Abstract
With increasing accessibility to geographic information systems (GIS) software, statisticians and data analysts routinely encounter scientific data sets with geocoded locations. This has generated considerable interest in statistical modeling for location-referenced spatial data. In public health, spatial data routinely arise as aggregates over regions, such as counts or rates over counties, census tracts, or some other administrative delineation. Such data are often referred to as areal data. This review article provides a brief overview of statistical models that account for spatial dependence in areal data. It does so in the context of two applications: disease mapping and spatial survival analysis. Disease maps are used to highlight geographic areas with high and low prevalence, incidence, or mortality rates of a specific disease and the variability of such rates over a spatial domain. They can also be used to detect hot spots or spatial clusters that may arise owing to common environmental, demographic, or cultural effects shared by neighboring regions. Spatial survival analysis refers to the modeling and analysis for geographically referenced time-to-event data, where a subject is followed up to an event (e.g., death or onset of a disease) or is censored, whichever comes first. Spatial survival analysis is used to analyze clustered survival data when the clustering arises from geographical regions or strata. Illustrations are provided in these application domains.