BSc Mathematics with Placement Year

How long do humans live? Or other living beings? How long does it take for some mechanical system to experience component failure? Or for the next economic crisis to happen? Or for a next major scientific breakthrough to shake up our lives? Or for it to stop raining in Manchester? These are the kind of questions that Survival Analysis is trying to answer: a branch of statistics that builds a fine grained model based on currently available data and predicts the expected waiting time until the next relevant event.

The first half of this course introduces and discusses Survival Analysis more in general, while the second half focuses on applications in life insurance and pensions as well as related techniques for mortality estimation and projection.

This course is fundamental for students on the BSc Actuarial Science & Maths, but is also very suited for other students with an interest in Statistics/Survival Analysis. The mathematical techniques are all rooted in Statistics and no prior knowledge of insurance related concepts is assumed. 

The unit aims to: discuss the field of Survival Analysis and related statistical techniques prominently used in life insurance, pensions, economics, engineering and elsewhere

• Derive whether a given censoring mechanism for the purpose of estimating survival times is independent or not.
• Perform estimation of truncated and censored survival times using non-parametric, parametric and semi-parametric methods and analyse the results.
• Perform a variety of hypothesis tests (in particular, 2-sample, likelihood related and graphical tests) associated with the estimation procedures and interpret the outcomes.
• Explain and apply a variety of commonly used methods for mortality forecasting.
• Use the census approximation in order to estimate mortality rates given census data.
• Apply any of a number of commonly used statistical tests to derive whether a given graduation of mortality rates is successful. 

1. Survival analysis: non-parametric models (incl. Kaplan-Meier & Nelson-Aalen); parametric models; survival & (cumulative) hazard function; residual & expected lifetimes; using the R package ‘survival’

2. The Cox proportional hazards model

3. Estimation of mortality rates: Poisson model; graduation; goodness of fit tests

4. Mortality projection: the Lee-Carter model 
 

The course will be delivered via 22 lectures in which the course materials will be explained and discussed, supported by a set of detailed, typeset lecture notes. Further there will be 11 tutorial sessions, during which students work on exercises to cement the materials and they can get individual feedback on their understanding. Solutions to the exercises will also be provided.

Note: prior to the exam students will be able to get individual feedback on their solutions of past exam paper questions (and otherwise). 

Generic feedback will be available after the exam period.

Coursework feedback is given as soon as marking is complete both individually as well as class level

No further reading required, lecture notes (and the example sheets) are sufficient.

Suggestions for further reading:

Aalen, Odd O., Borgan, Ørnulf and Gjessing, Håkon K. Survival and event history analysis: A process point of view. Springer, New York 2008.

Kleinbaum, David G. and Klein, Mitchel. Survival analysis: A self-learning text. 3rd edition, Springer, New York 2012.