Statistical Modelling (Full-time)

Module code: MD7442

This module introduces the theory and application of Linear and Generalised Linear Models. The module covers all stages in the modelling process, from selecting an initial model, through fitting to model checking and then interpretation and communication of the results and at each stage the necessary theory is developed.

In this module we aim to provide students with the tools to answer the following questions:

• How to select an appropriate model given data from a clinical study?
• How to assess whether a model fits data well?
• How to interpret the results of the statistical modelling?

Linear Models

This module will provide a review of basic regression techniques in the context of simple linear regression; introducing the mathematical formulation and software implementations for fitting simple regression models. The module then goes on to include the fundamentals of defining a purpose for a statistical model and also introduces the concepts of model building and model selection. The material also covers the inclusion of different types of covariate data in statistical models and introduces the ideas of statistical interaction and capturing non-linear effects of continuous covariates. We will conclude with further discussion of checking the assumptions of statistical models and talks about practical issues of fitting models in the context of a real-life application.

Generalised Linear Models

We will introducr the theory of Generalised Linear Models (GLMs) in terms of exponential family of distributions and discussing special cases of GLMs, such as normal, Poisson or binomial regression. This will cover identifying elements of GLMs including the canonical and dispersion parameters and the mean and variance and defining the linear predictor, offset and link functions. Selection and checking of a model for a given clinical problem will be discussed in lectures followed by fitting models and running checks for a range of examples using software in computer practical classes. Further extensions will include log-linear models for multinomial distributions, over-dispersion, quasi-likelihood.