In recent decades, disease mapping has drawn much attention worldwide. Due to the availability of Markov Chain Monte Carlo (MCMC) algorithms, fully Bayesian analysis of complex multistage data has been increasingly popular in the analysis of geographically and temporally referenced data. This dissertation aims to implement hierarchical Bayesian methods to address some issues in disease mapping.;In the Chapters 3 and 4, we analyze spatially referenced longitudinal data of a disease in a multivariate setting. We develop a serially correlated generalized multivariate conditional autoregressive model (SCGMCAR) with different propriety parameters for each time period. We show that introducing different propriety parameters provides a better fit. In addition, we also examine the effect of adjacent areal units in the estimation of the disease rates.;The effect of modeling the expected counts on small area disease mortality or incidence maps is examined in Chapter 5. A common approach in epidemiological studies is to map standardized mortality ratios (SMRs) at various levels of geographic units or socio-demographic subpopulations. Often, SMRs are calculated based on internally or externally standardized reference rates. Such reference rates, however, do not take into account the spatial correlation induced from the geographic proximity of nearby units and the variation in the rates across the units. Instead, we use model-based expected counts. We find that using model-based estimates of the expected counts produce improved disease maps compared to using reference rate-based expected counts.
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