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The long and short of it: a comprehensive assessment of axial length estimation in myopic eyes from ocular and demographic variables

Eye volume 38, pages 1333–1341 (2024)Cite this article

Subjects

A Correction to this article was published on 29 July 2024

This article has been updated

Abstract

Background/Objectives

Axial length, a key measurement in myopia management, is not accessible in many settings. We aimed to develop and assess machine learning models to estimate the axial length of young myopic eyes.

Subjects/Methods

Linear regression, symbolic regression, gradient boosting and multilayer perceptron models were developed using age, sex, cycloplegic spherical equivalent refraction (SER) and corneal curvature. Training data were from 8135 (28% myopic) children and adolescents from Ireland, Northern Ireland and China. Model performance was tested on an additional 300 myopic individuals using traditional metrics alongside the estimated axial length vs age relationship. Linear regression and receiver operator characteristics (ROC) curves were used for statistical analysis. The contribution of the effective crystalline lens power to error in axial length estimation was calculated to define the latter’s physiological limits.

Results

Axial length estimation models were applicable across all testing regions (p ≥ 0.96 for training by testing region interaction). The linear regression model performed best based on agreement metrics (mean absolute error [MAE] = 0.31 mm, coefficient of repeatability = 0.79 mm) and a smooth, monotonic estimated axial length vs age relationship. This model was better at identifying high-risk eyes (axial length >98th centile) than SER alone (area under the curve 0.89 vs 0.79, respectively). Without knowing lens power, the calculated limits of axial length estimation were 0.30 mm for MAE and 0.75 mm for coefficient of repeatability.

Conclusions

In myopic eyes, we demonstrated superior axial length estimation with a linear regression model utilising age, sex and refractive metrics and showed its clinical utility as a risk stratification tool.

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Fig. 1: The performance of the four newly developed machine learning models (linear regression, gradient boosting, multilayer perceptron, symbolic regression; shown in colour), as well as published axial length prediction algorithms (no colour).
Fig. 2: Relationships between predicted axial length and age in the four machine learning models.
Fig. 3: Impact of estimated or actual anterior chamber depth on prediction accuracy, ability to detect long eyes (>98th centile), accuracy of predicted change over 12 months and ability to detect rapid axial length change.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Change history

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Author information

Authors and Affiliations

  1. Centre for Eye Research Ireland, Environmental Sustainability & Health Institute, Technological University Dublin, Dublin, Ireland

    Gareth Lingham, James Loughman, Siofra Harrington, Emmanuel Kobia-Acquah & Daniel Ian Flitcroft

  2. Ocumetra Ltd., Dublin, Ireland

    Gareth Lingham, James Loughman, Davoud Shariat Panah & Daniel Ian Flitcroft

  3. Centre for Ophthalmology and Visual Science (incorporating the Lions Eye Institute), the University of Western Australia, Perth, WA, Australia

    Gareth Lingham

  4. School of Computer Science, Technological University Dublin, Dublin, Ireland

    Davoud Shariat Panah

  5. School of Physics and Clinical and Optometric Sciences, Technological University Dublin, Dublin, Ireland

    Siofra Harrington

  6. Centre for Optometry and Vision Science, School of Biomedical Sciences, Ulster University, Coleraine, Northern Ireland

    Kathryn J. Saunders

  7. Center for Preventive Ophthalmology and Biostatistics, Department of Ophthalmology, University of Pennsylvania Perelman School of Medicine, Philadelphia, USA

    Gui-Shuang Ying

  8. The First Affiliated Hospital, College of Medicine, Zhejiang University, Hangzhou, People’s Republic of China

    Hongguang Cui

  9. Department of Ophthalmology, Children’s Health Ireland at Temple Street Hospital, Dublin, Ireland

    Daniel Ian Flitcroft

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Contributions

GL, JL, DSP and DIF initiated and designed the study. JL, SH, KJS, GSY, HC, EKA and DIF acquired and collated data for the analysis. GL, DSP and DIF conducted the data and statistical analyses. All authors contributed to the interpretation of data, drafting and critical revision of the manuscript and approved the final version for submission.

Corresponding author

Correspondence to Daniel Ian Flitcroft.

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Competing interests

GL and DSP are employees of Ocumetra, and JL and DIF are co-founders of Ocumetra, a company providing data analytic tools to assist with the clinical management, including an axial length estimation tool. JL is a consultant/contractor for Dopavision, Topcon, EssilorLuxottica and Ebiga Vision and has received funding from Topcon, Ocumension, Kubota Vision, EssilorLuxottica, Vyluma, Dopavision and Coopervision, all in the area of myopia management. DIF is a consultant/contractor for Vyluma, Coopervision, Essilor, Thea, Ocumension and Johnson & Johnson and has received funding from Topcon, Ocumension and Coopervision in the area of myopia control. KJS is in receipt of research funding from HOYA Vision and Vyluma in the area of myopia management.

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The original online version of this article was revised: in equation 1, a − sign was corrected to a + sign before the coefficient for SER.

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Lingham, G., Loughman, J., Panah, D.S. et al. The long and short of it: a comprehensive assessment of axial length estimation in myopic eyes from ocular and demographic variables. Eye 38, 1333–1341 (2024). https://doi.org/10.1038/s41433-023-02899-w

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