Distance based methods for space time modelling of the health of populations

Studying patterns of disease in a population is an important aspect of disease surveillance. The ability to locate clusters of disease helps gain etiologic knowledge of the disease, and can enable direct public health interventions to reduce potential exposures. However, if there is a significant time delay between exposure to a disease causing agent and diagnosis of the disease, the true underlying patterns can be obscured. This thesis introduces a novel method to improve the surveillance of chronic diseases by accounting for this gap in time between an exposure and diagnosis. First, we extend the Al-statistic to detect the difference between the spatial distributions of two samples, such as cases and controls. We demonstrate how this two-sample M can be used to identify clustering in a spatial data set. Next we further extend this statistic to account for several possible locations for each point in a data set. This extension allows for the incorporation of a subject's complete residential history, which addresses the issue of a potential lag between exposure and diagnosis. Through simulations, we demonstrate the significant power gains which are achieved when one analyzes the data, accounting for residential history. The third chapter of this work discusses a method to estimate parameters of the incubation distribution of a disease, once a cluster has been established. The ability to estimate these parameters highlights the value of locating clusters of chronic disease. In the final chapter of this thesis we examine the relationship between the power of the M -statistic and the estimation of the associated variance-covariance matrix.