Spatial and spatiotemporal point process modelling in epidemiology : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Manawatu, New Zealand, December, 2011

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Massey University
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Geographical epidemiology encapsulates those problems that aim to understand space and/or space time trends in the disease(s) of interest, a goal clearly important in both public health and economic contexts. The increasing availability of point-location, coordinate data for studies in geographical epidemiology calls for a greater scrutiny of statistical point process theory with respect to these applications. Though the statistical analysis of planar point patterns is now theoretically well-established, there remain many aspects which warrant further research, especially from a practical perspective. The need becomes even greater when we consider the relative youth of methods for the analysis of spatiotemporal observations, where non-trivial variation and even dependence throughout the space-time continuum can exist. This work aims to address these issues by careful review, theoretical refinement, empirical testing, and real-world analyses of certain statistical tools used in point process problems in geographical epidemiology. We scrutinise the kernel-smoothed density-ratio estimator of the so called relative risk function, a particularly flexible approach given the anticipated spatial heterogeneity of the observations over a given geographical region. This discussion introduces the adaptive (i.e. variable bandwidth) risk function, as well as novel asymptotic methods for computation of tolerance contours designed to identify sub-regions of statistically significant fluctuations in risk. More sophisticated statistical methodology is warranted in certain situations, where it may be assumed that both ‘global’ heterogeneity and ‘local’ correlation drives the space and/or space-time disease dispersion. A comprehensive review of the stochastic log-Gaussian Cox process, in both purely spatial and spatiotemporal contexts, is conducted. A suite of novel numerical experiments investigate the performance of convenient, yet ad hoc, minimum contrast parameter estimation techniques for the dependence structure of the latent Gaussian process. The computer code arising from the review and refinement of the above methodologies was instrumental in the release of two separate software packages. These are available in the R environment, and also showcased here. A number of additional collaborations with applied researchers around the world serve to further highlight the contributions made throughout the course of this research project and the importance of sound statistical methods in geographical epidemiology.
Epidemiology, Mathematical models, Statistical models, Spatial point process modelling, Spatiotemporal point process modelling, Geographical epidemiology