MMath Mathematics and Statistics

Randomised controlled trials are planned experimental studies on human subjects designed to assess the benefit of medical treatments. Other important areas of application of statistical methods in medical research are epidemiological studies, which investigate the possible causes of disease from observational data, diagnostic studies, which methods of disease diagnosis and meta-analysis, which considers combining information from multiple studies. Many of the major developments in modern statistics have been motivated by problems in medical research. Whilst briefly outlining other areas of application in medical research, the lecture course will introduce the statistical issue associated design and analysis of randomised controlled trials and in meta-analyses.

MATH38072 Pre-Requisites: MATH27720

This course unit introduces the application of statistical ideas and methodology to medical research, in the context of clinical trials and observational research. The course touches on the basics of the design and analysis of medical research studies, and an introduction to the basics of causal inference.

On successful completion of this course unit students will be able to: 

1. Appraise the design, analysis and interpretation of the results of randomised controlled trials (RCTs), with specific reference to minimising bias.
2. Choose, with justification, the design, including calculation of the sample size, for a RCT with a continuous or binary outcome.
3. Analyse data from RCTs of various designs (including: parallel, crossover or cluster; superiority, non-inferiority or equivalence), including the meta-analysis of several RCTs, and interpret the findings in the relevant context.
4. Derive key mathematical expressions with applications to RCTs or meta-analyses of RCTs.

• Introduction to medical statistics. Randomised controlled trials: historical background and ethical issues concerning randomised experimentation on human subjects.
• Design and organisation of randomised controlled trials. Types of bias and methods for controlling bias including blinding and placebo treatments.
• Sample size estimation for continuous and binary outcome measures.
• Methods of treatment allocation including simple randomization, random permuted blocks, stratification and minimization.
• Implications of equivalence and non-inferiority hypotheses for sample size and statistical analyses.
• Statistical methods for the analysis of parallel group trials including methods for the adjustment for baseline data.
• Implications of protocol deviations and the motivation for the intention-to-treat principle.
• Multiplicity issues: sub-group analysis and multiple outcomes.
• Alternatives designs for randomised controlled trials: cross-over trials and cluster randomised trials.
• Meta-analysis and publication bias.

• Coursework: weighting 20%
• End of semester examination: weighting 80%

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.

An introduction to medical statistics    Bland, Martin,    Oxford University Press    2015    ISBN: 9780192518392

Essential medical statistics    Kirkwood, Betty R.    Blackwell Pub    2003    ISBN: 9781444392845

Practical statistics for medical research.    Altman, Douglas G.,    Chapman & Hall/CRC    1999    ISBN: 9781000228816

Statistical methods in medical research    Armitage, P.    Blackwell Scientific Publications    2002    ISBN: 9780470773666

An introduction to clinical trials    Cook, Jonathan A.,    Oxford University Press Incorporated    2023    ISBN: 9780191993879

Introduction to the new statistics : estimation, open science, and beyond    Cumming, Geoff,    Routledge Taylor & Francis Group    2024    ISBN: 9780367531508

Cochrane handbook for systematic reviews of interventions    Higgins, Julian P. T.,; Thomas, James; Chandler, Jacqueline,; Cumpston, Miranda,; Li, Tianjing; Page, Matthew J.,; Welch, Vivian A.,    Wiley-Blackwell    2019    ISBN: 9781119536611

Bad science    Goldacre, Ben.    Fourth Estate    2009    ISBN: 9780007284870

Bad pharma : how drug companies mislead doctors and harm patients    Goldacre, Ben    Fourth Estate    2012    ISBN: 9780007350742