lifetime data, including censoring, and of probability models for lifetime data: survival function, hazard and force of mortality
• Understand the theory underlying survival models and their estimation and of how to use R to fit models, including the Kaplan-Meier estimate of the survival function, parametric models and the Cox regression model
• Understand models for human mortality, including how to compute and interpret the life table in a variety of contexts and models for forecasting morality.
• Describe and apply models of mortality and similar events which are specified as continuous-time discrete-state Markov processes
• Understand the need to graduate crude data on mortality rates and an understanding of how to compare crude mortality rates against a standard of graduated set of rates
• analyse and interpret data, and especially to adopt a critical approach to numerical data
• solve problems, and especially to apply ideas learnt in one context to other contexts

### Syllabus

• Introduction to concepts of modelling, survival data and survival models; censoring; survival and hazard functions. • Estimating the survivor function non-parametrically (Kaplan-Meier and Nelson-Aalen estimators); parametric survival models; estimation using maximum likelihood. • Regression models for survival data; proportional hazards; the Cox regression model; accelerated failure time models. • Introduction to continuous-time, discrete-state Markov models; two-state and multiple-state models; Kolmogorov equations; estimating the parameters of multiple-state models. • Models for human mortality; the life table: theory and applications. • Comparison of models of mortality: Binomial, Poisson and multiple-state models. Estimation and inference using maximum likelihood and other methods. • Exposure to risk; the principle of correspondence; estimating the exposed-to-risk with aggregate data. • Comparison of mortality experiences; mortality rates and standardised mortality ratios; statistical tests appropriate for the comparison. • Graduation of mortality data; reasons for graduation; methods of graduation; tests of adherence to data and smoothness of a graduation. • Models for forecasting human mortality • Using R to analyse lifetime and survival data

### Learning and Teaching

#### Teaching and learning methods

Lectures, problem classes, office hours, computer laboratories.

TypeHours
Independent Study90
Teaching60
Total study time150

D. Collett (2003). Modelling survival data in medical research..

A. Hinde (1998). Demographic methods.

Reading List. A suggested reading list for each part, and starting references for each assessment, will be made available on Blackboard

### Assessment

#### Summative

MethodPercentage contribution
Coursework 30%
Written assessment 70%

#### Referral

MethodPercentage contribution
Written assessment 100%

#### Repeat Information

Repeat type: Internal & External

Pre-requisites: MATH2011 OR ECON2006

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Recommended texts for this module may be available in limited supply in the University Library and students may wish to purchase reading texts as appropriate.

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.