A Zero-Inflated Spatial Gamma Process Model With Applications to Disease Mapping

Abstract

In this paper, we introduce a novel discrete Gamma Markov random field (MRF) prior for modeling spatial relations among regions in geo-referenced health data. Our proposition is incorporated into a generalized linear mixed model zero-inflated (ZI) framework that accounts for excess zeroes not explained by usual parametric (Poisson or Negative Binomial) assumptions. The ZI framework categorizes subjects into low-risk and high-risk groups. Zeroes arising from the low-risk group contributes to structural zeroes, while the high-risk members contributes to random zeroes. We aim to identify explanatory covariates that might have significant effect on (i) the probability of subjects in low-risk group, and (ii) intensity of the high risk group, after controlling for spatial association and subject-specific heterogeneity. Model fitting and parameter estimation are carried out under a Bayesian paradigm through relevant Markov chain Monte Carlo (MCMC) schemes. Simulation studies and application to a real data on hypertensive disorder of pregnancy confirms that our model provides superior fit over the widely used conditionally auto-regressive proposition.