Module Catalogue 2026/27

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

To provide an appreciation of the need for and an understanding of, the principal statistical methods required in the analysis of survival data.

Module Summary

There are many areas where interest focuses on data which measures the time to some event. In recent decades the principal application for such data has been how long patients survive before some event occurs. The event may be death or it may be the recurrence of a disease which had been in remission, or some other event. Applications are not solely medical: how long it takes a battery to run down or how long a component in a machine lasts before it fails are just two industrial examples. Such data are known as survival data, or sometimes lifetime data, and their analysis is called survival analysis. The main complication with survival data is that many observations will be ‘censored’, i.e. they are only partially observed. For example, when a trial of a new treatment for cancer is terminated many of the patients will still be alive. Therefore the survival times of those who died will be known exactly whereas for those still alive at the end of the trial, their survival time is only known to exceed their present survival. Methods for dealing with this form of data will be considered.

Outline Of Syllabus

Time-to-event data, censoring patterns. Non-parametric survival analysis: calculation of Kaplan-Meier estimates; use of log-rank statistics. Parametric survival analysis: exponential, Weibull and loglogistic distributions; likelihood analysis of effect of covariates. Proportional hazards model: partial likelihood; diagnostics; time-varying effects. Frailty. Prediction and explained variation.

Intended Knowledge Outcomes

At the end of the module it is expected that a student will be able to:

- Outline the key statistical ideas underpinning the analysis of survival data.

- Apply standard estimation methods (such as maximum likelihood) to infer parameters from selected statistical models and assess the effects of covariates on survival.

- Assess the strengths and weaknesses of different types of survival analysis.

Intended Skill Outcomes

At the end of the module it is expected that a student will be able to:

- Analyse survival data using graphical and non-parametric methods.

- Formulate an appropriate statistical analysis of survival data using parametric models and assess the effects of covariates.

- Analyse real survival data appropriately in R.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem classes are used to help develop the students’ abilities at applying the theory to solving problems.

The teaching methods are appropriate to allow students to develop a wide range of skills. From understanding basic concepts and facts to higher-order thinking.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem-solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; the summative assessment has a secondary formative purpose as well as its primary summative purpose.

Note: the exam for MAS8612 is more challenging than the exam for MAS3924.

General Notes

N/A