Prediction of Cycloplegic Refractive Error based on Non-Cycloplegic Measurements in Chinese Children aged 3 to 17 years

Prediction of Cycloplegic Refractive Error based on Non-Cycloplegic Measurements in Chinese Children aged 3 to 17 years | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Prediction of Cycloplegic Refractive Error based on Non-Cycloplegic Measurements in Chinese Children aged 3 to 17 years Bichi Chen, Longfei Jiang, Li Tian, Maoyuan Yang, Fuyue Tian, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6478499/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Introduction Cycloplegic refraction remains the gold standard for pediatric refractive assessment, yet its implementation faces challenges in large-scale studies. This study aimed to develop a multivariable model predicting cycloplegic spherical equivalent refraction (SER) using non-cycloplegic measurements in Chinese children. Methods This retrospective study included 28901 children aged 3–17 years, who were allocated to development (n = 23121) and validation (n = 5780) datasets. Ocular biometric parameters were assessed with the IOL Master 500 optical biometer. Cycloplegic SER was measured using a Topcon autorefractor after 1% cyclopentolate. A prediction model was derived and validated, with performance evaluated by R 2 , correlation coefficient, mean error (ME), mean absolute error (MAE), and clinical accuracy proportions (predictions within ± 0.50 D/±1.00 D). Results The prediction model, incorporating age, gender, height, axial length, and axial length/corneal radius of curvature ratio, achieved R 2 = 0.854 (development) and 0.858 (validation), with ME = 0.00 ± 0.72 D and MAE = 0.56 ± 0.46 D in the validation dataset. Clinical accuracy proportions (± 0.50 D/±1.00 D) were 53.86% and 84.91%, respectively. Optimal performance was observed in children aged 3–10 years and those with cycloplegic SER between + 0.50 and + 2.00 D. Conclusions This prediction model based on simplified non-cycloplegic parameters provides reasonably accurate cycloplegic SER estimates in young children with low refractive error. It holds potential for epidemiological surveys in resource-limited settings and clinical management of children with cycloplegia contraindications. Clinical trial number not applicable. Cycloplegic refractive error prediction non-cycloplegic Chinese childre Figures Figure 1 Figure 2 Figure 3 1 Introduction Accurate assessment of refractive status in pediatric populations requires cycloplegic refraction to eliminate accommodation-induced measurement errors, establishing it as the gold standard for both clinical diagnosis and epidemiological investigations( 1 – 3 ). Substantial evidence demonstrates clinically significant discrepancies between cycloplegic and noncycloplegic measurements, with mean spherical equivalent differences ranging from 0.63 to 1.23 D( 4 – 8 ). These systematic errors lead to overestimated myopia prevalence and underestimated hyperopia rates in population-based studies, underscoring the necessity of cycloplegia for reliable refractive error characterization. Nevertheless, routine implementation of cycloplegia faces three major challenges in pediatric practice. Firstly, the procedure demands prolonged waiting periods (≥ 30 minutes) for full cycloplegic effect and causes transient photophobia during accommodation paralysis, significantly disrupting children's daily activities. Second, children receiving cycloplegic eyedrops may experience ocular irritation, which may result in a lack of cooperation from the children or their parents. Third, cycloplegic agents are associated with the risk for the development of mental disorders or toxicity due to central nervous system or cardiovascular disease( 9 – 11 ). These limitations, compounded by the logistical challenges of administering cycloplegia in large-scale epidemiological surveys (time constraints, resource intensiveness, and contraindication management), create an urgent need for validated prediction methodologies. Emerging research has attempted to address this challenge through predictive modeling using non-cycloplegic parameters. Previous investigations have explored combinations of demographic factors (age, gender), ocular biometric measures (e.g., axial length [AL], corneal curvature [CR]), and non-cycloplegic refraction values, and uncorrected visual acuity (UCVA), achieving variable predictive performance (R 2 ranging from 0.26 to 0.92)( 8 , 12 – 17 ). However, limitations persist in existing models: 1) restricted sample sizes (typically < 6000 participants) potentially compromising model generalizability, 2) limited age ranges failing to represent the full developmental spectrum of school-aged children. These constraints limit the translational potential of current models across diverse pediatric practice settings. In this study, detailed demographics and ocular biometric parameters from 28901 Chinese children aged 3 to 17 years- the largest cohort to date, were collected for cycloplegic refraction prediction modeling. This investigation extends previous work through following innovations: population-based design with broader age representation and rigorous model validation protocols accounting for age-group and refractive error-group heterogeneity. We hope the developed prediction model can potentially be used in future epidemiology studies of refraction and clinical practices in which administering cycloplegic agents on children is not feasible. 2 Materials and methods 2.1 Participants This retrospective study enrolled children aged 3–18 years who underwent ophthalmic examinations at the Eye Hospital of Wenzhou Medical University between October 2021 and March 2024. The inclusion criteria were as follows: ( 1 ) parental consent for cycloplegic procedures; ( 2 ) clinical information was available for before and after cyclopentolate application. Exclusion criteria comprised: ocular organic diseases, manifest strabismus or amblyopia, with a history of ocular surgery, or hypersensitivity to 1% cyclopentolate hydrochloride eye drops. A total of 28901 children was eventually enrolled. All participants were randomly divided into development and validation datasets at an 8:2 ratio. Models for predicting cycloplegic refraction were trained using the development dataset (n = 23121 children) and verified using the validation dataset (n = 5780 children). The study protocol was approved by the Institutional Ethics Committee of the Eye Hospital of Wenzhou Medical University (approval no. 2021-233-K-203-03) and adhered to the tenets of the Declaration of Helsinki. Informed consent was obtained from the parents of all participants. 2.2 Data collection Demographic information, including age, gender, and height was obtained. All participants underwent comprehensive ophthalmic examinations, including distance visual acuity test using retro-illuminated logMAR charts with tumbling-E optotypes, slit-lamp examination of the anterior segment, fundus examination with ophthalmoscopy, intraocular pressure measurement and the assessment of ocular biometrics under non-cycloplegic conditions (e.g., AL, CR) using a IOL Master 500 (Carl Zeiss Meditec, Oberkochen, Germany). The measurements were considered valid if individual measurements of AL varied by no more than 0.02mm. After the non-cycloplegic examinations, the children received two drops of 1% cyclopentolate (Alcon, Fortworth, TX, America) in each eye with an interval of 5 min between drops. Thirty minutes after application of cyclopentolate, loss of direct light reaction and mydriasis was confirmed and the cycloplegic refractive error were measured three times by an autorefractometry (KR 800, Topcon, Tokyo, Japan). Measurements were repeated if any spherical or cylindrical component differed by > 0.50 D between readings. The average of three valid measurements was recorded and used for analysis. All data underwent dual-entry verification (EpiData 3.1, Odense, Denmark) with source document reconciliation for discrepancies. 2.3 Prediction model development On the basis of the collected demographic, biometric and autorefractometric data, the prediction model for cycloplegic refractive error was developed by applying multiple regression analysis. Candidate variables included: AL( 12 , 14 ), CR( 12 ), Axial length/corneal radius of curvature ratio (AL/CR) ( 12 , 13 ), gender( 18 ), and age( 19 , 20 ) as independent variables, given that they had previously been identified as factors related to ocular refraction. Meanwhile, height was also factored into the modeling, considering that the ocular development is affected by the growth of the whole body( 21 , 22 ). Cycloplegic spherical equivalent refraction (SER) was considered as the dependent variable. A stepwise multiple regression analysis identified significant predictors of cycloplegic SER. Variance inflation factors < 10 confirmed absence of multicollinearity. 2.4 Statistical Analysis Right-eye data were analyzed to avoid interocular correlation bias. Cycloplegic SER values were calculated as sphere plus half of the cylinder for each eye. Myopia was defined as cycloplegic SER − 0.50 D or worse. Emmetropia was defined between − 0.50 D and + 0.50 D and hyperopia was defined as greater than + 0.50 D. Continuous variables were expressed as mean ± standard deviation (SD). Demographic and biometric characteristics were compared between the development and validation datasets using independent t-tests for continuous variables and chi-square tests for categorical variables to verify baseline comparability. Model performance was evaluated using the coefficient of determination ( R 2 ), correlation coefficient r , mean error (ME), and mean absolute error (MAE) of differences between predicted and measured cycloplegic SER (calculated as predicted – measured), as well as the clinical accuracy proportions (predictions within ± 0.50 D/±1.00 D). The predicted and measured cycloplegic SER were also statistically compared using paired t-test and Bland-Altman analysis. All statistical analysis was performed with SPSS Statistics software version 27 (SPSS Inc., Chicago, IL). A p value of < 0.05 was considered statistically significant. 3 Results A total of 28901 participants were enrolled in this study, the age ranged from 3 to 17 years, with a mean age of 9.72 ± 2.54 years old. Females (n = 13777) accounted for 47.67% of the study population. The development dataset included 23121 children (11014 girls), and the validation dataset included 5780 children (2763 girls), with a mean age of 9.73 ± 2.54 years and 9.68 ± 2.52 years, respectively. The basic characteristics were shown in Table 1 . The two groups were similar in age, gender, height, and most of the biometric measures. Figure 1 depicted the age-specific cycloplegic SER distribution based on all the enrolled refraction data. The results revealed a gradual decrease in SER with increasing age, which was consistent with the expected pattern of normal growth and development. The mean cycloplegic SER was − 0.77 ± 1.93 D in the development dataset and − 0.73 ± 1.92 D in the validation dataset, confirming balanced refractive status allocation. Table 1 Characteristics of the development and validation datasets Characteristics Development dataset (n = 23121) Validation dataset (n = 5780) P values Age (y), n (%) 3 106 (0.46) 29 (0.50) 4 300 (1.30) 82 (1.42) 5 456 (1.97) 121 (2.09) 6 2075 (8.97) 573 (9.91) 7 3548 (15.35) 836 (14.46) 8 3403 (14.72) 838 (14.50) 9 3459 (14.96) 876 (15.16) 10 2872 (12.42) 717 (12.40) 11 2050 (8.87) 541 (9.36) 12 1466 (6.34) 358 (6.19) 13 1759 (7.61) 467 (8.08) 14 1268 (5.48) 271 (4.69) 15 309 (1.34) 59 (1.02) 16 38 (0.16) 10 (0.17) 17 12 (0.05) 2 (0.03) Mean ± SD 9.73 ± 2.54 9.68 ± 2.52 0.141 Male: Female (%) 12107:11014 (52.36: 47.64) 3017:2763 (52.20: 47.80) 0.821 Height (cm) 140.85 ± 16.08 140.51 ± 16.05 0.152 AL (mm) 23.75 ± 1.16 23.71 ± 1.15 0.019 CR (mm) 7.81 ± 0.25 7.81 ± 0.25 0.533 AL/CR 3.04 ± 0.14 3.04 ± 0.14 0.037 Cycloplegic SER (D), n (%) ≤−6.0 304 (1.31) 74 (1.28) >−6.0, ≤−3.0 2950 (12.76) 691 (11.96) >−3.0, ≤−0.5 8658 (37.45) 2138 (36.99) >−0.5, ≤+0.5 4758 (20.58) 1256 (21.73) >+0.5, ≤+2.0 5840 (25.26) 1464 (25.33) >+2.0 611 (2.64) 157 (2,72) Mean ± SD -0.77 ± 1.93 -0.73 ± 1.92 0.148 3.1 Establishment of the prediction model With the clinical parameter values from the development dataset, a multivariable prediction model for cycloplegic SER was developed. The stepwise multiple regression analysis identified five significant predictors of cycloplegic SER ( p < 0.001 for all, Table 2 ): AL, AL/CR, height, gender, and age. The derived prediction model was: Cycloplegic SER = 39.921 − 0.028*age + 0.445*gender + 0.009*height-0.493*AL-9.941*AL/CR (gender: boy = 1, girl = 0; age in years; height in centimeters). The correlation coefficient r of this model was 0.924 ( R 2 = 0.854, Fig. 2A). The overall ME and MAE between predicted and measured cycloplegic SER were − 0.02 ± 0.74 D and 0.57 ± 0.47 D, respectively. Table 2 Multiple regression analysis for predicting cycloplegic SER based on clinical information in the development dataset (n = 23121) Parameter Regression Coefficient (standard error) P value Variance Inflation Factor Intercept 39.921 (0.143) <0.001 - Age -0.028 (0.005) <0.001 6.404 Gender (boy = 1, girl = 0) 0.445 (0.010) <0.001 1.110 Height 0.009 (0.001) <0.001 6.153 AL -0.493 (0.007) <0.001 2.916 AL/CR -9.941 (0.060) <0.001 2.818 When analyses of these differences were stratified by age, the ME and MAE between predicted and measured cycloplegic SER for each age group were within 0.19 D and 0.74 D in the development dataset (Table 3 ). When stratified by level of measured cycloplegic SER, the ME and MAE for each cycloplegic SER group were within − 0.15 D and 0.54 D, except when the cycloplegic SER was lower than − 3.00 D or greater than + 2.00 D, in which case the ME and MAE was larger (-0.79 ~ 0.50 D and 0.72 ~ 0.89 D, respectively). The Bland-Altman plot for the differences between predicted and measured cycloplegic SER in the development dataset was shown in Fig. 3A, with 95% limits of agreement ranging from − 1.467 to 1.431 D. The differences were all around 0 when cycloplegic SER measures were low myopia, emmetropia, or low hyperopia; and most of differences were negative when cycloplegic SER were medium or high hyperopia. The predicted cycloplegic SER within ± 0.50 D and ± 1.00 D of measured cycloplegic SER for 53.19% and 84.44% of the eyes, with a relatively higher proportion in the subgroup of age from 3 to 10 years old or cycloplegic SER from + 0.50 to + 2.00 D. Table 3 Difference between predicted and measured cycloplegic spherical equivalents in the development dataset and the validation dataset by age group and by cycloplegic refractive error group Development Dataset (n = 23121) Validation Dataset (n = 5780) Mean Difference Between Predicted and Measured Cycloplegic SER, Mean ± SD Mean Absolute Error Between Predicted and Measured Cycloplegic SER, Mean ± SD Difference Between Predicted and Measured Cycloplegic SER ≤ ± 0.50D, % Difference Between Predicted and Measured Cycloplegic SER ≤ ± 1.00D, % Mean Difference Between Predicted and Measured Cycloplegic SER, Mean ± SD Mean Absolute Error Between Predicted and Measured Cycloplegic SER, Mean ± SD Difference Between Predicted and Measured Cycloplegic SER ≤ ± 0.50D, % Difference Between Predicted and Measured Cycloplegic SER ≤ ± 1.00D, % Overall -0.02 ± 0.74 0.57 ± 0.47 53.19 84.44 0.00 ± 0.72 0.56 ± 0.46 53.86 84.91 By age (y) 3–6 0.19 ± 0.72 0.55 ± 0.50 56.21 85.26 0.19 ± 0.70 0.55 ± 0.46 57.14 85.84 7–10 -0.10 ± 0.68 0.53 ± 0.43 55.59 86.97 -0.07 ± 0.68 0.53 ± 0.43 56.23 86.99 11–14 0.04 ± 0.82 0.64 ± 0.52 47.55 79.66 0.04 ± 0.79 0.63 ± 0.49 48.14 80.76 15–18 0.15 ± 0.93 0.74 ± 0.58 42.62 71.31 0.35 ± 0.92 0.73 ± 0.66 39.44 74.65 By cycloplegic SER (D) ≤-6.0 0.15 ± 0.93 0.74 ± 0.58 11.84 30.59 1.34 ± 0.85 1.36 ± 0.81 18.92 36.49 > −6.0 to ≤ − 3.0 0.50 ± 0.77 0.72 ± 0.58 42.98 73.53 0.54 ± 0.71 0.71 ± 0.54 40.96 74.38 > −3.0 to ≤ − 0.5 -0.05 ± 0.67 0.53 ± 0.41 55.09 87.33 -0.05 ± 0.67 0.53 ± 0.42 55.47 86.81 > −0.5 to ≤ + 0.5 -0.10 ± 0.68 0.54 ± 0.43 54.25 85.98 -0.08 ± 0.64 0.52 ± 0.39 56.37 88.85 >+0.5 to ≤ + 2.0 -0.15 ± 0.62 0.50 ± 0.40 58.41 89.52 -0.11 ± 0.65 0.51 ± 0.41 59.02 87.98 >+2.0 -0.79 ± 0.81 0.89 ± 0.70 37.97 62.36 -0.69 ± 0.80 0.83 ± 0.66 36.94 68.15 3.2 Validation of the prediction model To validate the performance of the prediction model, the clinical information from the validation dataset were applied to the model and then compared the predicted cycloplegic SER with the measured cycloplegic SER for each eye. The model demonstrated a strong correlation with measured cycloplegic SER in the validation dataset ( r = 0.926, R 2 = 0.858, Fig. 2B). The overall ME and MAE between predicted and measured cycloplegic SER were 0.00 ± 0.72 D and 0.56 ± 0.46 D, respectively. The mean difference of cycloplegic predicted values and measured values were not significantly different ( p = 0.985). Stratified analyses revealed that the ME and MAE between predicted and measured cycloplegic SER across age subgroups were within 0.35 D and 0.73 D (Table 3 ). When analyses were stratified by level of measured cycloplegic SER, the ME and MAE for cycloplegic SER subgroups were within − 0.11 D and 0.53 D, except when the cycloplegic SER was lower than − 3.0 D or greater than + 2.0 D, in which case the ME ranged − 0.69 ~ 1.34 D and MAE ranged 0.71 ~ 1.36 D between the predicted and measured cycloplegic SER. Bland-Altman analysis showed a 95% limits of agreement of -1.420 ~ 1.421 D in the validation dataset (Fig. 3B). The proportion of the prediction errors within ± 0.50 D and ± 1.00 D were 53.86% and 84.91%, respectively, with peak performance in the subgroup of age from 3 to 10 years (56.23 ~ 57.14% within ± 0.50 D) or cycloplegic SER from + 0.50 to + 2.00 D (59.02% within ± 0.50 D). 4 Discussion In this study, we developed and validated a prediction model for predicting cycloplegic refractive error based on the non-cycloplegic data, including demographics (age, gender, and height) and ocular biometric parameters from the optical biometer IOL Master 500. In both the development and validation datasets, this model predicted cycloplegic SER moderately well, showing no clinically significant deviation from measured cycloplegic SER (e.g., mean difference less than 0.25 D) when the cycloplegic refractive error was low myopia, emmetropia, or low hyperopia ( ≤ + 2.0 D). This prediction model is therefore potentially applicable to large-scale screening in epidemiological studies and myopia risk assessment in clinical process. It would save time in the clinical evaluation as well as avoid the adverse effects of cycloplegic eyedrops. The correlation coefficients for comparisons of predicted cycloplegic SER with measured cycloplegic SER was 0.926 ( R 2 = 0.858) in the external validation dataset, suggesting that this prediction model yielded acceptable refractive information in children. This result outperformed earlier biometric-focused approaches using AL, CR, or the AL/CR ratio, which reported correlations of 0.53 to 0.81 between predicted and measured cycloplegic refractive error in children aged 3 to 13 years( 12 – 15 ). The other prediction models for the cycloplegic refractive error used ocular biometric measures( 16 ), non-cycloplegic refractive error( 8 , 17 ), and UCVA( 8 ), yielding mixed results. Magome et al.( 16 ) developed and validated prediction models for cycloplegic spherical and cylinder refraction in 2 ~ 9 years old Japanese children (n = 1040) using demographics (age and gender) and ocular biometric parameters (AL, anterior chamber depth, lens thickness, corneal refractive power, and corneal astigmatism). Their prediction models achieved a precision with mean differences of -0.12 D for sphere and − 0.01 D for cylinder between predicted and measured cycloplegic refraction, and the correlations between predicted and measured refraction were 0.96 ( R 2 = 0.924) for sphere and 0.89 ( R 2 = 0.799) for cylinder. Our prediction model differs from their model in that this model predicts the cycloplegic spherical equivalent, a measure commonly used to define the myopia. Similar to our study, He et al.( 23 ) developed prediction models for cycloplegic spherical equivalent based on age, gender, AL and AL/CR ratio. They reported a comparable R 2 of 0.87, but slightly lower clinical accuracy (47% within ± 0.5D and 79% within ± 1.0D), likely due to the differences in modeling approach (their non-linear regression vs. our linear regression) and predictors (the factor of height was additionally included in our prediction model). Sankaridurg et al.( 8 ) established prediction models based on 6017 Chinese children ages 4 to 15 years by using age, non-cycloplegic refractive error, and UCVA. Their prediction model yielded R 2 of 0.91. Wang et al. also( 17 ) developed and validated prediction models for cycloplegic spherical equivalent based on 3436 Chinese children ages 5 to 18 years by using age, gender, non-cycloplegic refractive error, UCVA, AL/CR ratios, intraocular pressure, and glasses-wearing status, with a mean difference of 0.06 ± 0.64 D and R 2 of 0.92. Compared with the studies by Sankaridurg et al. and Wang et al., the results of our model were slightly inferior, which may be attributed to the inclusion of non-cycloplegic refractive error as a modeling factor in their models. Previous studies have indicated that non-cycloplegic spherical equivalent, AL, and the AL/CR ratio are crucial factors in predicting cycloplegic refractive error( 24 , 25 ). In comparison to these studies, our five-variable model maintains clinical utility with simplified data collection, including age, gender, height, AL and AL/CR ratio, all of which are obtainable under non-cycloplegic conditions. Since our prediction model was developed in a large sample and independently validated in another large sample of children with a wide range of ages (3 to 17 years old) and refractive error status (cycloplegic spherical equivalent from − 10.25 to + 8.50 D), it has the potential to be applicable to population-based research when measuring cycloplegic refractive error in all children is not feasible. Notably, the model demonstrated superior performance in early childhood (aged 3 to 10 years) or for low hyperopia refractive status (cycloplegic SER from + 0.5 to + 2.00 D), which is a crucial window when hyperopic reserve depletion accelerates myopia onset. Epidemiological evidence indicated that children who are emmetropia at the first grade have a probability of developing myopia by the end of primary school as high as 92.6%. In contrast, the first-graders who possess a hyperopia reserve ≥ + 2.00D have a mere 4.6% myopia risk by graduation( 26 ). This finding underscores that children with low hyperopia reserve are at a significantly higher risk of developing myopia compared to those with high hyperopia reserve. Therefore, this prediction model may hold considerable potential for early warning of myopia risk in younger children with insufficient hyperopia reserve. The precise measurement of refraction data without the effect of accommodation in young children requires the use of cycloplegic eyedrops. However, application of cycloplegia faces practical challenges in large-scale epidemiological surveys due to time constraints, resource limitations, and potential contraindications. These disadvantages sometimes preclude the use of cycloplegic evaluation as a screening procedure to detect real refractive status in children. In the present study, a prediction model was developed on the basis of simple demographic and ocular biometric parameters obtained under the non-cycloplegic condition, and it provided predicted refraction values with moderate predictive accuracy. This approach enhances feasibility in resource-limited settings where cycloplegic agents are cost-prohibitive or contraindicated, and can potentially be applied to correct the well-known overestimation of myopia prevalence and underestimated hyperopia due to non-cycloplegic refractive error measurements. However, there were several limitations in this study. First of all, the prediction model did not include predictors such as non-cycloplegic refractive values and anterior chamber depth, which may explain the slightly inferior performance versus the existing optimal model. Future studies will improve the prediction accuracy by including more correlation factors and algorithm optimization. Secondly, this study used a IOL Master 500 optical biometer in Chinese children; thus, the findings may not be directly generalizable to different types of biometers or children of other races or ethnicities. The prediction model may have to be calibrated and further validated before its use in settings different from those in our study. Finally, the reduced accuracy in predicting medium to high myopia or hyperopia limits utility for these subgroups. 5 Conclusions In this study, we developed and validated a multivariable prediction model for predicting cycloplegic refractive error using the available demographics and ocular biometric data. This prediction model achieves a practical balance between accuracy and clinical feasibility for estimating cycloplegic refraction. It demonstrated reasonably accurate estimates of cycloplegic refractive error in young children with low magnitude refractive error (low myopia, emmetropia, and low hyperopia) while avoiding the possible side effects or patient refusal associated with the use of cycloplegic agents. While the model's predictive performance ( R² =0.858) slightly trails the optimal reported models, this study provides crucial evidence regarding the feasibility of large-scale cycloplegic prediction and identifies key determinants for future model optimization. The developed tool holds particular value for epidemiological surveys in resource-limited settings and clinical management of children with cycloplegia contraindications. Abbreviations AL axial length CR corneal curvature UCVA uncorrected visual acuity AL/CR Axial length/corneal radius of curvature ratio SER spherical equivalent refraction SD standard deviation ME mean error MAE mean absolute error Declarations 7.1 Ethics approval and consent to participate The study protocol was approved by the Ethics Committee of the Eye Hospital of Wenzhou Medical University (2021-233-K-203-03) in accordance with the Declaration of Helsinki. All participants were provided with and signed informed consent forms. 7.2 Consent for publication Not applicable. 7.3 Availability of data Not applicable. 7.4 Competing interests The authors declare no competing interests. 7.6 Funding The authors declare that no funds, grant, or other support were received during the preparation of this manuscript. 7.7 Authors' contributions Conception and design: BCC, LFJ, SZX; Data acquisition: BCC, LFJ, LT, MYY, FYT, QCY, MYZ; Data analysis and interpretation: BCC, LFJ, LT; Manuscript drafting and revisions: BCC, SZX. All authors read and approved the final manuscript. 7.8 Acknowledgements Not applicable. References Flitcroft DI, He M, Jonas JB, Jong M, Naidoo K, Ohno-Matsui K, et al. Imi - Defining and Classifying Myopia: A Proposed Set of Standards for Clinical and Epidemiologic Studies. Invest Ophthalmol Vis Sci. 2019;60(3):M20–30. 10.1167/iovs.18-25957 . Doherty SE, Doyle LA, McCullough SJ, Saunders KJ. 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Fotedar R, Rochtchina E, Morgan I, Wang JJ, Mitchell P, Rose KA. Necessity of Cycloplegia for Assessing Refractive Error in 12-Year-Old Children: A Population-Based Study. Am J Ophthalmol. 2007;144(2):307–9. 10.1016/j.ajo.2007.03.041 . Sankaridurg P, He X, Naduvilath T, Lv M, Ho A, Smith E 3, et al. Comparison of Noncycloplegic and Cycloplegic Autorefraction in Categorizing Refractive Error Data in Children. Acta Ophthalmol. 2017;95(7):e633–40. 10.1111/aos.13569 . Carpenter WT. Jr. Precipitous Mental Deterioration Following Cycloplegia with 0.2 Percent Cyclopentolate Hcl. Arch Ophthalmol. 1967;78(4):445–7. 10.1001/archopht.1967.00980030447006 . Kennerdell JS, Wucher FP. Cyclopentolate Associated with Two Cases of Grand Mal Seizure. Arch Ophthalmol. 1972;87(6):634–5. 10.1001/archopht.1972.01000020636004 . Shiuey Y, Eisenberg MJ. Cardiovascular Effects of Commonly Used Ophthalmic Medications. Clin Cardiol. 1996;19(1):5–8. 10.1002/clc.4960190104 . Foo VH, Verkicharla PK, Ikram MK, Chua SY, Cai S, Tan CS, et al. Axial Length/Corneal Radius of Curvature Ratio and Myopia in 3-Year-Old Children. Transl Vis Sci Technol. 2016;5(1):5. 10.1167/tvst.5.1.5 . Epub 20160209. He X, Zou H, Lu L, Zhao R, Zhao H, Li Q, et al. Axial Length/Corneal Radius Ratio: Association with Refractive State and Role on Myopia Detection Combined with Visual Acuity in Chinese Schoolchildren. PLoS ONE. 2015;10(2):e0111766. 10.1371/journal.pone.0111766 . Epub 20150218. Ip JM, Huynh SC, Kifley A, Rose KA, Morgan IG, Varma R, et al. Variation of the Contribution from Axial Length and Other Oculometric Parameters to Refraction by Age and Ethnicity. Invest Ophthalmol Vis Sci. 2007;48(10):4846–53. 10.1167/iovs.07-0101 . Kimura S, Hasebe S, Miyata M, Hamasaki I, Ohtsuki H. Axial Length Measurement Using Partial Coherence Interferometry in Myopic Children: Repeatability of the Measurement and Comparison with Refractive Components. Jpn J Ophthalmol. 2007;51(2):105–10. 10.1007/s10384-006-0410-5 . Epub 20070406. Magome K, Morishige N, Ueno A, Matsui TA, Uchio E. Prediction of Cycloplegic Refraction for Noninvasive Screening of Children for Refractive Error. PLoS ONE. 2021;16(3):e0248494. 10.1371/journal.pone.0248494 . Epub 20210315. Wang J, Wang X, Gao HM, Zhang H, Yang Y, Gu F, et al. Prediction for Cycloplegic Refractive Error in Chinese School Students: Model Development and Validation. Transl Vis Sci Technol. 2022;11(1):15. 10.1167/tvst.11.1.15 . Czepita D, Mojsa A, Ustianowska M, Czepita M, Lachowicz E. Role of Gender in the Occurrence of Refractive Errors. Ann Acad Med Stetin. 2007;53(2):5–7. Wu JF, Bi HS, Wang SM, Hu YY, Wu H, Sun W, et al. Refractive Error, Visual Acuity and Causes of Vision Loss in Children in Shandong, China. The Shandong Children Eye Study. PLoS ONE. 2013;8(12):e82763. 10.1371/journal.pone.0082763 . Epub 20131223. O'Donoghue L, Breslin KM, Saunders KJ. The Changing Profile of Astigmatism in Childhood: The Nicer Study. Invest Ophthalmol Vis Sci. 2015;56(5):2917–25. 10.1167/iovs.14-16151 . Wang D, Ding X, Liu B, Zhang J, He M. Longitudinal Changes of Axial Length and Height Are Associated and Concomitant in Children. Invest Ophthalmol Vis Sci. 2011;52(11):7949–53. 10.1167/iovs.11-7684 . Epub 20111010. Kearney S, Strang NC, Cagnolati B, Gray LS. Change in Body Height, Axial Length and Refractive Status over a Four-Year Period in Caucasian Children and Young Adults. J Optom. 2020;13(2):128–36. 10.1016/j.optom.2019.12.008 . Epub 20200125. He X, Sankaridurg P, Naduvilath T, Wang J, Xiong S, Weng R, et al. Normative Data and Percentile Curves for Axial Length and Axial Length/Corneal Curvature in Chinese Children and Adolescents Aged 4–18 Years. Br J Ophthalmol. 2023;107(2):167–75. 10.1136/bjophthalmol-2021-319431 . Epub 20210916. Ying B, Chandra RS, Wang J, Cui H, Oatts JT. Machine Learning Models for Predicting Cycloplegic Refractive Error and Myopia Status Based on Non-Cycloplegic Data in Chinese Students. Transl Vis Sci Technol. 2024;13(8):16. 10.1167/tvst.13.8.16 . Du B, Wang Q, Luo Y, Jin N, Rong H, Wang X, et al. Prediction of Spherical Equivalent Difference before and after Cycloplegia in School-Age Children with Machine Learning Algorithms. Front Public Health. 2023;11:1096330. 10.3389/fpubh.2023.1096330 . Epub 20230411. Li S, Kang M, Li L, Wei S, He X, Liu L, et al. Cohort Study on the Association between Hyperopia Reserve and Myopia Incidence in Primary School Students: The Anyang Childhood Eye Study. Chin J Ophthalmol. 2022;58(10):754–9. 10.3760/cma.j.cn112142-20211028-00509 . Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6478499","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":460111279,"identity":"1ad94aa4-d373-427f-88da-e99689265831","order_by":0,"name":"Bichi Chen","email":"","orcid":"","institution":"Wenzhou Medical University","correspondingAuthor":false,"prefix":"","firstName":"Bichi","middleName":"","lastName":"Chen","suffix":""},{"id":460111280,"identity":"14960890-35d2-43bb-8d65-ce38cc531ad8","order_by":1,"name":"Longfei Jiang","email":"","orcid":"","institution":"Wenzhou Medical University","correspondingAuthor":false,"prefix":"","firstName":"Longfei","middleName":"","lastName":"Jiang","suffix":""},{"id":460111281,"identity":"3cdcddd1-fc41-47d8-905b-d8b55286e893","order_by":2,"name":"Li Tian","email":"","orcid":"","institution":"Wenzhou Medical University","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Tian","suffix":""},{"id":460111282,"identity":"0a7d30b9-da68-4e05-be42-f4998639b711","order_by":3,"name":"Maoyuan Yang","email":"","orcid":"","institution":"Wenzhou Medical University","correspondingAuthor":false,"prefix":"","firstName":"Maoyuan","middleName":"","lastName":"Yang","suffix":""},{"id":460111283,"identity":"c5f66469-94bc-455d-9c72-5583cced999f","order_by":4,"name":"Fuyue Tian","email":"","orcid":"","institution":"Wenzhou Medical University","correspondingAuthor":false,"prefix":"","firstName":"Fuyue","middleName":"","lastName":"Tian","suffix":""},{"id":460111285,"identity":"924832d3-7ac7-4b68-8e33-0a590fe549cc","order_by":5,"name":"Qiaochu Yang","email":"","orcid":"","institution":"Wenzhou Medical University","correspondingAuthor":false,"prefix":"","firstName":"Qiaochu","middleName":"","lastName":"Yang","suffix":""},{"id":460111286,"identity":"598c8617-9c20-4674-aaff-bb1fd9df8f77","order_by":6,"name":"Mengyu Zhu","email":"","orcid":"","institution":"Wenzhou Medical University","correspondingAuthor":false,"prefix":"","firstName":"Mengyu","middleName":"","lastName":"Zhu","suffix":""},{"id":460111288,"identity":"866843bf-5c8d-471d-befd-1e64fb21f141","order_by":7,"name":"Suzhong Xu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBElEQVRIiWNgGAWjYLACxgYgwQ4kEgpI0sJzAKjFgCQtEglAghgtBjfSn0n+3GGTJx/5OvHDAwMGOYPjDYwffjDY5eHSIjkjx0xC8kxaseHt3M0SQIcZG5w5wCzZw5BcjEsLv0QOm4Rh2+HEjbNzN4C0JG64kcAgzcBwILEBhxY2ifRnEokgLTPPbv4B1FK/4f4D5t/4tPBLJJhJHARqmS/Buw1kS4LBDQY2vLZI9rwxtmxsS0vcwJO7zSLBQMJw5pnENsseg2ScWgyOpz+8+bPNJnF++9nNN39U2MjzHT98+MaPCjucWhB6D4ApCQaFA6BoIiaC5BvQGaNgFIyCUTAKoAAAVnFZ8vDszR0AAAAASUVORK5CYII=","orcid":"","institution":"Wenzhou Medical University","correspondingAuthor":true,"prefix":"","firstName":"Suzhong","middleName":"","lastName":"Xu","suffix":""}],"badges":[],"createdAt":"2025-04-18 11:08:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6478499/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6478499/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83436363,"identity":"c5abe572-d28b-4489-8686-e105b363149f","added_by":"auto","created_at":"2025-05-26 08:35:29","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":54809,"visible":true,"origin":"","legend":"\u003cp\u003eCycloplegic spherical equivalent distribution for children aged 3 to 17 years.\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6478499/v1/46bfee1cb2473b5a3c0ec4c0.jpg"},{"id":83436365,"identity":"31649259-d3a6-409b-8a21-082de235618c","added_by":"auto","created_at":"2025-05-26 08:35:29","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":74823,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation between measured and predicted cycloplegic spherical equivalent in the development dataset (\u003cstrong\u003eA\u003c/strong\u003e, n= 23121 children) and the validation dataset (\u003cstrong\u003eB\u003c/strong\u003e, n= 5780 children). Spherical equivalent estimated by the prediction model was highly correlated with cycloplegic spherical equivalent in the development dataset (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e=0.854) and the validation dataset (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e=0.858).\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6478499/v1/2fc8af811e7779babb48c0e8.jpg"},{"id":83436364,"identity":"a8b60b4c-92d7-4998-97f5-0e1f77e018d7","added_by":"auto","created_at":"2025-05-26 08:35:29","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":111831,"visible":true,"origin":"","legend":"\u003cp\u003eBland-Altman plots for the difference between the predicted and measured cycloplegic spherical equivalents in the development dataset (\u003cstrong\u003eA\u003c/strong\u003e, n=23121 children) and the validation dataset (\u003cstrong\u003eB\u003c/strong\u003e, n=5780 children). The dashed lines represent the mean difference and upper and lower limits for the 95% limits of agreement.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6478499/v1/d9587ec8a00c8ad5eb667e14.jpg"},{"id":83438336,"identity":"94bef21e-6cb8-4a29-9f31-5f71e9970942","added_by":"auto","created_at":"2025-05-26 08:59:29","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1064030,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6478499/v1/cb8ed596-377a-4497-a093-7ae12c6d3269.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Prediction of Cycloplegic Refractive Error based on Non-Cycloplegic Measurements in Chinese Children aged 3 to 17 years","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eAccurate assessment of refractive status in pediatric populations requires cycloplegic refraction to eliminate accommodation-induced measurement errors, establishing it as the gold standard for both clinical diagnosis and epidemiological investigations(\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e). Substantial evidence demonstrates clinically significant discrepancies between cycloplegic and noncycloplegic measurements, with mean spherical equivalent differences ranging from 0.63 to 1.23 D(\u003cspan additionalcitationids=\"CR5 CR6 CR7\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e). These systematic errors lead to overestimated myopia prevalence and underestimated hyperopia rates in population-based studies, underscoring the necessity of cycloplegia for reliable refractive error characterization. Nevertheless, routine implementation of cycloplegia faces three major challenges in pediatric practice. Firstly, the procedure demands prolonged waiting periods (\u0026ge;\u0026thinsp;30 minutes) for full cycloplegic effect and causes transient photophobia during accommodation paralysis, significantly disrupting children's daily activities. Second, children receiving cycloplegic eyedrops may experience ocular irritation, which may result in a lack of cooperation from the children or their parents. Third, cycloplegic agents are associated with the risk for the development of mental disorders or toxicity due to central nervous system or cardiovascular disease(\u003cspan additionalcitationids=\"CR10\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e). These limitations, compounded by the logistical challenges of administering cycloplegia in large-scale epidemiological surveys (time constraints, resource intensiveness, and contraindication management), create an urgent need for validated prediction methodologies.\u003c/p\u003e \u003cp\u003eEmerging research has attempted to address this challenge through predictive modeling using non-cycloplegic parameters. Previous investigations have explored combinations of demographic factors (age, gender), ocular biometric measures (e.g., axial length [AL], corneal curvature [CR]), and non-cycloplegic refraction values, and uncorrected visual acuity (UCVA), achieving variable predictive performance (R\u003csup\u003e2\u003c/sup\u003e ranging from 0.26 to 0.92)(\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan additionalcitationids=\"CR13 CR14 CR15 CR16\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e). However, limitations persist in existing models: 1) restricted sample sizes (typically\u0026thinsp;\u0026lt;\u0026thinsp;6000 participants) potentially compromising model generalizability, 2) limited age ranges failing to represent the full developmental spectrum of school-aged children. These constraints limit the translational potential of current models across diverse pediatric practice settings.\u003c/p\u003e \u003cp\u003eIn this study, detailed demographics and ocular biometric parameters from 28901 Chinese children aged 3 to 17 years- the largest cohort to date, were collected for cycloplegic refraction prediction modeling. This investigation extends previous work through following innovations: population-based design with broader age representation and rigorous model validation protocols accounting for age-group and refractive error-group heterogeneity. We hope the developed prediction model can potentially be used in future epidemiology studies of refraction and clinical practices in which administering cycloplegic agents on children is not feasible.\u003c/p\u003e"},{"header":"2 Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Participants\u003c/h2\u003e \u003cp\u003eThis retrospective study enrolled children aged 3\u0026ndash;18 years who underwent ophthalmic examinations at the Eye Hospital of Wenzhou Medical University between October 2021 and March 2024. The inclusion criteria were as follows: (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) parental consent for cycloplegic procedures; (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) clinical information was available for before and after cyclopentolate application. Exclusion criteria comprised: ocular organic diseases, manifest strabismus or amblyopia, with a history of ocular surgery, or hypersensitivity to 1% cyclopentolate hydrochloride eye drops. A total of 28901 children was eventually enrolled. All participants were randomly divided into development and validation datasets at an 8:2 ratio. Models for predicting cycloplegic refraction were trained using the development dataset (n\u0026thinsp;=\u0026thinsp;23121 children) and verified using the validation dataset (n\u0026thinsp;=\u0026thinsp;5780 children).\u003c/p\u003e \u003cp\u003e The study protocol was approved by the Institutional Ethics Committee of the Eye Hospital of Wenzhou Medical University (approval no. 2021-233-K-203-03) and adhered to the tenets of the Declaration of Helsinki. Informed consent was obtained from the parents of all participants.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Data collection\u003c/h2\u003e \u003cp\u003eDemographic information, including age, gender, and height was obtained. All participants underwent comprehensive ophthalmic examinations, including distance visual acuity test using retro-illuminated logMAR charts with tumbling-E optotypes, slit-lamp examination of the anterior segment, fundus examination with ophthalmoscopy, intraocular pressure measurement and the assessment of ocular biometrics under non-cycloplegic conditions (e.g., AL, CR) using a IOL Master 500 (Carl Zeiss Meditec, Oberkochen, Germany). The measurements were considered valid if individual measurements of AL varied by no more than 0.02mm. After the non-cycloplegic examinations, the children received two drops of 1% cyclopentolate (Alcon, Fortworth, TX, America) in each eye with an interval of 5 min between drops. Thirty minutes after application of cyclopentolate, loss of direct light reaction and mydriasis was confirmed and the cycloplegic refractive error were measured three times by an autorefractometry (KR 800, Topcon, Tokyo, Japan). Measurements were repeated if any spherical or cylindrical component differed by \u0026gt;\u0026thinsp;0.50 D between readings. The average of three valid measurements was recorded and used for analysis. All data underwent dual-entry verification (EpiData 3.1, Odense, Denmark) with source document reconciliation for discrepancies.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Prediction model development\u003c/h2\u003e \u003cp\u003eOn the basis of the collected demographic, biometric and autorefractometric data, the prediction model for cycloplegic refractive error was developed by applying multiple regression analysis. Candidate variables included: AL(\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e), CR(\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e), Axial length/corneal radius of curvature ratio (AL/CR) (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e), gender(\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e), and age(\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e) as independent variables, given that they had previously been identified as factors related to ocular refraction. Meanwhile, height was also factored into the modeling, considering that the ocular development is affected by the growth of the whole body(\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e). Cycloplegic spherical equivalent refraction (SER) was considered as the dependent variable. A stepwise multiple regression analysis identified significant predictors of cycloplegic SER. Variance inflation factors\u0026thinsp;\u0026lt;\u0026thinsp;10 confirmed absence of multicollinearity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Statistical Analysis\u003c/h2\u003e \u003cp\u003eRight-eye data were analyzed to avoid interocular correlation bias. Cycloplegic SER values were calculated as sphere plus half of the cylinder for each eye. Myopia was defined as cycloplegic SER \u0026minus;\u0026thinsp;0.50 D or worse. Emmetropia was defined between \u0026minus;\u0026thinsp;0.50 D and +\u0026thinsp;0.50 D and hyperopia was defined as greater than +\u0026thinsp;0.50 D. Continuous variables were expressed as mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation (SD). Demographic and biometric characteristics were compared between the development and validation datasets using independent t-tests for continuous variables and chi-square tests for categorical variables to verify baseline comparability. Model performance was evaluated using the coefficient of determination (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e), correlation coefficient \u003cem\u003er\u003c/em\u003e, mean error (ME), and mean absolute error (MAE) of differences between predicted and measured cycloplegic SER (calculated as predicted \u0026ndash; measured), as well as the clinical accuracy proportions (predictions within \u0026plusmn;\u0026thinsp;0.50 D/\u0026plusmn;1.00 D). The predicted and measured cycloplegic SER were also statistically compared using paired t-test and Bland-Altman analysis. All statistical analysis was performed with SPSS Statistics software version 27 (SPSS Inc., Chicago, IL). A \u003cem\u003ep\u003c/em\u003e value of \u0026lt;\u0026thinsp;0.05 was considered statistically significant.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results","content":"\u003cp\u003eA total of 28901 participants were enrolled in this study, the age ranged from 3 to 17 years, with a mean age of 9.72\u0026thinsp;\u0026plusmn;\u0026thinsp;2.54 years old. Females (n\u0026thinsp;=\u0026thinsp;13777) accounted for 47.67% of the study population. The development dataset included 23121 children (11014 girls), and the validation dataset included 5780 children (2763 girls), with a mean age of 9.73\u0026thinsp;\u0026plusmn;\u0026thinsp;2.54 years and 9.68\u0026thinsp;\u0026plusmn;\u0026thinsp;2.52 years, respectively. The basic characteristics were shown in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The two groups were similar in age, gender, height, and most of the biometric measures. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e depicted the age-specific cycloplegic SER distribution based on all the enrolled refraction data. The results revealed a gradual decrease in SER with increasing age, which was consistent with the expected pattern of normal growth and development. The mean cycloplegic SER was \u0026minus;\u0026thinsp;0.77\u0026thinsp;\u0026plusmn;\u0026thinsp;1.93 D in the development dataset and \u0026minus;\u0026thinsp;0.73\u0026thinsp;\u0026plusmn;\u0026thinsp;1.92 D in the validation dataset, confirming balanced refractive status allocation.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eCharacteristics of the development and validation datasets\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"9\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eCharacteristics\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eDevelopment dataset\u003c/p\u003e\n \u003cp\u003e(n\u0026thinsp;=\u0026thinsp;23121)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eValidation dataset\u003c/p\u003e\n \u003cp\u003e(n\u0026thinsp;=\u0026thinsp;5780)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e\u003cem\u003eP\u003c/em\u003e values\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eAge (y), n (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e106 (0.46)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e29 (0.50)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e300 (1.30)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e82 (1.42)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e456 (1.97)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e121 (2.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e2075 (8.97)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e573 (9.91)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e3548 (15.35)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e836 (14.46)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e3403 (14.72)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e838 (14.50)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e3459 (14.96)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e876 (15.16)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e2872 (12.42)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e717 (12.40)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e2050 (8.87)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e541 (9.36)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e1466 (6.34)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e358 (6.19)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e1759 (7.61)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e467 (8.08)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e1268 (5.48)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e271 (4.69)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e309 (1.34)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e59 (1.02)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e38 (0.16)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e10 (0.17)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e12 (0.05)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e2 (0.03)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e9.73\u0026thinsp;\u0026plusmn;\u0026thinsp;2.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e9.68\u0026thinsp;\u0026plusmn;\u0026thinsp;2.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e0.141\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMale: Female (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e12107:11014 (52.36: 47.64)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e3017:2763 (52.20: 47.80)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e0.821\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eHeight (cm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e140.85\u0026thinsp;\u0026plusmn;\u0026thinsp;16.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e140.51\u0026thinsp;\u0026plusmn;\u0026thinsp;16.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e0.152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eAL (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e23.75\u0026thinsp;\u0026plusmn;\u0026thinsp;1.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e23.71\u0026thinsp;\u0026plusmn;\u0026thinsp;1.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e0.019\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eCR (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e7.81\u0026thinsp;\u0026plusmn;\u0026thinsp;0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e7.81\u0026thinsp;\u0026plusmn;\u0026thinsp;0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e0.533\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eAL/CR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e3.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e3.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e0.037\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eCycloplegic SER (D), n (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e\u0026le;\u0026minus;6.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e304 (1.31)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e74 (1.28)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e\u0026gt;\u0026minus;6.0, \u0026le;\u0026minus;3.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e2950 (12.76)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e691 (11.96)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e\u0026gt;\u0026minus;3.0, \u0026le;\u0026minus;0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e8658 (37.45)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e2138 (36.99)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e\u0026gt;\u0026minus;0.5, \u0026le;+0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e4758 (20.58)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e1256 (21.73)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e\u0026gt;+0.5, \u0026le;+2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e5840 (25.26)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e1464 (25.33)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e\u0026gt;+2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e611 (2.64)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e157 (2,72)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-0.77\u0026thinsp;\u0026plusmn;\u0026thinsp;1.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-0.73\u0026thinsp;\u0026plusmn;\u0026thinsp;1.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e0.148\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"1\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Establishment of the prediction model\u003c/h2\u003e\n \u003cp\u003eWith the clinical parameter values from the development dataset, a multivariable prediction model for cycloplegic SER was developed. The stepwise multiple regression analysis identified five significant predictors of cycloplegic SER (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001 for all, Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e): AL, AL/CR, height, gender, and age. The derived prediction model was: \u003cem\u003eCycloplegic SER\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003e39.921\u0026thinsp;\u0026minus;\u0026thinsp;0.028*age\u0026thinsp;+\u0026thinsp;0.445*gender\u0026thinsp;+\u0026thinsp;0.009*height-0.493*AL-9.941*AL/CR\u003c/em\u003e (gender: boy\u0026thinsp;=\u0026thinsp;1, girl\u0026thinsp;=\u0026thinsp;0; age in years; height in centimeters). The correlation coefficient r of this model was 0.924 (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.854, Fig.\u0026nbsp;2A). The overall ME and MAE between predicted and measured cycloplegic SER were \u0026minus;\u0026thinsp;0.02\u0026thinsp;\u0026plusmn;\u0026thinsp;0.74 D and 0.57\u0026thinsp;\u0026plusmn;\u0026thinsp;0.47 D, respectively.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eMultiple regression analysis for predicting cycloplegic SER based on clinical information in the development dataset (n\u0026thinsp;=\u0026thinsp;23121)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRegression Coefficient (standard error)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eP\u003c/em\u003e value\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVariance Inflation Factor\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIntercept\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e39.921 (0.143)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAge\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.028 (0.005)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.404\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGender (boy\u0026thinsp;=\u0026thinsp;1, girl\u0026thinsp;=\u0026thinsp;0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.445 (0.010)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.110\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHeight\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.009 (0.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.153\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAL\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.493 (0.007)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.916\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAL/CR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-9.941 (0.060)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.818\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eWhen analyses of these differences were stratified by age, the ME and MAE between predicted and measured cycloplegic SER for each age group were within 0.19 D and 0.74 D in the development dataset (Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). When stratified by level of measured cycloplegic SER, the ME and MAE for each cycloplegic SER group were within \u0026minus;\u0026thinsp;0.15 D and 0.54 D, except when the cycloplegic SER was lower than \u0026minus;\u0026thinsp;3.00 D or greater than +\u0026thinsp;2.00 D, in which case the ME and MAE was larger (-0.79\u0026thinsp;~\u0026thinsp;0.50 D and 0.72\u0026thinsp;~\u0026thinsp;0.89 D, respectively). The Bland-Altman plot for the differences between predicted and measured cycloplegic SER in the development dataset was shown in Fig.\u0026nbsp;3A, with 95% limits of agreement ranging from \u0026minus;\u0026thinsp;1.467 to 1.431 D. The differences were all around 0 when cycloplegic SER measures were low myopia, emmetropia, or low hyperopia; and most of differences were negative when cycloplegic SER were medium or high hyperopia. The predicted cycloplegic SER within \u0026plusmn;\u0026thinsp;0.50 D and \u0026plusmn;\u0026thinsp;1.00 D of measured cycloplegic SER for 53.19% and 84.44% of the eyes, with a relatively higher proportion in the subgroup of age from 3 to 10 years old or cycloplegic SER from +\u0026thinsp;0.50 to +\u0026thinsp;2.00 D.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eDifference between predicted and measured cycloplegic spherical equivalents in the development dataset and the validation dataset by age group and by cycloplegic refractive error group\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"9\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eDevelopment Dataset (n\u0026thinsp;=\u0026thinsp;23121)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eValidation Dataset (n\u0026thinsp;=\u0026thinsp;5780)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean Difference Between Predicted and Measured Cycloplegic SER, Mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean Absolute Error Between Predicted and Measured Cycloplegic SER, Mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDifference Between Predicted and Measured Cycloplegic SER\u0026thinsp;\u0026le;\u0026thinsp;\u0026plusmn;\u0026thinsp;0.50D, %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDifference Between Predicted and Measured Cycloplegic SER\u0026thinsp;\u0026le;\u0026thinsp;\u0026plusmn;\u0026thinsp;1.00D, %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean Difference Between Predicted and Measured Cycloplegic SER, Mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean Absolute Error Between Predicted and Measured Cycloplegic SER, Mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDifference Between Predicted and Measured Cycloplegic SER\u0026thinsp;\u0026le;\u0026thinsp;\u0026plusmn;\u0026thinsp;0.50D, %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDifference Between Predicted and Measured Cycloplegic SER\u0026thinsp;\u0026le;\u0026thinsp;\u0026plusmn;\u0026thinsp;1.00D, %\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOverall\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.02\u0026thinsp;\u0026plusmn;\u0026thinsp;0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.57\u0026thinsp;\u0026plusmn;\u0026thinsp;0.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e53.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e84.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u0026thinsp;\u0026plusmn;\u0026thinsp;0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.56\u0026thinsp;\u0026plusmn;\u0026thinsp;0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e53.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e84.91\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBy age (y)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u0026ndash;6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.19\u0026thinsp;\u0026plusmn;\u0026thinsp;0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.55\u0026thinsp;\u0026plusmn;\u0026thinsp;0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e56.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e85.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.19\u0026thinsp;\u0026plusmn;\u0026thinsp;0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.55\u0026thinsp;\u0026plusmn;\u0026thinsp;0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e57.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e85.84\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u0026ndash;10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.07\u0026thinsp;\u0026plusmn;\u0026thinsp;0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e56.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11\u0026ndash;14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.64\u0026thinsp;\u0026plusmn;\u0026thinsp;0.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e47.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e79.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.63\u0026thinsp;\u0026plusmn;\u0026thinsp;0.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e48.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e80.76\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15\u0026ndash;18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.74\u0026thinsp;\u0026plusmn;\u0026thinsp;0.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e42.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e71.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.35\u0026thinsp;\u0026plusmn;\u0026thinsp;0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.73\u0026thinsp;\u0026plusmn;\u0026thinsp;0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e39.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e74.65\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eBy cycloplegic SER (D)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026le;-6.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.74\u0026thinsp;\u0026plusmn;\u0026thinsp;0.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.34\u0026thinsp;\u0026plusmn;\u0026thinsp;0.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.36\u0026thinsp;\u0026plusmn;\u0026thinsp;0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e36.49\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026gt; \u0026minus;6.0 to \u0026le;\u0026thinsp;\u0026minus;\u0026thinsp;3.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.50\u0026thinsp;\u0026plusmn;\u0026thinsp;0.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.72\u0026thinsp;\u0026plusmn;\u0026thinsp;0.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e42.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e73.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.54\u0026thinsp;\u0026plusmn;\u0026thinsp;0.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.71\u0026thinsp;\u0026plusmn;\u0026thinsp;0.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e40.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e74.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026gt; \u0026minus;3.0 to \u0026le;\u0026thinsp;\u0026minus;\u0026thinsp;0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.05\u0026thinsp;\u0026plusmn;\u0026thinsp;0.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e87.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.05\u0026thinsp;\u0026plusmn;\u0026thinsp;0.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86.81\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026gt; \u0026minus;0.5 to \u0026le;\u0026thinsp;+\u0026thinsp;0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.54\u0026thinsp;\u0026plusmn;\u0026thinsp;0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e54.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e85.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.08\u0026thinsp;\u0026plusmn;\u0026thinsp;0.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.52\u0026thinsp;\u0026plusmn;\u0026thinsp;0.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e56.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e88.85\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026gt;+0.5 to \u0026le;\u0026thinsp;+\u0026thinsp;2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.50\u0026thinsp;\u0026plusmn;\u0026thinsp;0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e58.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e89.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.11\u0026thinsp;\u0026plusmn;\u0026thinsp;0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.51\u0026thinsp;\u0026plusmn;\u0026thinsp;0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e59.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e87.98\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026gt;+2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.79\u0026thinsp;\u0026plusmn;\u0026thinsp;0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.89\u0026thinsp;\u0026plusmn;\u0026thinsp;0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e37.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e62.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.69\u0026thinsp;\u0026plusmn;\u0026thinsp;0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.83\u0026thinsp;\u0026plusmn;\u0026thinsp;0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e36.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e68.15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Validation of the prediction model\u003c/h2\u003e\n \u003cp\u003eTo validate the performance of the prediction model, the clinical information from the validation dataset were applied to the model and then compared the predicted cycloplegic SER with the measured cycloplegic SER for each eye. The model demonstrated a strong correlation with measured cycloplegic SER in the validation dataset (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.926, \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.858, Fig.\u0026nbsp;2B). The overall ME and MAE between predicted and measured cycloplegic SER were 0.00\u0026thinsp;\u0026plusmn;\u0026thinsp;0.72 D and 0.56\u0026thinsp;\u0026plusmn;\u0026thinsp;0.46 D, respectively. The mean difference of cycloplegic predicted values and measured values were not significantly different (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.985).\u003c/p\u003e\n \u003cp\u003eStratified analyses revealed that the ME and MAE between predicted and measured cycloplegic SER across age subgroups were within 0.35 D and 0.73 D (Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). When analyses were stratified by level of measured cycloplegic SER, the ME and MAE for cycloplegic SER subgroups were within \u0026minus;\u0026thinsp;0.11 D and 0.53 D, except when the cycloplegic SER was lower than \u0026minus;\u0026thinsp;3.0 D or greater than +\u0026thinsp;2.0 D, in which case the ME ranged \u0026minus;\u0026thinsp;0.69\u0026thinsp;~\u0026thinsp;1.34 D and MAE ranged 0.71\u0026thinsp;~\u0026thinsp;1.36 D between the predicted and measured cycloplegic SER. Bland-Altman analysis showed a 95% limits of agreement of -1.420\u0026thinsp;~\u0026thinsp;1.421 D in the validation dataset (Fig.\u0026nbsp;3B). The proportion of the prediction errors within \u0026plusmn;\u0026thinsp;0.50 D and \u0026plusmn;\u0026thinsp;1.00 D were 53.86% and 84.91%, respectively, with peak performance in the subgroup of age from 3 to 10 years (56.23\u0026thinsp;~\u0026thinsp;57.14% within \u0026plusmn;\u0026thinsp;0.50 D) or cycloplegic SER from +\u0026thinsp;0.50 to +\u0026thinsp;2.00 D (59.02% within \u0026plusmn;\u0026thinsp;0.50 D).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eIn this study, we developed and validated a prediction model for predicting cycloplegic refractive error based on the non-cycloplegic data, including demographics (age, gender, and height) and ocular biometric parameters from the optical biometer IOL Master 500. In both the development and validation datasets, this model predicted cycloplegic SER moderately well, showing no clinically significant deviation from measured cycloplegic SER (e.g., mean difference less than 0.25 D) when the cycloplegic refractive error was low myopia, emmetropia, or low hyperopia (\u0026thinsp;\u0026le;\u0026thinsp;+\u0026thinsp;2.0 D). This prediction model is therefore potentially applicable to large-scale screening in epidemiological studies and myopia risk assessment in clinical process. It would save time in the clinical evaluation as well as avoid the adverse effects of cycloplegic eyedrops.\u003c/p\u003e \u003cp\u003eThe correlation coefficients for comparisons of predicted cycloplegic SER with measured cycloplegic SER was 0.926 (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.858) in the external validation dataset, suggesting that this prediction model yielded acceptable refractive information in children. This result outperformed earlier biometric-focused approaches using AL, CR, or the AL/CR ratio, which reported correlations of 0.53 to 0.81 between predicted and measured cycloplegic refractive error in children aged 3 to 13 years(\u003cspan additionalcitationids=\"CR13 CR14\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e). The other prediction models for the cycloplegic refractive error used ocular biometric measures(\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e), non-cycloplegic refractive error(\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e), and UCVA(\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e), yielding mixed results. Magome et al.(\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e) developed and validated prediction models for cycloplegic spherical and cylinder refraction in 2\u0026thinsp;~\u0026thinsp;9 years old Japanese children (n\u0026thinsp;=\u0026thinsp;1040) using demographics (age and gender) and ocular biometric parameters (AL, anterior chamber depth, lens thickness, corneal refractive power, and corneal astigmatism). Their prediction models achieved a precision with mean differences of -0.12 D for sphere and \u0026minus;\u0026thinsp;0.01 D for cylinder between predicted and measured cycloplegic refraction, and the correlations between predicted and measured refraction were 0.96 (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.924) for sphere and 0.89 (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.799) for cylinder. Our prediction model differs from their model in that this model predicts the cycloplegic spherical equivalent, a measure commonly used to define the myopia. Similar to our study, He et al.(\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e) developed prediction models for cycloplegic spherical equivalent based on age, gender, AL and AL/CR ratio. They reported a comparable \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e of 0.87, but slightly lower clinical accuracy (47% within \u0026plusmn;\u0026thinsp;0.5D and 79% within \u0026plusmn;\u0026thinsp;1.0D), likely due to the differences in modeling approach (their non-linear regression vs. our linear regression) and predictors (the factor of height was additionally included in our prediction model). Sankaridurg et al.(\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e) established prediction models based on 6017 Chinese children ages 4 to 15 years by using age, non-cycloplegic refractive error, and UCVA. Their prediction model yielded \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e of 0.91. Wang et al. also(\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e) developed and validated prediction models for cycloplegic spherical equivalent based on 3436 Chinese children ages 5 to 18 years by using age, gender, non-cycloplegic refractive error, UCVA, AL/CR ratios, intraocular pressure, and glasses-wearing status, with a mean difference of 0.06\u0026thinsp;\u0026plusmn;\u0026thinsp;0.64 D and \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e of 0.92. Compared with the studies by Sankaridurg et al. and Wang et al., the results of our model were slightly inferior, which may be attributed to the inclusion of non-cycloplegic refractive error as a modeling factor in their models. Previous studies have indicated that non-cycloplegic spherical equivalent, AL, and the AL/CR ratio are crucial factors in predicting cycloplegic refractive error(\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). In comparison to these studies, our five-variable model maintains clinical utility with simplified data collection, including age, gender, height, AL and AL/CR ratio, all of which are obtainable under non-cycloplegic conditions. Since our prediction model was developed in a large sample and independently validated in another large sample of children with a wide range of ages (3 to 17 years old) and refractive error status (cycloplegic spherical equivalent from \u0026minus;\u0026thinsp;10.25 to +\u0026thinsp;8.50 D), it has the potential to be applicable to population-based research when measuring cycloplegic refractive error in all children is not feasible.\u003c/p\u003e \u003cp\u003eNotably, the model demonstrated superior performance in early childhood (aged 3 to 10 years) or for low hyperopia refractive status (cycloplegic SER from +\u0026thinsp;0.5 to +\u0026thinsp;2.00 D), which is a crucial window when hyperopic reserve depletion accelerates myopia onset. Epidemiological evidence indicated that children who are emmetropia at the first grade have a probability of developing myopia by the end of primary school as high as 92.6%. In contrast, the first-graders who possess a hyperopia reserve\u0026thinsp;\u0026ge;\u0026thinsp;+\u0026thinsp;2.00D have a mere 4.6% myopia risk by graduation(\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e). This finding underscores that children with low hyperopia reserve are at a significantly higher risk of developing myopia compared to those with high hyperopia reserve. Therefore, this prediction model may hold considerable potential for early warning of myopia risk in younger children with insufficient hyperopia reserve.\u003c/p\u003e \u003cp\u003eThe precise measurement of refraction data without the effect of accommodation in young children requires the use of cycloplegic eyedrops. However, application of cycloplegia faces practical challenges in large-scale epidemiological surveys due to time constraints, resource limitations, and potential contraindications. These disadvantages sometimes preclude the use of cycloplegic evaluation as a screening procedure to detect real refractive status in children. In the present study, a prediction model was developed on the basis of simple demographic and ocular biometric parameters obtained under the non-cycloplegic condition, and it provided predicted refraction values with moderate predictive accuracy. This approach enhances feasibility in resource-limited settings where cycloplegic agents are cost-prohibitive or contraindicated, and can potentially be applied to correct the well-known overestimation of myopia prevalence and underestimated hyperopia due to non-cycloplegic refractive error measurements.\u003c/p\u003e \u003cp\u003eHowever, there were several limitations in this study. First of all, the prediction model did not include predictors such as non-cycloplegic refractive values and anterior chamber depth, which may explain the slightly inferior performance versus the existing optimal model. Future studies will improve the prediction accuracy by including more correlation factors and algorithm optimization. Secondly, this study used a IOL Master 500 optical biometer in Chinese children; thus, the findings may not be directly generalizable to different types of biometers or children of other races or ethnicities. The prediction model may have to be calibrated and further validated before its use in settings different from those in our study. Finally, the reduced accuracy in predicting medium to high myopia or hyperopia limits utility for these subgroups.\u003c/p\u003e"},{"header":"5 Conclusions","content":"\u003cp\u003eIn this study, we developed and validated a multivariable prediction model for predicting cycloplegic refractive error using the available demographics and ocular biometric data. This prediction model achieves a practical balance between accuracy and clinical feasibility for estimating cycloplegic refraction. It demonstrated reasonably accurate estimates of cycloplegic refractive error in young children with low magnitude refractive error (low myopia, emmetropia, and low hyperopia) while avoiding the possible side effects or patient refusal associated with the use of cycloplegic agents. While the model's predictive performance (\u003cem\u003eR\u0026sup2;\u003c/em\u003e=0.858) slightly trails the optimal reported models, this study provides crucial evidence regarding the feasibility of large-scale cycloplegic prediction and identifies key determinants for future model optimization. The developed tool holds particular value for epidemiological surveys in resource-limited settings and clinical management of children with cycloplegia contraindications.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eAL\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eaxial length\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCR\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003ecorneal curvature\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eUCVA\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003euncorrected visual acuity\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eAL/CR\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAxial length/corneal radius of curvature ratio\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSER\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003espherical equivalent refraction\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSD\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003estandard deviation\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eME\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003emean error\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eMAE\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003emean absolute error\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e7.1 Ethics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study protocol was approved by the Ethics Committee of the Eye Hospital of Wenzhou Medical University (2021-233-K-203-03) in accordance with the Declaration of Helsinki. All participants were provided with and signed informed consent forms.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.2 Consent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.3 Availability of data\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.4 Competing interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.6 Funding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that no funds, grant, or other support were received during the preparation of this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.7 Authors' contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConception and design: BCC, LFJ, SZX; Data acquisition: BCC, LFJ, LT, MYY, FYT, QCY, MYZ; Data analysis and interpretation: BCC, LFJ, LT; Manuscript drafting and revisions: BCC, SZX. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.8 Acknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eFlitcroft DI, He M, Jonas JB, Jong M, Naidoo K, Ohno-Matsui K, et al. Imi - Defining and Classifying Myopia: A Proposed Set of Standards for Clinical and Epidemiologic Studies. Invest Ophthalmol Vis Sci. 2019;60(3):M20\u0026ndash;30. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1167/iovs.18-25957\u003c/span\u003e\u003cspan address=\"10.1167/iovs.18-25957\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDoherty SE, Doyle LA, McCullough SJ, Saunders KJ. Comparison of Retinoscopy Results with and without 1% Cyclopentolate in School-Aged Children. 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Cohort Study on the Association between Hyperopia Reserve and Myopia Incidence in Primary School Students: The Anyang Childhood Eye Study. Chin J Ophthalmol. 2022;58(10):754\u0026ndash;9. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3760/cma.j.cn112142-20211028-00509\u003c/span\u003e\u003cspan address=\"10.3760/cma.j.cn112142-20211028-00509\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-ophthalmology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"boph","sideBox":"Learn more about [BMC Ophthalmology](http://bmcophthalmol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/boph","title":"BMC Ophthalmology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Cycloplegic, refractive error, prediction, non-cycloplegic, Chinese childre","lastPublishedDoi":"10.21203/rs.3.rs-6478499/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6478499/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eIntroduction\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCycloplegic refraction remains the gold standard for pediatric refractive assessment, yet its implementation faces challenges in large-scale studies. This study aimed to develop a multivariable model predicting cycloplegic spherical equivalent refraction (SER) using non-cycloplegic measurements in Chinese children.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis retrospective study included 28901 children aged 3–17 years, who were allocated to development (n = 23121) and validation (n = 5780) datasets. Ocular biometric parameters were assessed with the IOL Master 500 optical biometer. Cycloplegic SER was measured using a Topcon autorefractor after 1% cyclopentolate. A prediction model was derived and validated, with performance evaluated by \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e, correlation coefficient, mean error (ME), mean absolute error (MAE), and clinical accuracy proportions (predictions within ± 0.50 D/±1.00 D).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe prediction model, incorporating age, gender, height, axial length, and axial length/corneal radius of curvature ratio, achieved \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e = 0.854 (development) and 0.858 (validation), with ME = 0.00 ± 0.72 D and MAE = 0.56 ± 0.46 D in the validation dataset. Clinical accuracy proportions (± 0.50 D/±1.00 D) were 53.86% and 84.91%, respectively. Optimal performance was observed in children aged 3–10 years and those with cycloplegic SER between + 0.50 and + 2.00 D.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis prediction model based on simplified non-cycloplegic parameters provides reasonably accurate cycloplegic SER estimates in young children with low refractive error. It holds potential for epidemiological surveys in resource-limited settings and clinical management of children with cycloplegia contraindications.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eClinical trial number\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003enot applicable.\u003c/p\u003e","manuscriptTitle":"Prediction of Cycloplegic Refractive Error based on Non-Cycloplegic Measurements in Chinese Children aged 3 to 17 years","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-26 08:35:24","doi":"10.21203/rs.3.rs-6478499/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"172718491455318605475500524366707412283","date":"2026-05-03T22:38:23+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-06T02:42:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"97112562046997927221117235319865624781","date":"2025-05-26T00:09:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"317517663612117252757027323925765797940","date":"2025-05-21T22:57:45+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-21T12:50:50+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-04-22T05:24:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-04-21T02:51:17+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-21T02:50:32+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Ophthalmology","date":"2025-04-18T10:55:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-ophthalmology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"boph","sideBox":"Learn more about [BMC Ophthalmology](http://bmcophthalmol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/boph","title":"BMC Ophthalmology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bea736cf-5a00-4d4d-9733-da44dc2f3701","owner":[],"postedDate":"May 26th, 2025","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"172718491455318605475500524366707412283","date":"2026-05-03T22:38:23+00:00","index":97,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-05-26T08:35:24+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-26 08:35:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6478499","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6478499","identity":"rs-6478499","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}