Methods and Applications: Predicting Cycloplegic Spherical Equivalent Refraction Among Children and Adolescents Using Non-cycloplegic Data and Machine Learning — China, 2020–2024

Refractive error screening in children is a major public health challenge in China. A Chinese study projects that by 2050, urban myopia rates will be 27.1% [95% confidence interval (95% CI]: 10.0%–44.4%) for 7–9 year olds and 81.5% (95% CI: 74.7%–88.3%) for 16–18 year olds, with rural rates at 20.1% (95% CI: 8.6%–31.7%) and 74.1% (95% CI: 63.2%–84.8%), respectively. High myopia in 16–18 year olds is expected to increase from 7.3% in 2001 to 22.1% by 2050 (1). Despite its status as the gold standard for accurate measurements (2), the implementation of cycloplegic refraction in large-scale school screenings is often impractical because of logistical constraints and potential side effects (3). Current reliance on non-cycloplegic refraction introduces substantial variability, with studies reporting mean differences in the range of 0.60–1.23 diopters (D) compared with cycloplegic measurements (4), particularly in younger children with strong accommodative responses. Recent advances in machine learning (ML) have shown promise in the prediction of ophthalmic parameters. However, their application in bridging cycloplegic and non-cycloplegic measurements remains underexplored in population-based settings. Ocular biometric parameters are important indicators for assessing far-vision reserve in children and for objectively evaluating the development of refraction (5). This study aimed to develop and validate ML-based models to predict cycloplegic spherical equivalent (SE) in children aged 5–18 years using non-cycloplegic refraction, axial length (AL), corneal radius (CR), AL/CR ratio, and uncorrected visual acuity (UCVA). These models may offer practical alternatives to cycloplegic refraction for the surveillance of myopia in large populations.

This study used data from a national cross-sectional survey of ocular development in children and adolescents organized by the National Disease Control and Prevention Administration of China between 2020 and 2024. The survey was conducted in 10 provincial-level administrative divisions (PLADs): Beijing, Shanxi, Liaoning, Zhejiang, Shandong, Henan, Hunan, Guangdong, Chongqing, and Shaanxi. In most PLADs, two cities were selected on the basis of their levels of economic development. A multistage cluster sampling method was used to recruit students from kindergarten to high school. The detailed survey protocol has been previously described (5). A flowchart of the data collection procedure is presented in Supplementary Figure S1.

All participants underwent standardized eye examinations, including noncycloplegic and cycloplegic autorefraction, using the same desktop autorefractor model at all sites. For cycloplegia, 0.5% tropicamide was applied four times at 5-min intervals. Trained personnel performed all assessments using a unified protocol. Owing to the high inter-eye correlation, only the right-eye data were analyzed. SE was calculated as the spherical power plus half the cylindrical power. For variable selection, univariate analyses were performed to assess the associations between each potential predictor and refractive error. Additionally, we calculated the variance inflation factors (VIFs) to evaluate multicollinearity and applied the least absolute shrinkage and selection operator (LASSO) regression to refine the variable set. Variables with significant univariate P-values, acceptable VIFs (<5), and retention in the LASSO model were included in the final analyses. These included AL, CR, AL/CR ratio, UCVA, and patient age. Gender and region, despite their theoretical importance, were not retained in the LASSO model and were thus excluded from the final analysis. UCVA was recorded on a Chinese 5-point scale, where 5.0 corresponded to 0 logarithm of the minimum angle of resolution (logMAR) (Snellen 20/20).

The dataset was randomly divided into training (80%) and test (20%) datasets. At the baseline, a multivariate linear regression model was fitted using all the non-cycloplegic variables. On the test set, this model achieved an R-squared (R²) value of 0.79, root mean square error (RMSE) of 0.73 D, and mean absolute error (MAE) of 0.54 D, suggesting the need for more flexible ML algorithms. Random forest regression and eXtreme Gradient Boosting (XGBoost) regression were used to develop predictive models, and model performance was evaluated using R², RMSE, actual-predicted SE plots, and Bland–Altman plots. All analyses were performed using R software (version 4.5.1, R Foundation for Statistical Computing, Vienna, Austria, 2024).

This study included 58,252 participants: 46,603 (80.0%) in the training set and 11,649 (20.0%) in the test set. As summarized in Table 1, the baseline characteristics were well balanced between the two groups: The mean ages were 8.25±2.82 years in the training set and 8.27±2.86 years in the test set, gender distributions were similar (51.7% vs. 51.8% male), and urban–rural residence patterns were comparable (76.6% vs. 76.1% urban residents). Ocular measurements exhibited similar refractive profiles between groups, including non-cycloplegic SE (−0.63±1.44 D vs. −0.64±1.46 D), cycloplegic SE (both 0.09±1.57 D), AL (23.20±1.04 mm vs. 23.21±1.05 mm), CR (7.78±0.26 mm vs. 7.79±0.26 mm), AL/CR ratio (both 2.98±0.12), and UCVA (both 4.85±0.28 logMAR). Descriptive characteristics of the study population are summarized in Table 1.

Both the random forest and XGBoost models exhibited strong performance in predicting cycloplegic SE using non-cycloplegic refraction and ocular biometric parameters. In the test set, random forest achieved an R² of 0.88 with an RMSE of 0.55 D and MAE of 0.40 D, whereas XGBoost exhibited comparable performance (R²=0.89, RMSE=0.54 D, and MAE=0.39 D). The performance of the training set was superior (random forest: R²=0.94, RMSE=0.39 D; XGBoost: R²=0.90, RMSE=0.51 D) (Table 2). The importance of the features of each ML model in the training and test sets is shown in Figure 1. Non-cycloplegic SE, the AL/CR ratio, AL, and UCVA were consistently among the four most important features for predicting cycloplegic SE in these models. Scatter plots of the predicted versus actual cycloplegic SE demonstrated satisfactory alignment along the identity line for both models (Figure 2). Bland–Altman plots showed that 95% of prediction errors were within ±2.0 D for both models, indicating acceptable agreement (Figure 3).

Figure 1. 

Permutation feature importance for predicting cycloplegic spherical equivalent (RMSE metric). (A) Random Forest, test set; (B) Random Forest, training set; (C) XGBoost, test set; (D) XGBoost, training set.

Abbreviation: SE=spherical equivalent; AL/CR=axial length/corneal radius ratio; AL=axial length; UCVA=uncorrected visual acuity; CR=corneal radius; XGBoost=eXtreme Gradient Boosting.

Figure 2. 

Actual vs. predicted cycloplegic SE by ML models. (A) Random Forest, test set (R²=0.878); (B) Random Forest, training set (R²=0.941); (C) XGBoost, test set (R²=0.886); (D) XGBoost, training set (R²=0.897).

Note: Dashed line represents perfect agreement; solid line represents the fitted linear regression.

Abbreviation: XGBoost=eXtreme Gradient Boosting; SE=spherical equivalent; ML=machine learning.

Figure 3. 

Bland–Altman analysis of ML model performance in predicting cycloplegic spherical equivalent. (A) Random Forest, test set; (B) Random Forest, training set; (C) XGBoost, test set; (D) XGBoost, training set.

Note: Plots display the differences between predicted and actual cycloplegic spherical equivalent (SE) values (in diopters, D) against their means. Solid horizontal lines represent mean differences, whereas dashed lines indicate 95% limits of agreement (±1.96 SD). The training sets (B and D) demonstrate narrower limits of agreement than those of test sets (A and C), reflecting expected performance variations between training and validation datasets.

Abbreviation: XGBoost=eXtreme Gradient Boosting.