Title: Disease mapping and statistical issues in public health surveillance
Description: As an approach to studying the relationship between an individual's location and occurrence of disease, disease mapping encompasses many techniques, from the simple plotting of cases' locations, like the cholera map of John Snow, to smoothed rates of disease, accounting for the influence of neighboring points and population density. Disease mapping methods aim to estimate a risk surface across a region. In public health surveillance, these methods provide an alternative to detection of clustering or clusters, allowing for fine precision in assessing complex spatial risk patterns. When precise point locations are available, current methods use kernel density estimates, which are not easily applicable to higher dimensions due to the curse of dimensionality. In the first chapter. we develop a distanced-based mapping (DBM) method for point data within the framework of comparing two multidimensional distributions. We propose a non-parametric approach inspired by the dimension reduction concept of tomographic imaging. We show that its accuracy in mapping a dichotomized risk in the unit disk is similar to that of a ratio of kernel density estimates, provided both are implemented with an appropriate choice of parameters. If DBM can generalize to higher dimensions with no increase in the number of parameters, and to arbitrary metric spaces.

Spatial data are often available aggregated by areas. In the second chapter, we adapt the implementation of DBM to such data and present an application to leukemia in upstate New York. Consistent with previous studies, we show that aggregation negatively affects the accuracy of the mapping. Since individuals are mobile, location at diagnosis might not supply the most relevant information. While time and location of exposure are unknown, incorporating residential history of cases has been shown to increase the power of some methods to detect clustering. In the third chapter, we extend DBM to residential history data and show that the accuracy in mapping a dichotomized risk in the unit square is improved, compared to only using location at diagnosis.