Bayesian spatial models with application to HIV, TB and STI modeling in Kenya.
This dissertation is concerned with developing and extending statistical models in the area of spatial modeling with particular interest towards application to HIV, TB and HSV-2 data. Hierarchical spatial modeling is a common and useful approach for modeling complex spatially correlated data in many settings in epidemiological, public health and ecological studies. Chapter 1 of this thesis gives a chronological development of disease mapping models, from non-spatial to spatial and from single disease models to multiple disease models. In Chapter 2, a new model that relaxes the over-restrictive normal distribution assumption on the spatially unstructured random effect by using the generalised Gaussian distribution is introduced and investigated. The third chapter provides a framework for including sampling weights into the Bayesian hierarchical disease mapping model. In this model, design effect is used to re-scale the sample sizes. A new model for over dispersed spatially correlated binary data is developed in chapter 4 of this thesis; in this model, the over dispersion parameter is modeled by a beta random effect which is allowed to vary spatially also. In chapter 5, the common multiple spatial disease mapping models are reviewed and adopted for the binary data at hand since the original models were developed based on Poisson count data. The methodologies developed in this dissertation widen the toolbox for spatial analysis and disease mapping in applications in epidemiology and public health studies.
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