# Statistical Modelling (Part-time)

Module code: MD7467

This module introduces the theory and application of linear models and survival analysis. The module covers all stages in the linear modelling and survival analysis 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

The week will start with 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. The module concludes 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.

## Survival Analysis

Survival analysis is concerned with data where we measure the time to an event. In medicine we are often interested in death, i.e. we want to keep people alive and make them live longer. We thus measure the time (from some suitable starting point) to death. The outcome of interest is the time to an event and we are unlikely to observe the event on all subjects.

• Introduction to Survival Analysis – censoring, the survival function, the Kaplan-Meier estimate, median survival, life-tables
• Comparing Survival Curves - the log rank test, hazard ratio
• Modelling Survival - proportional hazards, exponential model, Weibull model, the Cox model, partial likelihood, tied observations, interpreting regression coefficients
• Model fitting and selection
• Model checking and regression diagnostics for the Cox model