Bayesian Modeling of Health Data in Space and Time
Bauer, Cici Xi Chen
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In recent years spatial-temporal modeling has become increasingly popular in the field of public health and epidemiology. Motivated by two datasets, we address three issues in the Bayesian modeling of health data in space and time. The first motivating example is provided by data from the Behavioral Risk Factor Surveillance System (BRFSS). In a survey sampling context we develop a method for incorporating the sampling weights in a complex survey design, within a spatial smoothing model. A simulation study is presented to demonstrate the performance of the proposed approach and to compare results from models with and without the sampling weights. The results show that mean squared error can be greatly reduced using the proposed model, when compared with standard approaches. Bias reduction occurs through the incorporation of sampling weights, with variance reduction being achieved through hierarchical spatial smoothing. The second motivating example concerns the surveillance data for Hand-Foot-Mouth disease (HFMD) collected in China between 2009 and 2010. The overall strategy we take is to decompose the log relative risk of disease into three components: a large-scale temporal trend, a large-scale spatial trend and a spatial-temporal interaction. We fit the model in a Bayesian framework and the structure of the interaction between space and time is imposed through a prior on the coefficients of the basis functions, which are constructed as a tensor product of cubic B-splines. This model is amenable to prediction through the use of Gaussian Markov Random Field (GMRF) space-time priors. Finally, we consider the situation in which a disease can be caused by multiple virus strains. The data we analyze again concern HFMD in China and contain total disease counts along with a limited amount of strain-specific information gathered on a subset of individuals. We propose a Bayesian hierarchical model that provides a coherent approach to estimating the total number of cases by strain. When data is available for multiple areas and time points, the spatial and temporal variability can again be modeled via smoothing priors. The model can also be extended to accommodate multiple virus strains or multiple clinically-diagnosed severity categories.
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