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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Date
2011
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Massey University
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Abstract
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.
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Keywords
Epidemiology, Mathematical models, Statistical models, Spatial point process modelling, Spatiotemporal point process modelling, Geographical epidemiology