Spatial regression and estimation of disease risks: A clustering-based approach

Detection of clustering and estimation of incidence risks are important and useful in public health and epidemiological research. The popular spatial regression models for disease risks, such as conditional autoregressive (CAR) models, assume a known spatial dependence structure for the error distribution and a set of common regression parameters for the mean structure. While it is often difficult to justify the structural assumption on spatial dependence, the assumption on a common regression surface may not be practical for a large spatial domain. We conceptualize a study region as a union of spatially connected clusters where a cluster is composed of geographically adjacent regions. We propose a regression model with cluster-wise varying regression parameters. Our model is able to capture a spatial clustering structure, while the corresponding cluster-wise regression parameters are estimated given the estimated clustering configuration. The proposed model is flexible in terms of regional and global shrinking as well as the number of clusters, cluster memberships and cluster locations. We develop an algorithm based on the reversible jump Markov chain Monte Carlo (MCMC) method for model estimation. The numerical study shows effectiveness of the proposed methodology. The method is computationally efficient and thus amenable to large datasets. © 2016 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2016