Accuracy of NK and KS Formulas in Predicting Postoperative Vault at One Month After Implantable Collamer Lens Implantation: A Retrospective Study of 327 Eyes
- 1Shenzhen Eye Hospital; Shenzhen Eye Medical Center, Southern Medical University, Shenzhen, People’s Republic of China
Abstract
Purpose: To evaluate the agreement and accuracy of the Nakamura–Kamiya (NK) and Kimura–Sato (KS) formulas in predicting postoperative vault at one month after implantable collamer lens (ICL) implantation, and to assess the agreement between the ICL sizes recommended by these formulas and the sizes actually implanted.
Methods: This retrospective study included 327 eyes of 168 patients who underwent ICL V4c implantation. Predicted vaults from the NK and KS formulas were compared with achieved vaults at one month. Linear mixed-effects models and generalized estimating equations were used to account for inter-eye correlation, with a one-eye sensitivity analysis. Agreement was assessed using Bland–Altman analysis, the intraclass correlation coefficient, and Cohen’s kappa. Prediction accuracy was assessed using mean absolute error(MAE) and root mean square error(RMSE).
Results: The actual ideal vault rate was 63.61%. The NK formula overestimated vault (median 664 µm vs 574 µm; P < 0.001), whereas the KS formula slightly underestimated it (562 µm vs 574 µm; P = 0.040). The KS formula showed better consistency with actual vault than the NK formula (R2 = 0.264 vs 0.147) and narrower 95% limits of agreement on Bland-Altman analysis.In mixed-effects models, the NK slope was 0.385 (95% CI, 0.238–0.532) and the KS slope was 1.117 (95% CI, 0.856–1.378; both P < 0.001). MAE was 225.91 µm (NK) and 184.18 µm (KS); RMSE was 291.35 µm (NK) and 246.86 µm(KS), respectively. The NK formula recommended the implanted size in 60.24% of eyes and the KS formula in 83.79% (kappa 0.283 and 0.729). Ultrasound biomicroscopy (UBM) measured anterior chamber depth(ACD),crystalline lens rise(CLR), horizontal and vertical sulcus-to-sulcus (STS), and age were independently associated with achieved vault (All P < 0.05).
Conclusion: The KS formula showed better agreement with achieved vault and more frequently recommended the implanted ICL size than the NK formula. However, both formulas showed variable accuracy across ICL sizes, highlighting the need for further refinement to optimize ICL size selection. Because vault was assessed at one month, these findings should be regarded as short-term observations.
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BibTeX
@article{liu2026accuracy,
title = {{Accuracy of NK and KS Formulas in Predicting Postoperative Vault at One Month After Implantable Collamer Lens Implantation: A Retrospective Study of 327 Eyes}},
author = {Zixiao Liu and Xinhua Liu and Xue Yao and Jiantao Wang and Jing Zhang},
journal = {Clinical Ophthalmology (Auckland, N.Z.)},
year = {2026},
month = oct,
doi = {10.2147/opth.s649572},
url = {https://doi.org/10.2147/opth.s649572},
note = {CC BY-NC 4.0},
}
RIS
TY - JOUR
TI - Accuracy of NK and KS Formulas in Predicting Postoperative Vault at One Month After Implantable Collamer Lens Implantation: A Retrospective Study of 327 Eyes
AU - Zixiao Liu
AU - Xinhua Liu
AU - Xue Yao
AU - Jiantao Wang
AU - Jing Zhang
PY - 2026
DA - 2026/10/27
JO - Clinical Ophthalmology (Auckland, N.Z.)
DO - 10.2147/opth.s649572
UR - https://doi.org/10.2147/opth.s649572
AB - Purpose: To evaluate the agreement and accuracy of the Nakamura–Kamiya (NK) and Kimura–Sato (KS) formulas in predicting postoperative vault at one month after implantable collamer lens (ICL) implantation, and to assess the agreement between the ICL sizes recommended by these formulas and the sizes actually implanted. Methods: This retrospective study included 327 eyes of 168 patients who underwent ICL V4c implantation. Predicted vaults from the NK and KS formulas were compared with achieved vaults at one month. Linear mixed-effects models and generalized estimating equations were used to account for inter-eye correlation, with a one-eye sensitivity analysis. Agreement was assessed using Bland–Altman analysis, the intraclass correlation coefficient, and Cohen’s kappa. Prediction accuracy was assessed using mean absolute error(MAE) and root mean square error(RMSE). Results: The actual ideal vault rate was 63.61%. The NK formula overestimated vault (median 664 µm vs 574 µm; P < 0.001), whereas the KS formula slightly underestimated it (562 µm vs 574 µm; P = 0.040). The KS formula showed better consistency with actual vault than the NK formula (R2 = 0.264 vs 0.147) and narrower 95% limits of agreement on Bland-Altman analysis.In mixed-effects models, the NK slope was 0.385 (95% CI, 0.238–0.532) and the KS slope was 1.117 (95% CI, 0.856–1.378; both P < 0.001). MAE was 225.91 µm (NK) and 184.18 µm (KS); RMSE was 291.35 µm (NK) and 246.86 µm(KS), respectively. The NK formula recommended the implanted size in 60.24% of eyes and the KS formula in 83.79% (kappa 0.283 and 0.729). Ultrasound biomicroscopy (UBM) measured anterior chamber depth(ACD),crystalline lens rise(CLR), horizontal and vertical sulcus-to-sulcus (STS), and age were independently associated with achieved vault (All P < 0.05). Conclusion: The KS formula showed better agreement with achieved vault and more frequently recommended the implanted ICL size than the NK formula. However, both formulas showed variable accuracy across ICL sizes, highlighting the need for further refinement to optimize ICL size selection. Because vault was assessed at one month, these findings should be regarded as short-term observations.
SN - 1177-5467
SN - 1177-5483
ER -