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# BSc Actuarial Science and Mathematics / Course details

Year of entry: 2021

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## Course unit details:Survival Analysis for Actuarial Science

Unit code MATH39512 10 Level 3 Semester 2 Department of Mathematics No

### Overview

This course unit deals with classical survival analysis where the focus is on the time to a single event. Standard statistical methods to estimate these survival times do not work due to the presence of censoring and more sophisticated techniques are required. The course units covers some of the classical techniques in modelling and analysing survival data and also provides an introduction to the theory of counting processes and its application to survival analysis.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Actuarial Insurance MATH20972 Pre-Requisite Compulsory

### Aims

This course unit aims to provide a foundation of survival analysis, both from a theoretical and an applied point of view.

### Learning outcomes

After following this course, students should:

• Be able to determine whether or not a given censoring mechanism for the purpose of estimating survival times is independent.
• Be able to perform estimation of truncated and censored survival times using non- parametric, parametric and semi-parametric methods.
• Be able to carry out a variety of hypothesis tests (in particular, 2-sample, likelihood related and graphical tests) associated with the estimation procedures and interpret the outcomes.
• Be able to use martingales associated with counting processes for computing expectations and variances of estimators and test statistics of survival times.
• Be able to explain the frailty effect in a proportional frailty model.

### Syllabus

- Survival times: examples, censoring and truncation. [2]
- Counting processes: multiplicative intensity model, martingale methods, independent censoring. [4]
- Non-parametric estimation: Kaplan-Meier and Nelson-Aalen estimator, small and large sample properties, two-sample tests. [4]
- Parametric models: maximum likelihood estimation, hypothesis tests, diagnostic methods. [4]
- Cox proportional hazards model: Cox partial likelihood estimation, hypothesis tests, large sample properties. [5]
- Frailty models. [3]

### Assessment methods

Method Weight
Other 20%
Written exam 80%

Other: handing in homework for a number of selected exercises, 20%.
Examination: examination at the end of the semester, 80%.

### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

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

Kleinbaum, David G. and Klein, Mitchel. Survival analysis: A selflearning text. 3rd edition, Springer, New York

### Study hours

Scheduled activity hours
Lectures 22
Tutorials 11
Independent study hours
Independent study 67

### Teaching staff

Staff member Role
Ronnie Loeffen Unit coordinator

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.

Please see Blackboard / course unit related emails for any further updates