Bayesian nonparametric modeling for disease incidence data

Disease incidence or mortality data are routinely recorded as summary counts for contiguous geographical regions (e.g., census tracts, zip codes, districts, or counties) and collected over discrete time periods. The count responses are typically accompanied by covariate information associated with the region (e.g., median family income, or percent with a specific type of education), and occasionally, by covariate information associated with each incidence case (e.g., sex, race, age), even though we only know the region into which the case falls. A key inferential objective in the analysis of disease incidence data is identification and explanation of spatial and spatio-temporal patterns of disease risk (disease mapping). Also of interest is forecasting of disease risk. The statistical literature of the past twenty five years or so has witnessed a growing emphasis on fairly sophisticated methods to model heterogeneity in disease event rates. Most of the methodology has been developed within a hierarchical framework through introduction of spatial and spatio-temporal models tailored to the disease mapping inference goals. In this context, the Bayesian approach to modeling and inference is naturally attractive. In this chapter, we review Bayesian nonparametric spatial and spatio-temporal modeling approaches for disease incidence data. Section 2 provides the necessary background on nonparametric priors, mainly the Dirichlet process prior, and its extension to spatial Dirichlet process models. Bayesian nonparametric work has focused on modeling methods for the stochastic mechanism that generates the region-specific count responses, and this is where we place the emphasis in this review, providing only brief discussion on modeling the covariate information. We thus focus on distributional specifications for the disease incidence counts (number of observed cases of the disease). These count responses are denoted by yit, where i = 1, ...,m indexes the geographic regions Ai, and t = 1, ..., T indexes the (discrete) time periods. Note that although cases occur at specific spatial point locations, the available responses are associated with entire ∗Athanasios Kottas ([email protected]) is Professor, Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA, 95064, USA. The author wishes to thank Andrew Lawson and Sudipto Banerjee for the invitation to write this book chapter, as well as a reviewer for useful feedback. This work was supported in part by the National Science Foundation under award DMS 1310438.