  In this paper, we develop a computationally efficient discrete approximation
to log-Gaussian Cox process (LGCP) models for the analysis of spatially
aggregated disease count data. Our approach overcomes an inherent limitation of
spatial models based on Markov structures, namely that each such model is tied
to a specific partition of the study area, and allows for spatially continuous
prediction. We compare the predictive performance of our modelling approach
with LGCP through a simulation study and an application to primary biliary
cirrhosis incidence data in Newcastle-Upon-Tyne, UK. Our results suggest that
when disease risk is assumed to be a spatially continuous process, the proposed
approximation to LGCP provides reliable estimates of disease risk both on
spatially continuous and aggregated scales. The proposed methodology is
implemented in the open-source R package SDALGCP.
