Iterative estimating equations for disease mapping with spatial zero‐inflated Poisson data

Spatial epidemiology often involves the analysis of spatial count data with an unusually high proportion of zero observations. While Bayesian hierarchical models perform very well for zero‐inflated data in many situations, a smooth response surface is usually required for the Bayesian methods to converge. However, for infectious disease data with excessive zeros, a Wombling issue with large spatial variation could make the Bayesian methods infeasible. To address this issue, we develop estimating equations associated with disease mapping by including over‐dispersion and spatial noises in a spatial zero‐inflated Poisson model. Asymptotic properties are derived for the parameter estimates. Simulations and data analysis are used to assess and illustrate the proposed method.