In the present study, we selected preoperative parameters by removing features with low variance, recursive feature elimination, embedded method, and physician experience. Then, RFR, XGBoost, and LR were trained to predict the vault at 1 week after ICL V4c implantation. MAE, MedAE, RMSE, and SMAPE were used to assess the error between the predicted vault and the actual vault. Furthermore, a Bland‒Altman plot was used to evaluate the prediction consistency of these machine learning models. Our results demonstrated that XGBoost had the lowest prediction error, with mean MAE, RMSE, and SMAPE values of 121.70 µm, 148.87 µm, and 19.13%, respectively. The Bland‒Altman plots of RFR and XGBoost showed better prediction consistency than LR. However, XGBoost showed narrower 95% LoA than RFR, ranging from −307.12 to 256.59 µm. This study proposed to evaluate the feasibility of using machine learning methods to predict the vault after ICL implantation, and XGBoost showed better performance than RFR and LR. It can not only reduce complications caused by too high or too low vaults but also reduce the secondary surgery rate.
Previous studies have shown that ICL V4c size, ICL V4c MRSE, ACD, ATA, ACW, CLR, LT, and PD are important parameters in predicting the vault after ICL V4c implantation.
22–27 In our study, the physician experience selection method included the aforementioned parameters and showed the lowest MAE value (119.79 µm) among the four parameter selection methods. This result suggests that the best training quality of the model was obtained when applying parameters selected by this method as input. Furthermore, compared to previous machine learning models, our study included the inferior surface curvature of the iris measured by a self-developed program to indirectly reflect the iris morphological characteristics. Chen et al.
28 analyzed parameters associated with the vault after ICL V4c implantation and showed a 4% increase in the odds of a vault greater than 1000 µm for every 1° reduction in the iris–ciliary angle. The inferior surface curvature of the iris showed an opposite trend to changes in the iris–ciliary angle. This result indicates that a greater inferior surface curvature of the iris is associated with a higher probability of high vault after ICL V4c implantation. Shen et al.
21 compared the prediction results of different machine learning models and found that RFR had the best performance in predicting the vault after ICL V4c implantation. Our study also adopted RFR to predict the vault, but the RMSE was lower than that of the study by Shen et al.
21 We speculated that the difference in RMSE is related to the inferior iris surface curvature, which may improve the prediction performance of the model.
In 2018, Nakamura et al.
29 applied ASOCT to measure the anterior segmental parameters and used multiple linear regression analysis to establish an ICL vault size prediction formula, where ICL vault (mm) = 0.5 + 1.1 × (implanted ICL size – 4.575–0.688 × ACW [mm] – 0.388 × CLR [mm]). However, that study was based on few variables and a relatively small sample size. Therefore, Igarashi et al.
12 added preoperative parameters and obtained a different ICL vault size prediction formula: Ks formula (ICL vault [mm]) = 660.9 × (ICL size – ATA [mm] + 86.6). However, Ando et al.
30 performed a study to compare the achieved vault using a manufacturer's nomogram and the predicted vault using the KS formula. Their results showed that the predicted vault tended to overestimate the actual vault, especially when selecting a larger ICL size. This might be related to the ignorance of nonlinear factors associated with the postoperative vault. Compared to multiple linear regression analysis, RFR has superior performance because it does not have to consider issues related to the independence of variables, multicollinearity, and the normal distribution of residuals, and it can calculate the nonlinear effect between input variables.
31 Based on the findings of Kamiya et al.,
20 it was suggested that RFR performed better than LR in predicting the vault after ICL V4c implantation. Shen et al.
21 used various machine learning methods to predict the vault after ICL V4c implantation and found that RFR was the method with the best prediction. Our study also found that MAE, MedAE, RMSE, and SMAPE values of the RFR were lower than those of LR. Additionally, the 95% LoA of RFR were narrower than those of LR, indicating that the prediction performance of RFR is better than that of LR. It could be that the preoperative biometric variables may not exhibit a simple linear correlation with the postoperative vault, and LR has limitations in explaining the relationships between measurements. Thus, LR performance was inferior to that of RFR and XGBoost.
32
XGBoost is a machine learning that could be used for both classification and regression.
33,34 Xu et al.
35 used XGBoost and RFR to predict subretinal fluid absorption at 1, 3, and 6 months after laser treatment in patients with central serous chorioretinopathy, and the results indicated that XGBoost had better performance than RFR in the external validation. The study revealed that XGBoost has the advantage of avoiding overfitting. Shen et al.
21 also found that XGBoost was more accurate than RFR in predicting the ICL V4c size at 12.1 mm. In our study, we found that XGBoost had a lower prediction error and narrower 95% LoA than RFR. Additionally, although RFR (136 cases) had a larger sample size of MAE within 50 to 200 µm than XGBoost (125 cases), RFR (95 cases) had a larger sample size of MAE above 200 µm than XGBoost (88 cases), which indirectly reduced the RFR prediction performance.
This study has several strengths. First, our study added anterior chamber angle parameters, developed annotation tools to obtain the inferior surface curvature of the iris, and controlled the direction of ICL V4c implantation. These measures could further improve the predictive performance of machine learning models. Second, XGBoost was used to predict the central vault at 1 week postoperatively, indicating the feasibility of this method in ophthalmic regression studies. However, this study also has limitations. First, our study performed only internal validation, but we will perform external validation in future studies. Second, the preoperative parameters of machine learning methods require manual input, which may lead to accidental errors. Third, our study had a large number of independent variables for the input parameters, and the sample size was not the largest compared to other studies.
20,21 Thus, in a future study, we would use some other machine learning methods to predict the postoperative vault. Finally, the ICL V4c size distribution in the samples was not balanced, which was related to the anterior segment characteristics of the Chinese population. Thus, the sample size of patients implanted with the 13.7-mm and 12.1-mm ICL V4c was small, so the machine learning model may have better performance in predicting the postoperative vault after 12.6-mm and 13.2-mm ICL V4c implantation. We also found that the ICL V4c size had characteristics similar to those reported by Shen et al.,
21 whose study was related to the anterior segmental characteristics of the Chinese population.