TOPICS IN APPLIED STATISTICS - 2021/2

Module code: MATM056

Module Overview

At each presentation of the module several topics involving statistical modelling and statistical methodology will be offered.

Example topics are:

Epidemiology; Generalized Linear Models; Multivariate Statistics; Survival analysis and Bootstrapping.

Statistical software is used to ensure that the emphasis is on methodological considerations rather than on calculation. Computer lab sessions relating to real life situations will reinforce topics covered and, where possible, will use real data.

Module provider

Mathematics

WOLF Martin (Physics)

Module cap (Maximum number of students): N/A

Independent Learning Hours: 108

Lecture Hours: 33

Laboratory Hours: 9

Semester 1

None.

Module content

Indicative content includes:

Epidemiology:

Prevalence. Diagnostic testing – sensitivity and specificity. Receiver Operator Characteristic curves. Odds ratios/relative risk/risk difference – link between OR and RR when prevalence is low. Cross-sectional studies. Longitudinal studies: case-control/cohort.

Generalized Linear Models:

Introduction to generalized linear models. Binary logistic regression with a single categorical predictor. Binary logistic regression for k-way tables. Binary logistic regression with continuous covariates. The Poisson regression model: for count data; for rate data. Model diagnostics. Log-linear models and their use for for two-way and three-way contingency tables.

Multivariate Statistics

Graphical representations of multivariate data. Principal components and correspondence analyses. Use of clustering analysis to identify and characterize subgroups in the population. Classification and discrimination methods to assign individuals to groups. The multivariate normal distribution.

Survival Analysis:

Survival data, types of censoring. Failure times and hazard functions. Accelerated failure time model. Parametric models, exponential, piecewise exponential, Weibull. Nonparametric estimates: the Kaplan-Meier estimator and asymptotic confidence regions. Parametric inference. Survival data with covariates. Proportional hazards. Cox’s model and inference.

Bootstrapping:

Resampling methods for use with single samples from parametric and non-parametric models. Delta methods for variance approximation based on different forms of jackknife. Extension to: several samples; semiparametric and smooth models; data from a finite population; incomplete data through censoring or missing values. Bootstrap diagnostics. Monte Carlo tests, including those using Markov Chain simulation. Parametric bootstrap tests. Construction of confidence intervals.

Assessment pattern

Assessment type Unit of assessment Weighting
Examination Examination 80
Coursework Coursework assignment 20

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Analytical ability by solution of unseen problems in the exam.

• Subject knowledge through the recall of key definitions, theorems and their proofs.

• An understanding of practical considerations when completing the coursework.

• The ability to analyse data, to interpret the analysis and report comprehensively on the results.

Thus, the summative assessment for this module consists of:

• One two hour examination (students have the choice of three questions out of four to contribute to exam mark) at the end of the semester; weighted at 80% of the module mark.

• One coursework; weighted at 20% of the module mark.

Formative assessment and feedback

Students receive written feedback via a number of marked unassessed coursework assignments over an 11 week period. Formative guidance is given on the coursework.

Module aims

• Provide students with a detailed understanding of the principles and methods of several areas of statistical modelling and methodology.
• Give students practical experience of investigating data using statistical software.
• Equip students with the tools and techniques to be able to independently conduct an appropriate statistical analysis using R and provide a systematic report within the range of topics covered.

Learning outcomes

 Attributes Developed 001 Demonstrate systematic understanding of key aspects of some selected topics within modern statistics CK 002 Demonstrate the capability to use established approaches appropriately and accurately to analyse and solve problems in modern statistical modelling and statistical methods. CKPT 003 Apply key aspects of selected topics in statistics in well-defined contexts, showing judgement in the selection and application of tools and techniques. CKP 004 Show judgement in the application of R and in the interpretation of R output. CKT 005 Analyse experimental data and interpret and explain the results in a way comprehensible to a layman. CKPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A comprehensive treatment of principles and methods underlying a selection of statistical topics.

• Experience in problem solving for the cognitive skills.

• Practical experience in statistical analysis and reporting.

The learning and teaching methods include:

• 3 x 1 hour lectures per week x 11 weeks. 1 x 1 hour computer lab session per week for 9 weeks. Students will gain experience in using R to analyse data from experimental designs.

• Assessed coursework to give students practical experience of implementing techniques covered in lectures and lab sessions in an extended piece of work.

• Several pieces of unassessed coursework to give students experience of using techniques introduced in the module and to receive formative feedback.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.