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Spatial Linear Mixed Effects Modelling for OCT Images: SLME Model^{†}

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Department of Eye and Vision Science, Institute of Life Course and Medical Sciences, University of Liverpool, a Member of Liverpool Health Partners, Liverpool L7 8TX, UK

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St Paul’s Eye Unit, Liverpool University Hospitals NHS Foundation Trust, a Member of Liverpool Health Partners, Liverpool L7 8XP, UK

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Department of Health Data Science, Institute of Population Health, University of Liverpool, a Member of Liverpool Health Partners, Liverpool L69 3GL, UK

^{4}

Department of Applied Mathematics, Liverpool John Moores University, Liverpool L3 3AF, UK

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Author to whom correspondence should be addressed.

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This paper is an extended version of our paper published in: Zhu, W.; Ku, J.Y.; Zheng, Y.; Knox, P.; Harding, S.P.; Kolamunnage-Dona, R.; Czanner, G. Spatial Modelling of Retinal Thickness in Images from Patients with Diabetic Macular Oedema. Annual Conference on Medical Image Understanding and Analysis. Springer: Cham, Switzerland, 2019; pp. 114–126.

Received: 28 April 2020 / Revised: 27 May 2020 / Accepted: 30 May 2020 / Published: 5 June 2020

(This article belongs to the Special Issue MIUA2019)

Much recent research focuses on how to make disease detection more accurate as well as “slimmer”, i.e., allowing analysis with smaller datasets. Explanatory models are a hot research topic because they explain how the data are generated. We propose a spatial explanatory modelling approach that combines Optical Coherence Tomography (OCT) retinal imaging data with clinical information. Our model consists of a spatial linear mixed effects inference framework, which innovatively models the spatial topography of key information via mixed effects and spatial error structures, thus effectively modelling the shape of the thickness map. We show that our spatial linear mixed effects (SLME) model outperforms traditional analysis-of-variance approaches in the analysis of Heidelberg OCT retinal thickness data from a prospective observational study, involving 300 participants with diabetes and 50 age-matched controls. Our SLME model has a higher power for detecting the difference between disease groups, and it shows where the shape of retinal thickness profiles differs between the eyes of participants with diabetes and the eyes of healthy controls. In simulated data, the SLME model demonstrates how incorporating spatial correlations can increase the accuracy of the statistical inferences. This model is crucial in the understanding of the progression of retinal thickness changes in diabetic maculopathy to aid clinicians for early planning of effective treatment. It can be extended to disease monitoring and prognosis in other diseases and with other imaging technologies.