Developing novel ways to represent spatial patterns in disease risk

Disease mapping is a field of statistics which is interested in identifying the spatial pattern in disease risk across a region. The goal of such analysis is typically to identify high (and low) risk areas and subsequently to investigate the factors which lead to these differences in risk. Understanding the extent of the health inequalities which exist within a region allow public health interventions to be made in the appropriate locations.

This analysis is traditionally carried out via generalised linear mixed models, where the spatial structure of the data is accounted for via the correlation structure of the random effects using what are known as conditional autoregressive (CAR) models. The basic premise of a CAR model is that areas which are closer together geographically are likely to have more in common than those which are further apart, in other words we assume that disease risk is likely to evolve smoothly across our region.

However, this assumption does not always hold in practice, with many cities having more localised patterns of inequality. Here in Glasgow, the suburb of Bearsden to the north of the city has an average life expectancy of 82.3, compared to just 70 in neighbouring Drumchapel. Therefore, the goal of this project will be to identify different ways of representing these spatial patterns within our models to provide more accurate estimation of the disease inequality.

In addition to more traditional statistical approaches, the project will also make use of novel combinatorial algorithms to identify optimal spatial patterns; the relative emphasis on the design of algorithmic techniques and their use to carry out statistical analysis will depend on the background and interests of the student. The project is therefore suitable for a student looking to carry out research in any of statistics, combinatorics, or theoretical algorithm design.