Estimation of cycloplegic spherical refraction from non-cycloplegic clinical and biometric data in children using machine learning: a retrospective pilot study for screening triage

To develop and evaluate non-cycloplegic clinical and biometric models for estimating cycloplegic spherical power (DS), spherical equivalent (SE), and astigmatic power-vector components (J0 and J45) in children, and to assess their utility as a preliminary screening-triage aid rather than a substitute for cycloplegic refraction. This retrospective pilot study included 590 children aged 2.4–14.8 years who underwent cycloplegic refraction at the Children’s Hospital, Zhejiang University School of Medicine. The children were randomly divided at the patient level into training and held-out test sets at a ratio of 7:3, ensuring that both eyes from the same child remained in the same set. Astigmatism was expressed using J0 and J45. Power-vector components were calculated separately for non-cycloplegic and post-cycloplegic refraction, and post-cycloplegic J0/J45 served as prediction targets. Seven algorithms were screened; DT, BPNN, GPR, and LR were selected for clinically oriented evaluation using regression metrics, error thresholds, screening indices, subgroup analyses, GEE analysis, and Bland-Altman plots. Age, axial length, corneal astigmatism, corneal power, and UCVA were the main predictors for spherical refraction. After patient-level splitting, DT, BPNN, GPR, and LR showed moderate performance for DS and SE. DT achieved RMSE/R 2 values of 0.776 D/0.819 for DS and 0.781 D/0.823 for SE; BPNN achieved 0.752 D/0.802 for DS and 0.759 D/0.798 for SE. GPR achieved 0.921 D/0.806 for DS and 0.941 D/0.800 for SE, while LR achieved 0.876 D/0.824 for DS and 0.949 D/0.797 for SE. The vector-based analysis showed interpretable J0 outputs for several models, including GPR (R 2 = 0.671), but J45 was weak across models (R 2 approximately − 0.08 to 0.06). For SE-based screening, GPR achieved sensitivity/specificity of 94.09%/86.46% for myopia and 80.00%/98.20% for hyperopia. Only 53.75% of GPR SE estimates were within +/-0.50 D. Non-cycloplegic clinical and biometric variables provided moderate estimates of cycloplegic DS and SE after patient-level data partitioning. The J0/J45 vector analysis indicated partial predictability of J0, whereas J45 prediction was clinically unreliable. This approach should be regarded as an exploratory triage aid for spherical refractive estimation rather than a substitute for cycloplegic refraction.