# A Spatially Discrete Approximation to Log-Gaussian Cox Processes for Modelling Aggregated Disease Count Data

## TL;DR

This paper introduces a computationally efficient discrete approximation to log-Gaussian Cox processes, enabling continuous spatial prediction of disease risk from aggregated count data, and demonstrates its effectiveness through simulations and real data analysis.

## Contribution

The paper presents a novel discrete approximation to LGCP models that overcomes partition dependence and allows for continuous spatial prediction.

## Key findings

- The approximation provides reliable disease risk estimates on continuous and aggregated scales.
- The method outperforms traditional models in predictive accuracy.
- Implementation is available in the open-source R package SDALGCP.

## Abstract

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.