An analysis of the areas occupied by vessels in the ocular surface of diabetic patients: an application of a nonparametric tilted additive model

Farzaneh Boroumand, Mohammad Taghi Shakeri*, Touka Banaee, Hamidreza Pourreza, Hassan Doosti*

*Corresponding author for this work

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(1) Background: As diabetes melllitus (DM) can affect the microvasculature, this study evaluates different clinical parameters and the vascular density of ocular surface microvasculature in diabetic patients. (2) Methods: In this cross-sectional study, red-free conjunctival photographs of diabetic individuals aged 30–60 were taken under defined conditions and analyzed using a Radon transform-based algorithm for vascular segmentation. The Areas Occupied by Vessels (AOV) images of different diameters were calculated. To establish the sum of AOV of different sized vessels. We adopt a novel approach to investigate the association between clinical characteristics as the predictors and AOV as the outcome, that is Tilted Additive Model (TAM). We use a tilted nonparametric regression estimator to estimate the nonlinear effect of predictors on the outcome in the additive setting for the first time. (3) Results: The results show Age (p-value = 0.019) and Mean Arterial Pressure (MAP) have a significant linear effect on AOV (p-value = 0.034). We also find a nonlinear association between Body Mass Index (BMI), daily Urinary Protein Excretion (UPE), Hemoglobin A1C, and Blood Urea Nitrogen (BUN) with AOV. (4) Conclusions: As many predictors do not have a linear relationship with the outcome, we conclude that the TAM will help better elucidate the effect of the different predictors. The highest level of AOV can be seen at Hemoglobin A1C of 9% and AOV increases when the daily UPE exceeds 600 mg. These effects need to be considered in future studies of ocular surface vessels of diabetic patients.

Original languageEnglish
Article number3735
Pages (from-to)1-14
Number of pages14
JournalInternational Journal of Environmental Research and Public Health
Issue number7
Publication statusPublished - 1 Apr 2021

Bibliographical note

Copyright the Author(s) 2021. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • diabetes
  • ocular surface
  • area occupied by vessels
  • metabolic syndrome
  • generalized additive model
  • nonparametric regression
  • tilted estimator
  • bootstrap confidence band


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