- Title
- Bayesian spatial modelling of tuberculosis and its effects on socio-economic and demographic factors in South Africa : a case study of the Eastern Cape Province
- Creator
- Obaromi, Abiodun Davies
- Subject
- Tuberculosis -- South Africa -- Eastern Cape Tuberculosis -- Epidemiology -- Statistics
- Date
- 2018
- Type
- Thesis
- Type
- Doctoral
- Type
- PhD
- Identifier
- http://hdl.handle.net/10353/9648
- Identifier
- vital:34813
- Description
- This dissertation is concerned with evolving and extending statistical models in the area of Bayesian spatial modelling, an increasingly important field of spatial epidemiology with particular interest towards application to Tuberculosis data in the Eastern Cape province of South Africa. In spatial epidemiology, the diseases to be examined usually occur within a map that needs spatial statistical methods that are appropriate, to model the observed data in the presence of some covariates and also cater for the variation of the disease. In this thesis, the Bayesian models were developed in such a way that they allowed several factors classified as fixed and random effects, to be included in the models and using the Bayesian approach. The basic model used in disease mapping is the Besag, York and Mollie model, which incorporates two random effects; one which is spatially structured and the other random effect which is spatially unstructured. The effects (fixed and random) were the covariate effects, socio-economic and demographic variability and the spatial variability respectively, which were all investigated in seven different hierarchical/multilevel Bayesian models. These factors showed varying and substantial effects in the posterior relative risk estimation of the disease. We assumed a negative binomial and generalized Poisson distributions to the response variable or relative risk estimate, 𝑦𝑖 ,to capture the over-dispersion phenomenon that is common and inherent with Poisson density for counts data. Spatial and non-spatial models were developed to model over-dispersion with all the distributions; Poisson, negative binomial and generalized Poisson. Negative binomial and generalized Poisson showed varying properties from comparisons with DIC values and parameter estimates to standard errors, which made either of them fit depending on the choice of model selection. It was found that a lower DIC value could be insufficient to determine a best fit model, if other models present estimates with lower variances even at higher DIC values. The generalized Poisson, a two parameter distribution like the negative binomial, which also has the ability to capture both under-dispersion and over-dispersion, was found to perform better in the results than the negative binomial on the basis of a lower variance and with more exact parameter estimates. A new weighted prior distribution, the “Besag2” ICAR model for the structured spatial random effects, which is an extension of the traditional ICAR prior model with two hyperparameters, was also developed and compared with some existing prior models; BYM and ICAR, to measure for spatial dependency in the regions. This new prior distribution was found to show a better fit, when compared to the basic ICAR prior usually assumed for the spatial random effect in the BYM model. This newly parameterized prior distribution in the Besag, York and Mollie model also led to improved parameter control, as the hyperparameters can be seen independently from each other. The result also showed that the new model performed well, both presenting good learning abilities and good shrinkage behaviour. In terms of model choice criteria, the proposed model performed at least equally well and better than the existing models, and the new formulation also gave parameters that are interpretable and have a clearer meaning. To interpolate scattered or regularly distributed data, there are imprecise or exact methods, but there are some of these methods that could be used for interpolating data in a regular grid and others in an irregular grid. Linear and biharmonic spline methods were implemented in MATLAB, to compare for smoothing in the distribution patterns of tuberculosis in the province. This smoothing spline is a method of fitting a smooth curve to a set of noisy observations using a spline function. This new method is rarely used in disease mapping applications, but it has a superior advantage to be assessed at subjective locations rather than only on a rectangular grid as seen in most traditional GIS methods of geospatial analyses. The proposed new models and methods in this thesis were found to be flexible and robust, since they can be reduced or extended according to the nature of the data. Nevertheless, great care must be considered in the choice of prior densities. The approaches developed in this dissertation helped to broaden the scope for spatial analysis and disease mapping applications in epidemiology and public health studies.
- Format
- 183 leaves
- Format
- Publisher
- University of Fort Hare
- Publisher
- Faculty of Science and Agriculture
- Language
- English
- Rights
- University of Fort Hare
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