Bayesian spatial and temporal methods for public health data

Abstract

In this thesis, we develop flexible models to analyze public health data in time and/or in space. The development of our methodology is motivated by two examples: cancer incidence data in Washington State and birth outcome data in North Carolina. First, we describe a temporal cancer incidence model and demonstrate how to use this model to forecast incidence for future years, identify the relevant time scales on which disease incidence changes, and estimate the effects of screening rates and tobacco use on female breast cancer and male lung cancer. In the next chapter, we introduce the negative G-Wishart prior for the covariance matrix of Gaussian spatial random effects. We show via a simulation study that this new prior has advantages over the more rigid Gaussian Markov random field (GMRF) priors, and we apply this new prior in a multivariate setting using the cancer incidence data. Finally, we use binary trees together with graphical log-linear models to capture spatial interactions as well as interactions between outcomes in sets of spatially dependent binary tables. This approach is illustrated using the North Carolina data.