Sophisticated computer programs known as geographic information systems (GISs) have revolutionized the analysis of spatially referenced datasets, through their ability to ``layer'' multiple data sources over a common study area. However, methods for statistical inference on these complex datasets are only now beginning to develop. In this proposal we develop statistical methodology in five specific aim areas related to cancer control and epidemiology. First, we develop hierarchical predictive process approaches to easing the problems associated with the need to repeatedly invert large matrices in fitting geostatistical models to large datasets. Second, we propose new methods for handling multivariate marked point processes, as would be required for a spatial point pattern where the points are marked by the type of cancer or perhaps treatment selection of each individual. Third, we consider semiparametric hierarchical models for cancer survival data using mixtures of Polya trees. Fourth, we consider the analysis of continuous-time spatiotemporal data arising from longitudinal experiments designed to estimate functional relationships. Fifth, describe a suite of R packages that help integrate necessary georeferenced database and display components with hierarchical modeling capability, thus bringing the hierarchical spatial analysis we propose to a far broader potential audience than is currently possible. We provide several cancer-related examples to illustrate the methods we propose.
The relevance of this work to public health lies in its ability to improve the understanding and decision-making abilities of state-based professionals engaged in planning for comprehensive cancer control programs. Our focus is squarely on real problems in cancer research, including determining whether women with breast cancer who live further from radiation treatment facilities are significantly more likely to opt for mastectomy over breast conserving surgery (``lumpectomy""""""""), and investigating the change in estimated UV exposure levels over time by geographic region, and whether these levels are associated with higher rates of skin cancer. ? ? ?
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