Unprecedented growth in computing power, the advent of artificial intelligence (AI)/machine learning technologies, and global data platforms are changing the way in which we approach real-world healthcare challenges. This interdisciplinary unit will introduce students from different backgrounds to the fundamental concepts of data analytics and AI, and their practical applications in healthcare. Throughout the unit, students will learn about the key concepts in data analytics and AI techniques, and obtain hands-on experience in applying these techniques to a broad range of healthcare problems. At the same time, they will develop an understanding of the ethical considerations in health data analytics and AI, and how their use impacts society: from the patient, to the doctor, to the broader community. A key element of the learning process will be a team-based Datathon project where students will deploy their knowledge to address an open-ended healthcare problem, in particular developing a practical solution and analysing how it's use may change things in the healthcare domain. Upon completion of this unit, students will understand and be able to enlist data analytics and AI tools to design solutions to healthcare problems.

The aim of this unit is to develop a strong mathematical and conceptual foundation in the methods of statistical inference, which underlie many of the methods utilised in subsequent units of study, and in biostatistical practice. The unit provides an overview of the concepts and properties of estimators of statistical model parameters, then proceeds to a general study of the likelihood function from first principles. This will serve as the basis for likelihood-based methodology, including maximum likelihood estimation, and the likelihood ratio, Wald, and score tests. Core statistical inference concepts including estimators and their ideal properties, hypothesis testing, p-values, confidence intervals, and power under a frequentist framework will be examined with an emphasis on both their mathematical derivation, and their interpretation and communication in a health and medical research setting. Other methods for estimation and hypothesis testing, including a brief introduction to the Bayesian approach to inference, exact and non-parametric methods, and simulation-based approaches will also be explored.

The aim of this unit is to enable students to apply methods based on linear models to biostatistical data analysis, with proper attention to underlying assumptions and a major emphasis on the practical interpretation and communication of results. This unit will cover: the method of least squares; regression models and related statistical inference; flexible nonparametric regression; analysis of covariance to adjust for confounding; multiple regression with matrix algebra; model construction and interpretation (use of dummy variables, parametrisation, interaction and transformations); model checking and diagnostics; regression to the mean; handling of baseline values; the analysis of variance; variance components and random effects.
NOTE: Linear Models is an important foundation unit. Students who do not develop a strong grasp of this material will struggle to become successful biostatisticians.

This unit will focus on applying the calculus-based techniques learned in Mathematical Background for Biostatistics (MBB) to the study of probability and statistical distributions. These two units, together with the subsequent Principles of Statistical Inference (PSI) unit, will provide the core prerequisite mathematical statistics background required for the study of later units in the Graduate Diploma or Masters degree. Content: This unit begins with the study of probability, random variables, discrete and continuous distributions, and the use of calculus to obtain expressions for parameters of these distributions such as the mean and variance. Joint distributions for multiple random variables are introduced together with the important concepts of independence, correlation and covariance, marginal and conditional distributions. Techniques for determining distributions of transformations of random variables are discussed. The concept of the sampling distribution and standard error of an estimator of a parameter is presented, together with key properties of estimators. Large sample results concerning the properties of estimators are presented with emphasis on the central role of the Normal distribution in these results. General approaches to obtaining estimators of parameters are introduced. Numerical simulation and graphing with Stata is used throughout to demonstrate concepts.

This unit introduces Business School HDR students to quantitative techniques for research. It provides students with a review or introduction to the types of quantitative analyses that they may be required to know, discuss or conduct, both during their PhD and in their future working lives. It aims to provide a basic training with a focus on statistical and business analysis methods.

This unit provides students with an introduction to advanced quantitative analysis techniques that they may be required to know, discuss or conduct, both during their PhD and in their future working lives. The unit is divided into four segments. The first segment reviews basic quantitative methods covered in BUSS7902 before considering issues around estimation and forecasting. Focus then switches to approaches for dealing with repeated measures including panel estimation methods and time series analysis, before consideration of ANOVA techniques and analogous non-parametric methods. Consideration is then given to the most widely used multivariate methods including factor analysis, multiple discriminant analysis, cluster analysis and structural equation modelling. The final segment covers categorical and discrete choice data analysis covering both the theory and practice of designing choice experiments and conducting sophisticated logit modelling applications. The unit covers both the theory and application of the various techniques with hands-on lab-based sessions and assignments crucial to the quality of the learning experience.

The objective of this unit is to provide students with fundamental knowledge of finite element analysis and how to apply this knowledge to the solution of civil engineering problems at intermediate and advanced levels.
At the end of this unit, students should acquire knowledge of methods of formulating finite element equations, basic element types, the use of finite element methods for solving problems in structural, geotechnical and continuum analysis and the use of finite element software packages. The syllabus comprises introduction to finite element theory, analysis of bars, beams and columns, and assemblages of these structural elements; analysis of elastic continua; problems of plane strain, plane stress and axial symmetry; use, testing and validation of finite element software packages; and extensions to apply this knowledge to problems encountered in engineering practice.
On completion of this unit, students will have gained the following knowledge and skills:
1. Knowledge of methods of formulating finite element equations. This will provide students with an insight into the principles at the basis of the FE elements available in commercial FE software.
2. Knowledge of basic element types. Students will be able to evaluate the adequacy of different elements in providing accurate and reliable results.
3. Knowledge of the use of finite element methods for solving problems in structural and geotechnical engineering applications. Students will be exposed to some applications to enable them to gain familiarity with FE analyses.
4. Knowledge of the use of finite element programming and modeling.
5. Extended knowledge of the application of FE to solve civil engineering problems.

The unit develops the basic principles of data description and analysis, the idea of using the concept of probability to model data generation, and the statistical concepts of estimation and statistical inference, including hypothesis testing. It then develops these concepts and techniques in the context of the linear regression model to show how econometric models can be used to analyse data in a wide range of potential areas of application in economics, business and the social sciences. The unit combines theory and application. The emphasis is upon the interpretation of econometric estimation results and requires software for hands-on experience.

This unit of study aims to enhance mathematical ability to provide a skill set that enables students to thrive in their study of economics. Themes such as algebra, the plotting of points, lines, and functions in two and three dimensional space, differential calculus and simultaneous equations are the basis on which the skills are taught.

This unit is an introduction to mathematical economics. It has three purposes. First, to introduce students to the mathematical concepts and methods that are central to modern economics. Second, to give a set of economic applications of the mathematical methods. Third, to develop the students' ability to formulate logical arguments with the degree of precision and rigour demanded in modern economics. The mathematical topics covered include introductory analysis and topology, convex analysis, linear algebra, calculus of functions of several variables, optimisation, and introduction to dynamic programming and dynamical systems.

This unit introduces students to the basic principles and procedures of quantitative research. Both experimental and survey research strategies are considered; starting with design and development of the research tools (measures, questionnaires, interviews, observation) and progressing to basic analytical statistical methods. The unit provides a thorough introduction to simple statistics and often looks at real research data examples. By the end of the semester students will have developed various research skills as well as a critical perspective on the appropriate application of those skills.

This unit introduces students to the principles and foundations of health research methodologies and ethics. Students will learn about the main methodologies used to conduct research that is scientifically and ethically sound and be able to critically appraise and review literature. We will introduce common study designs and research methodologies, including qualitative, epidemiologic and clinical studies, and discuss their strengths and limitations. We will introduce students to the main principles of conducting data analysis and the basis to choose amongst different statistical methods. Obtaining ethics approval is necessary for any study involving the collection or analysis of data involving humans, animals or their tissues. Hence, in this unit we will cover ethics in research and when and how to apply for ethics approval. Students will also learn about main concepts in health economics and economical evaluations of interventions and health policies.

This unit introduces students to statistical methods relevant in medicine and health. Students will learn how to build datasets and basic data management procedures, summarise and visualise data, choose the correct statistical analysis, conduct this analysis using statistical software, interpret its results, and report statistical findings in a format suitable for inclusion in scientific publications. Students will also learn to consider the difference between statistical significance and practical importance, and how to determine the appropriate sample size when planning a research study. Specific analysis methods covered in this unit include: descriptive methods; hypothesis tests for one sample, paired samples and two independent groups for continuous and categorical data; correlation and linear regression; power and sample size estimation for simple studies. All these topics are introduced with an emphasis on practical application and interpretation and are supported using statistical software. The general principles developed in this unit can be easily extended to more advanced methods; students who wish to continue with their statistical learning after this unit are encouraged to take PUBH5217 Biostatistics: Statistical Modelling.

This unit of study introduces you to qualitative research in health. It is designed for beginners and people who want an advanced level introduction. We will examine core concepts like methodology and reflexivity; consider approaches to research design (including sampling and developing research questions), data collection (including interviewing, focus group, observation, visual methods) and analysis; and discuss frameworks for thinking about research ethics and research quality. You will get practical experience in research design, data collection, data analysis and evaluating published qualitative literature. Throughout we will consider the value of qualitative approaches for constructing knowledge about health and hear from working qualitative researchers about how they use qualitative methods in their work.

This advanced unit of study extends students' practical and theoretical knowledge of qualitative research to provide advanced concepts and skills in qualitative data analysis and writing. We will explore the principles of qualitative analysis, review different analytic strategies and key analytic tools. You will learn how to develop codes and themes, use memos and analytic maps, and interpret data through the process of writing. You will learn about starting writing, structuring articles, making analytic arguments, and editing your own work. Throughout, we will consider what it means to think and write 'qualitatively'. Students will conduct a Thematic Analysis on a portfolio of qualitative data and produce a results and discussion section for a journal article. After completing this unit, you will have increased your experience, skills and confidence in qualitative data analysis and writing.

Algebra is one of the broadest fields of mathematics, underlying most aspects of mathematics. It is sometimes considered "the mathematics of symmetry" or the "language of mathematics". In its most general description, algebra includes number theory, algebraic geometry and the classical study of algebraic structures such as rings and groups as well as their representations. Advanced algebra intersects other fields of modern mathematics, for instance via algebraic topology, homological algebra and categorical representation theory; and modern physics, via Lie groups and Lie algebras. You will learn about fundamental concepts of a branch of advanced algebra and its role in modern mathematics and its applications. You will develop problem-solving skills using algebraic techniques applied to diverse situations. Learning an area of pure mathematics means building a mental framework of theoretical concepts, stocking that framework with plentiful examples with which to develop an intuition of what statements are likely to be true, testing the framework with specific calculations, and finally gaining the deep understanding required to create technically sophisticated proofs of general results. The selection of topics is guided by their relevance for current research. Having gained an abstract understanding of symmetry, you will discover the manifestation of algebraic structures everywhere!

"Mathematical modelling applies mathematical frameworks, such as ordinary and partial differential equations, to capture the dynamics of natural phenomena, including fluid dynamics, Newtonian and relativistic mechanics, climate, ecology, and physiology. Modelling often falls into two styles, mechanistic and phenomenological. Mechanistic modelling seeks to understand how large-scale phenomena are driven by simple, local dynamics usually governed by physical or biological laws or properties. On the other hand, phenomenological modelling seeks to capture large-scale trends of a system, such as growth, decay, and oscillations, without necessarily accounting for smaller-scale dynamics. In practice, most models combine elements of both styles. In this unit you will learn about how these mathematical frameworks are constructed and applied for particular types of phenomena which may include mathematical oncology, high Reynolds number fluid flow, stellar atmosphere, terrestrial climates, populations of cells or organisms or other areas of mathematical interest. You will analyse both classical and new models and critique their applicability and use their predictions to explore aspects of the natural world. Inspired by these ideas, you will have the opportunity to create new models in tutorials and assignments and to use them to solve complex mathematical and scientific problems. By doing this unit, you will learn how mathematics is applied in both simple and complicated models and explore the ways that mathematical analysis creates insight into natural phenomena. "

Data comes in many and varied formats, it can be tall or wide, big or small, structured or unstructured. Regardless of where you get your data from, it will almost always require some wrangling. Data wrangling is the convolution, alignment and preparation of data before use. This unit provides an overview of best practices in organising your research data from the point of discovery through to its use for scientific applications. You will learn the principles of data handling and how to maintain rigour and integrity of your data throughout your research, including documenting data provenance, how to access major databases, and data licensing. After calculating summary statistics to aid in the identification of outliers and missing values, you will learn how to clean and wrangle data in a reproducible manner in R, at a variety of scales. You will "wrangle" your research data using R, identifying outliers and missing values and ensuring provenance.

Linear models form the bedrock of many real-world data analyses. They are versatile, interpretable and easily implemented. This unit provides an overview of two of the most common methods of statistical analysis of data: analysis of variance and regression. You will generate data visualisation and diagnostics plots to interpret and discover the limitations of linear models and identify when more complex approaches may be needed. You will learn to code your analyses and perform reproducible research using the open source statistical package R. A key component of this unit involves generating visualisations, estimating and selecting appropriate linear models using your data. By doing this unit you will learn how to generate, interpret, visualise, discover and critique linear models applied to your original research.

When undertaking research and critically judging the research of others with many variables, a key approach is use of multivariate data analysis. This online unit provides comprehensive skills essential for postgraduate students doing multivariate data analysis and for critically judging the research of others. We focus on the underlying principles you need to explore multivariate data sets and test hypotheses. In so doing, the unit provides you with an understanding of how multivariate research is designed, analysed and interpreted using statistics. The unit will cover the commonly used multivariate data analyses of principal components analysis, cluster analysis, discriminant functions analysis and non-metric multidimensional scaling, as well as parametric and permutational hypothesis testing techniques. Examples of data will be cross-disciplinary, enabling students from many disciplines to appreciate the techniques. Analyses will use the R statistical environment, furthering student skills in this programming environment. By doing this unit, you will be able to use multivariate data analyses using a wide-range of data and present in a format for publication.

Throughout our lives, information about our health and the care we receive is recorded and stored across various health-related databases, e.g., hospital admissions, ambulance service, cancer registry. Data linkage is a process that brings together information from different databases about the same individual, family, place or event. This process creates a chronological sequence of health events or individual 'health story' that can be combined into a much larger story about the health of people. This information can be used for research or to improve health services. This unit is suitable for health services researchers, policy makers, clinical practitioners, biostatisticians and data managers. We explain how data linkage is conducted, illustrate how data linkage can be used for research, highlighting the advantages, and the dangers and pitfalls. We describe how to design linked data studies, outline the data management steps required before analysing the data, and discuss some of the methods and issues of analysing linked data. Students will have access to data from a real data linkage and will gain hands-on experience to develop their programming skills for handling large complex dataset

In this unit, you will learn how to analyse health data using statistical models. In particular, how to fit and interpret the results of different statistical models which are commonly used in medicine and health research: linear models, logistic models, and survival models. This unit is ideal for those who wish to further develop their research skills and/or improve their literacy in reading and critiquing journal articles in medicine and health.
The focus of the unit is very applied and not mathematical. Students gain hands on experience in fitting statistical models in real data. You will learn how to clean data, build an appropriate model, and interpret results. This unit serves as a prerequisite for PUBH5218 Advanced Statistical Modelling.

This unit combines decision theory and more advanced health economic concepts to provide students with hands-on skills in specialised analysis methods, and modelling techniques, for evaluating healthcare options and reaching recommendations in the face of uncertainty. Students will calculate and analyse data from clinical studies, extrapolate clinical study results to other settings, and construct models that synthesise evidence (and expert opinion) from multiple sources. Specific topics of study include: decision trees; expected utility theory; sensitivity and threshold analysis; the value of information (including screening and diagnostic tests); the calculation and analysis of costs and quality-adjusted survival using individual patient data (including bootstrapping techniques); Markov processes and micro-simulation; and presenting and interpreting the results of (health economic) evaluations. Lectures are accompanied by practical exercises and readings. Students gain experience applying the methods presented in lectures via computer practicals using Excel and decision analysis software (TreeAge).

Quantitative methods are vital to social science. This unit introduces students to commonly used techniques for collecting and analysing numerical data to answer empirical questions about social, cultural, and political phenomena. It addresses the description of data with graphs and tables, descriptive statistics, statistical models, hypothesis testing, and other topics. The unit is appropriate for beginners, who will gain perspective and confidence conducting their own quantitative research and critically understanding that of others. It is taught in a computer lab, giving students practical experience with statistical software.

Social science research abounds with data of different nature, sources, and forms. In many situations, available data can be summarised and analysed quantitatively to identify trends, uncover patterns, or test hypotheses. This unit presents fundamental ideas behind modern data analytics and provides students with hands-on experience of analysing social science data. First, we cover data manipulation, data cleaning, and basic visualisation. We will then move on to the methods of exploratory data analysis and finding patterns in data. The unit will conclude with an introduction to statistical inference, linear regression analysis and its limitations for causal analysis.

The rise of big data, mobile phones, digital media, and other new ICT has not only affected the way we live and created new social phenomena worth of studying, but has also enabled social scientists to address a variety of important social science questions using new data, methods, and approaches. This unit serves as an introduction to the emerging field of the Computational Social Sciences. We are going to learn how to collect digital data via web scraping and how to analyse it using a variety of methods developed for computational text and network analysis.

The aim of the unit is to introduce students to basic statistical concepts and methods for further studies. Particular attention will be paid to the development of methodologies related to statistical data analysis and Data Mining. A number of useful statistical models will be discussed and computer oriented estimation procedures will be developed. Smoothing and nonparametric concepts for the analysis of large data sets will also be discussed. Students will be exposed to the R computing language to handle all relevant computational aspects in the course.