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

Abstract

Spatio-temporal count data relating to a set of non-overlapping areal units are prevalent in many fields, including epidemiology and social science. The spatial autocorrelation inherent in these data is typically modelled by a set of random effects that are assigned a conditional autoregressive prior distribution, which is a special case of a Gaussian Markov random field. The autocorrelation 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 either a static or a temporally varying neighbourhood matrix for the data that better represents its spatial correlation structure, by viewing the areal units as the vertices of a graph and the neighbour relations as the set of edges. The improved estimation performance of our methodology compared to the commonly used border sharing rule is evidenced by simulation, before the method is applied to a new respiratory disease surveillance study in Scotland between 2011 and 2017.

Identifying boundaries in spatially continuous risk surfaces from spatially aggregated disease count data

“…However, if this is not the case then it suggests that IZ-level inference is not appropriate for these data. Finally, we note that existing methods such as Lee, Meeks and Pettersson (2021) are not able to answer questions 1 -3 for our study, firstly because of the IZ border changes in 2012 causing spatial misalignment in the areal units over time, and secondly because it only delivers IZ-level inference. }, where k denotes the IZ and t denotes the year.…”

“…Aims and questions of interest. This paper is motivated by a new study of respiratory hospitalisation risk in Glasgow, Scotland, between 2008, which extends Lee and Mitchell (2013 and Lee, Meeks and Pettersson (2021) by using data for a longer time period that crosses the IZ border changes in 2012. The overarching aim is to estimate the spatiotemporal variation in disease risk and the locations of risk boundaries across the city, and we specifically focus on the following questions.…”

“…The areal units used in this study and in the two previous studies listed above are Intermediate Zones (IZ), which have an average population of around 4,000 people. Assumptions (i) and (ii) maybe unrealistic for areal units comprising around 4,000 people, and if they are then this would adversely affect the accuracy of the risks and boundaries estimated by Lee and Mitchell (2013) and Lee, Meeks and Pettersson (2021). Furthermore, the IZ borders were spatially redrawn in 2012 following the 2011 UK census, which means that areal unit level inference, such as that conducted by the above studies would not be comparable before and after this boundary change.…”

“…For example, Banerjee and Gelfand (2006) propose curvilinear boundary detection for point-level data, Qu, Bradley and Niu (2021) extend this to multivariate and multiscale data, while Syring and Li (2017) identify boundaries in an image of pixels. For areal unit level data Ma, Carlin and Banerjee (2010), Lee and Mitchell (2012), Berchuck, Mwanza and Warren (2019) and Lee, Meeks and Pettersson (2021) identify boundaries by jointly modelling disease risk and the underlying neighbourhood structure of the areal units utilising conditional autoregressive (CAR) priors.…”

“…This paper aims to estimate the spatial locations and temporal evolution of boundaries in the risk of hospitalisation due to respiratory disease across the city of Glasgow, Scotland, so that the spatial extents of high-risk areas can identified allowing resources to be targeted at areas with the greatest need. Glasgow is chosen for our study because it exhibits large health inequalities (http://www.healthscotland.scot/ health-inequalities/), which has led Lee and Mitchell (2013) and Lee, Meeks and Pettersson (2021) to identify numerous risk boundaries between geographically adjacent areal units. However, as these studies undertake inference on the areal unit level they implicitly assume that: (i) disease risk is constant within each areal unit; and (ii) the risk boundaries must coincide with the geographical borders separating neighbouring areal units.…”