Prediction of vaults in eyes with vertical implantable collamer lens implantation

Purpose: To design formulas for predicting postoperative vaults in vertical Implantable Collamer Lens (ICL) implantation and to achieve more precise predictions using machine learning models. Design: Retrospective observational study Setting: XXXX (anonymized for review) Methods: We retrospectively reviewed the medical records of 720 eyes in 408 patients who underwent vertical ICL implantation. The data included age, sex, refractions, anterior segment biometric data, and surgical records. We designed three formulas (named V1-V3 formulas) using multiple linear regression analysis, and tested four machine learning models. Results: Predicted vaults by V1-V3 formulas were 444.17 ± 93.83 μm, 444.08 ± 98.64 μm, and 444.27 ± 108.81 μm, with mean absolute error of 127.97 ± 107.92, 126.41 ± 105.86, and 122.90 ± 103.00 μm. There were no significant differences in error among the V1-V3 formulas, despite the fact that the V1 and V2 formulas referred to limited parameters (three and four, respectively), and the V3 formula referred to all 12 parameters. Two of four machine learning models, XGBoost and Random Forest Regressor, showed a better performance in predicted vaults: 444.52 ± 120.51 and 446.00 ± 102.55 μm and mean absolute error: 118.31 ± 100.55 and 118.63 ± 99.34 μm, respectively. Conclusions: This is the first study to design V1-V3 formulas for vertical ICL implantation. The V1 and V2 formulas exhibited good performance despite the limited parameters. In addition, two of the four machine learning models predicted more precise results.