The University of Southampton
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# DEMO3001 Survival Models

## Module Overview

### Aims and Objectives

#### Module Aims

To introduce some of the fundamental ideas and issues of demography, including the life table, the modelling of survival and other longitudinal event history data and the graduation of demographic rates.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Demonstrate knowledge and understanding of applying the life table in a variety of contexts
• Analyse and interpret data, and especially to adopt a critical
• Solve problems, and especially to apply ideas learnt in one context to other contexts
• Demonstrate knowledge and understanding of the theory underlying survival models of mortality and other events which assume that future life time is a random variable
• Demonstrate knowledge and understanding of models of mortality and similar events which are specified as continuous-time discrete-state Markov processes
• Use the models in (2) and (3) to estimate the rates of occurrence of mortality and other events by applying them to suitable data;
• Demonstrate knowledge and understanding of factors associated with mortality differentials, and how to evaluate their importance, in particular using the Cox regression model
• Demonstrate knowledge and understanding of the advantages and disadvantages of the models in (2) and (3) compared with the traditional binomial model of mortality
• Demonstrate knowledge and understanding of the principle of correspondence in the context of demographic rates, and how to estimate the correct exposed-to-risk in common situations with both individual and aggregate data
• Demonstrate knowledge and understanding of the need to graduate crude data on demographic rates, and knowledge of how graduation might be achieved and tested
• Demonstrate knowledge and understanding of population dynamics and the principles of population projection

### Syllabus

The life table: theory and applications. Introduction to survival models; estimating the survival function non-parametrically (Kaplan-Meier and Nelson-Aalen estimators); parametric estimation of the survival function; proportional hazards models; the Cox regression model. Introduction to continuous-time, discrete-state Markov models; two-state and multiple-state models; Chapman-Kolmogorov equations; estimating the parameters of multiple-state models. Comparison of models of mortality: Binomial, Poisson and multiple-state models. The principle of correspondence; exposed-to-risk; estimating the exposed-to-risk with aggregate data. Comparison of mortality experiences; statistical tests appropriate for the comparison; reasons for graduation; methods of graduation; tests of adherence to data and smoothness of a graduation. Population dynamics and projections.

#### Special Features

A good performance in this module, together with a module in Stochastic Processes taught by the School of Mathematics, potentially confers exemption from the Actuarial Profession’s examination in subject CT4 – Models.

### Learning and Teaching

#### Teaching and learning methods

30 lectures and 5 small group tutorials.

TypeHours
Teaching40
Independent Study110
Total study time150

### Assessment

#### Summative

MethodPercentage contribution
Coursework 10%
Exam  (3 hours) 90%

#### Referral

MethodPercentage contribution
Exam  (3 hours) 100%
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