Some issues in disease map modelling and surveillance of diseases
The first part of this thesis is dedicated to the study of edge effects in maps of disease. The aim of the analyses is to find out how the estimation of the risk from a disease near boundaries can be affected by the boundary position. The behaviour of a selection of models for disease mapping is evaluated when different edge conditions exist in the data. Disease mapping plays an important role in monitoring the health of a community. Plotting new cases on a map is a frequently used technique for monitoring the spread of infectious diseases and from a statistical point of view it is relevant to consider how statistical methods can be developed or employed to aid the task of surveillance. In the second part of this thesis, methodological and practical issues in developing a rapid response in a spatial surveillance system are discussed. In particular, I review and propose methods for the detection of changes. A simulation study is set up to assess if these methods are good at detecting changes in risk over space and time. An application to a real data set is also given. Surveillance should be performed as quickly as possible but complex Bayesian models require the use of sampling methods to provide estimates of posterior expectations, and these estimates may be computationally expensive to obtain. To aid this, special computational approaches can be considered. One option is to resample the output form initial iterations to provide reweighted estimates as time protocols. This is known a filtration or sequential Monte Carlo. In the third part of this thesis I review the use of sequential Monte Carlo methods (in particular, the Resample-Move algorithm) for dynamic systems, focusing on their use in a surveillance context. This is followed by an application to a real data set where a comparison between the use of McMC methods and the Resample-Move algorithm is carried out.