Computationally efficient localised spatial smoothing of disease rates using anisotropic basis functions and penalised regression fitting

Lee, D. (2024) Computationally efficient localised spatial smoothing of disease rates using anisotropic basis functions and penalised regression fitting. Spatial Statistics, 59, 100796. (doi: 10.1016/j.spasta.2023.100796)

Abstract

The spatial variation in population-level disease rates can be estimated from aggregated disease data relating to N areal units using Bayesian hierarchical models. Spatial autocorrelation in these data is captured by random effects that are assigned a Conditional autoregressive (CAR) prior, which assumes that neighbouring areal units exhibit similar disease rates. This approach ignores boundaries in the disease rate surface, which are locations where neighbouring units exhibit a step-change in their rates. CAR type models have been extended to account for this localised spatial smoothness, but they are computationally prohibitive for big data sets. Therefore this paper proposes a novel computationally efficient approach for localised spatial smoothing, which is motivated by a new study of mental ill health across N = 32,754 Lower Super Output Areas in England. The approach is based on a computationally efficient ridge regression framework, where the spatial trend in disease rates is modelled by a set of anisotropic spatial basis functions that can exhibit either smooth or step change transitions in values between neighbouring areal units. The efficacy of this approach is evidenced by simulation, before using it to identify the highest rate areas and the magnitude of the health inequalities in four measures of mental ill health, namely antidepressant usage, benefit claims, depression diagnoses and hospitalisations.

• Item Type: Articles
• Keywords: Anisotropic spatial basis functions, big data disease mapping, mental ill health, ridge regression.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Lee, Professor Duncan
• Authors: Lee, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Spatial Statistics
• Publisher: Elsevier
• ISSN: 2211-6753
• ISSN (Online): 2211-6753
• Published Online: 29 November 2023
• Copyright Holders: Copyright © 2023 The Author
• First Published: First published in Spatial Statistics 59: 100796
• Publisher Policy: Reproduced under a Creative Commons License