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2024/25 Taught Postgraduate Module Catalogue

MATH5092M Mixed Models with Medical Applications

15 creditsClass Size: 60

Module manager: Dr Duncan Wilson

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2024/25

Pre-requisite qualifications

MATH2715 or MATH2735

This module is mutually exclusive with


This module is not approved as an Elective

Module summary

Clustering and hierarchical structures are common in scientific research. For example, in a medical study, patients could be clustered by surgeon, with surgeons clustered by hospital. Patient outcomes within clusters are likely to be correlated, thus violating the independence assumptions of many statistical methods. Mixed models overcome this obstacle, by extending familiar models such as linear regression to include additional random terms that account for variability between clusters. Mixed models are essential tools in the medical, environmental and social sciences. Students undertaking this module will learn how to apply mixed models to a broad range of realistic examples from these sciences. With a focus on advanced medical applications, students will also learn how clustering can be incorporated into the design of experiments and how to properly analyse data with non-hierarchical clustering.


This module aims to introduce students to mixed models for the analysis of data with complex hierarchical or clustered structures. These models will be demonstrated through real-life examples from the medical, environmental and social sciences. More advanced models for clustered data with non-hierarchical structures, such as cross-classification and multiple membership, will be introduced through their applications in medical statistics. The optimal design of experiments with clustered data will be covered, with reference to clinical trials.

Learning outcomes
By the end of this module, the student should be able to:
1.Understand and explain mixed models and how they are estimated.
2.Apply appropriate mixed models to problems in the medical, environmental or social sciences.
3.Estimate a variety of mixed models using statistical software.
4.Report and interpret the results of a mixed model analysis.
5.Understand, explain and estimate mixed models that allow cross-classification and multiple membership.
6.Understand the implications of clustered data on experimental design, and apply appropriate methods for sample size determination in clinical trials with clustering.


1.Basic two-level hierarchical models, including variance components models, random intercept models and random slope models.
2.Three-level hierarchical models and complex variance structures.
3.Parameter and residual estimation for mixed models.
4.Mixed models for longitudinal data.
5.Fitting and checking models using statistical software.
6.Design of experiments with clustered data.
7.Models for multiple membership and cross-classification.

Teaching methods

Delivery typeNumberLength hoursStudent hours
Independent online learning hours22.00
Private study hours93.00
Total Contact hours35.00
Total hours (100hr per 10 credits)150.00

Opportunities for Formative Feedback

Students will complete and receive written feedback on three homework assignments. Students will receive face-to-face feedback on tasks completed during practical sessions.

Methods of assessment

Assessment typeNotes% of formal assessment
ReportA short report (< 10 pages) on an analysis of a data set.20.00
Total percentage (Assessment Coursework)20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exam typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc)2 hr 30 mins80.00
Total percentage (Assessment Exams)80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 29/04/2024 16:16:33


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