# Rapid and accurate prediction of cycloplegic refraction in Chinese children: development and validation of machine learning models

## TL;DR

This study develops machine learning models to predict cycloplegic refraction in children using non-cycloplegic data and ocular biometrics, offering a potential solution for low-resource settings.

## Contribution

The novel contribution is a machine learning model that accurately predicts cycloplegic refraction using accessible non-cycloplegic measurements and biometric data.

## Key findings

- The stacked ML model achieved an R2 of 0.982 and a mean absolute error of 0.360D in predicting cycloplegic spherical equivalent.
- Segmented models showed better agreement between predicted and actual cycloplegic refraction in specific age and refractive groups.
- External validation datasets had MAEs of 0.284D and 0.306D, indicating strong but not fully aligned predictions.

## Abstract

Uncorrected refractive error affects approximately 19 million children globally, resulting in preventable vision loss. However, cycloplegic refraction, the gold standard for assessment, remains largely inaccessible in low-resource settings. We aimed to develop and validate machine learning (ML) prediction models based on non-cycloplegic results to estimate the cycloplegic spherical equivalent (cSE).

The internal dataset comprised refractive measurements and ocular biometric parameters collected from 3035 children’s eyes at the Eye & ENT Hospital of Fudan University, the research team’s primary hospital. The external validation sets consisted of 160 and 120 eyes, respectively, from two different centres. Based on ocular biometric parameters and non-cycloplegic spherical equivalent, we employed single and stacked ML models to predict cSE. We used regression metrics and agreement analysis between the predicted spherical equivalent (pSE) and cSE to assess prediction performances. We also created segmented models based on age and refractive groups. The generalisation performance of the models was assessed using evaluation metrics as well as correlation and agreement analyses in the external validations.

The stacked overall model outperformed single-algorithm models, achieving an R2 of 0.982 and a mean absolute error(MAE) of 0.360D. The MAE in segmented models ranged from 0.239D to 0.466D in the middle-aged groups and 0.226D to 0.420D in the high-aged groups, with better 95% limits of agreement between pSE and cSE than those in the overall model. External validation showed MAEs of 0.284D and 0.306D for the two datasets, with significant correlations, but lack of agreement between pSE and cSE.

The ML models enable cSE prediction based on non-cycloplegic refraction data and ocular biometric parameters, providing a fast, practical method for estimating refractive error. Multicenter validation and targeted oversampling of rare refractive subgroups are required, however, before robust clinical implementation of the models.