Improved inference for areal unit count data using graph-based optimisation

TL;DR

This paper introduces a new graph-based optimization method to estimate spatial neighborhood structures in areal unit count data, improving upon traditional border-sharing assumptions, with demonstrated benefits through simulations and real disease data analysis.

Contribution

It presents a novel algorithm for inferring neighborhood matrices from data, enhancing spatial correlation modeling in areal count data.

Findings

Method outperforms border-sharing rule in simulations

Effective in modeling spatial correlation in disease data

Applicable to real-world epidemiological studies

Abstract

Spatial correlation in areal unit count data is typically modelled by a set of random effects that are assigned a conditional autoregressive (CAR) prior distribution. The spatial correlation structure implied by this model depends on a binary neighbourhood matrix, where two random effects are assumed to be partially autocorrelated if their areal units share a common border, and are conditionally independent otherwise. This paper proposes a novel graph-based optimisation algorithm for estimating the neighbourhood matrix from the data, by viewing the areal units as the vertices of the graph and the neighbour relations as the set of edges. The superiority of our methodology compared to using the border sharing rule is comprehensively evidenced by simulation, before the method is applied to a new respiratory disease surveillance study in the Greater Glasgow and Clyde Health board in Scotland between 2011 and 2017.