## Actuarial Models 2

 Unit code: MATH39512 Credit Rating: 10 Unit level: Level 3 Teaching period(s): Semester 2 Offered by School of Mathematics Available as a free choice unit?: N

Prerequisite

#### Aims

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

#### 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.

#### Learning outcomes

After following this course, students should be able to:

• 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.

#### Assessment methods

• Other - 20%
• Written exam - 80%

#### Assessment Further Information

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

#### 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]

Subject CT4, Models. Produced by the Actuarial Education Company.

#### 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.

#### Study hours

• Lectures - 22 hours
• Tutorials - 11 hours
• Independent study hours - 67 hours

#### Teaching staff

Ronnie Loeffen - Unit coordinator