Abstract
Purpose
To evaluate the performance of seven modern intraocular lens (IOL) power calculation formulas in two different PARTIAL-Range of Field (RoF) extend IOL designs, and a novel IOL constant optimization method.
Methods
200 eyes implanted with Acrysof IQ Vivity or Tecnis Symfony IOL were included. Postoperative refractive outcomes of the Barrett Universal II (BUII), Cooke K6, EVO 2.0, Hill-RBF 3.0, Hoffer QST, Kane, and Pearl DGS formulas were compared. IOL constant is optimized by using ‘three variable optimization’ (TVO) (https://ioloptimization.com/calculator). Formula Performance Index (FPI), root-mean-square absolute prediction error (RMSAE), and SD of prediction errors were selected as the primary endpoints.
Results
In the Vivity group, the FPI in descending order was Cooke K6 (0.613), Kane (0.496), Hill-RBF 3.0 (0.478), Pearl DGS (0.474), BUII (0.430), EVO 2.0 (0.405), and Hoffer QST (0.341). No significant inter-formula differences were found in RMSAE and SD. In the Symfony group, the FPI in descending order was Cooke K6 (0.495), Pearl DGS (0.473), Hill-RBF 3.0 (0.428), BUII (0.403), Kane (0.385), EVO 2.0 (0.352), and Hoffer QST (0.310). Cooke K6 outperformed Hoffer QST (P = 0.032) and Pearl DGS (P = 0.027) in SD. The optimized A-constants vary among formulas derived from the same IOL model (Vivity: range 118.97 to 119.14; Symfony: range 119.17 to 119.36). All formulas achieved a mean prediction error of less than 0.012 D after constant optimization.
Conclusions
Modern IOL power calculation formulas exhibit high accuracy for PARTIAL-RoF extend IOLs, with performance varying by IOL model. The TVO proved to be an effective and convenient tool.
Supplementary Information
The online version contains supplementary material available at 10.1186/s12886-026-04725-9.
Keywords: IOL power calculation formula, IOL constant optimization, PARTIAL-Range of Field IOL
Introduction
Premium intraocular lenses (IOLs) represent a rapidly advancing field in cataract and refractive surgery. Emerging PARTIAL-Range of Field (RoF) extend IOL technologies are designed to enhance intermediate vision without compromising distance visual acuity [1, 2]. The PARTIAL-RoF extend IOLs offer favorable outcomes for both far and intermediate vision, alongside functional near vision, while exhibiting fewer photic phenomena and superior contrast sensitivity compared to traditional multifocal IOLs [3–5]. Clinical studies have suggested that PARTIAL-RoF extend IOLs require precise refractive outcomes, as even small deviations from emmetropia can impact far vision [6]. As patient expectations for visual outcomes continue to rise, achieving optimal surgical results increasingly depends on the precision of IOL power calculation. Inaccurate IOL power calculations are caused by errors in the measurements of anterior chamber depth (ACD), axial length (AL), and corneal keratometry (Sim K) in 42%, 36%, and 22% of cases, respectively [7]. It is estimated that the percentage of eyes with prediction error (PE) within ± 0.5 diopter (D) is 73.7% [8].
With the growing adoption of two specific PARTIAL-RoF extend IOL models—the Acrysof IQ Vivity (Alcon Laboratories, Inc.) and Tecnis Symfony (Johnson & Johnson Vision, Inc.)—evaluating the performance of IOL power calculation formulas for these lenses has become critically important. However, limited research has focused on accuracy of IOL calculation formula for PARTIAL-RoF extend IOLs. The AcrySof IQ Vivity IOL’s X-WAVE technology features a 1 mm high central plateau across its 2.2 mm optic. This design creates two surface transitions that induce a “stretch and shift” of the wavefront: the first transition slows paraxial light, stretching the wavefront; the second shifts part of the reshaped wavefront anterior to the retina [1]. The Tecnis Symfony IOL utilizes an achromatic diffractive pattern with two primary foci to extend the focus range and correct corneal chromatic aberration, incorporating a biconvex wavefront-designed anterior aspheric surface and a posterior achromatic diffractive surface [2]. The Vivity and Symfony IOLs employ distinct optical strategies to extend the depth of focus, wherein differences in near-add design and IOL architecture lead to varied refractive outcomes, consequently affecting the accuracy of IOL power calculation formulas.
Modern IOL calculation formulas demonstrate satisfactory predictive accuracy, but these formulas are unpublished, making it hard to optimize the constant [9, 10]. Recently, Buonsanti et al. proposed a novel constant optimization method termed “three variable optimization (TVO),” which simplifies the process by utilizing only the initial constant, average IOL power, and average PE [11]. Despite its potential, no studies have yet validated the TVO method in the constant optimization of modern IOL power calculation formulas.
The present study aims to (1) evaluate the performance of modern IOL power calculation formulas in two different PARTIAL-RoF extend IOL models implantation and (2) assess the efficacy of TVO constant optimization method.
Materials and methods
Study design
This retrospective case series was approved by the Institutional Ethics Committee of Xiamen Eye Center, Xiamen University, which waived the requirement for informed consent due to the study’s retrospective nature. The protocol adhered to the tenets of the Declaration of Helsinki.
We reviewed the medical records of 200 eyes of 200 patients who underwent phacoemulsification with implantation of either the Acrysof IQ Vivity IOL (Alcon Laboratories, Inc.) or Tecnis Symfony IOL (Johnson & Johnson Vision) at Xiamen Eye Center between June 2021 and May 2025. Exclusion criteria included postoperative corrected distance visual acuity (CDVA) worse than 20/30, poor retinal function, prior corneal or vitreoretinal surgery, intraoperative capsular damage, or postoperative complications. All surgeries were performed by a single experienced surgeon (G.Z.) using standardized phacoemulsification via a 2.2 mm temporal clear corneal incision with the Centurion Active-Fluidics System (Alcon Laboratories, Inc.). The study protocol for IOL power calculation formulas comparison was based on the methodology previously described by Hoffer and Savini [12].
Outcome measures
Preoperative biometric data—including AL, lens thickness (LT), ACD, Sim K, horizontal corneal diameter (CD), and central corneal thickness (CCT)—were obtained using the IOLMaster 700 (Carl Zeiss Meditec AG). Subjective manifest refraction was assessed postoperatively at 1 to 3 months after surgery, with testing performed at 6 m. The examination was conducted by two experienced optometrists following a standardized protocol. Uncorrected distance visual acuity (UDVA) and CDVA were recorded. The following modern IOL power calculation formulas were evaluated (ESCRS IOL calculator, accessed November 2025): Barrett Universal II (BUII), Cooke K6, Emmetropia Verifying Optical 2.0 (EVO 2.0), Hill-RBF 3.0, Hoffer QST, Kane, and Pearl DGS.
The PE was calculated as the difference between the measured and predicted postoperative spherical equivalent (SE) (actual refraction – predicted refraction). The mean prediction error (ME) is the average of all the PE for each formula. The mean absolute prediction error (MAE), median absolute prediction error (MedAE), root-mean-square absolute prediction error (RMSAE), and percentage of eyes within ± 0.25 D, ± 0.5 D, ± 0.75 D and ± 1.0 D of the PE were also evaluated.
Formula accuracy was further quantified using the IOL Formula Performance Index (FPI), a metric proposes by Wolfgang Haigis [13]:
 |
Here, SDME is the standard deviation of PE; |m| and |k| are the absolute gradient of the relationship of PE with AL and K, respectively; n5 and n10 are the percentage of eyes within ± 0.50 D and ± 1.00 D of PE, respectively. The FPI is a comprehensive metric enables an objective ranking of formulas, offering clinicians a practical reference for selecting the best formula. The higher the FPI, the more accurate the formula [14,15].
Constant optimization
The TVO method proposed that constant optimization can be calculated as follow: Optimized lens constant = original lens constant + (mean PE/optimization coefficient). Buonsanti et al. [11]. found that the optimization coefficient depends on IOL power. This coefficient represents the change in predicted refraction induced by a change of one unit in the IOL constant. They used a dataset of 876 eyes (AL from 17.83 mm to 35 mm) to calculate the optimization coefficient for each IOL power. Constants were optimized for the BUII, Cooke K6, Haigis, Hoffer Q, Holladay 1, Holladay 2, RBF 3.0, SRK/T and T2 with this method, and after constant optimization, the mean PEs ranged between 0 and − 0.03 D in the whole dataset.
Three variables are needed to optimize the lens constant: the mean power of all implanted IOLs in the study group, the mean PE of the entire dataset, and the original lens constant used for the preoperative calculations. The optimization coefficient is provided at ioloptimization.com, so the user only needs to input the three variables into the website and calculate the optimized lens constant. In this study, original lens constants and TVO optimized lens constants are shown in Table 3.
Table 3.
Constant optimization of Vivity and Symfony IOL
| Formula | Vivity group | Symfony group | ||||||
|---|---|---|---|---|---|---|---|---|
| unoptimized constant | unoptimized PE | TVO constant | optimized PE for TVO | unoptimized constant | unoptimized PE | TVO constant | optimized PE for TVO | |
| BUIIa | 1.96 | -0.0655 | 1.91 | 0.010 | 1.91 | 0.1539 | 2.02 | -0.0057 |
| Cooke K6b | 119.16 | -0.0136 | 119.1423 | 0.003 | 119.3 | 0.0483 | 119.3612 | -0.0070 |
| EVO 2.0b | 119.1 | -0.0490 | 119.0398 | 0.003 | 119.3 | -0.1057 | 119.1744 | -0.0038 |
| Hill-RBF 3.0b | 119.16 | -0.1372 | 118.9659 | -0.003 | 119.34 | -0.1113 | 119.1848 | -0.0043 |
| Hoffer QSTc | 5.644 | -0.1544 | 5.5278 | 0.007 | 5.59 | 0.0854 | 5.6525 | -0.0081 |
| Kaneb | 119.08 | -0.0275 | 119.0478 | -0.007 | 119.056 | 0.1293 | 119.2028 | -0.0108 |
| Pearl DGSb | 119.08 | 0.0248 | 119.1097 | 0.001 | 119.3 | 0.0412 | 119.3480 | -0.0124 |
aconstant-Lens Factor; bconstant-A constant; cconstant-pACD
PE = prediction error; TVO = three variable optimization
Statistical analysis
Analyses were performed using SPSS 26.0 (IBM Corporation) and R 4.2.1. Data normality was assessed via the Kolmogorov-Smirnov test. One-sample t test was performed to test whether the mean PE of formula differs significantly from zero. The nonparametric Wilcoxon was used if data was not normally distributed. The RMSAEs of PEs were compared with a bootstrap-t method, according to the statistical analysis suggested by Holladay et al. [16]. SD of PEs were compared using the heteroscedastic HC4 Morgan-Pitman test extension. The Friedman test was used to compare the absolute prediction error of formulas. The Cochran’s Q test was used to compare the proportion of eyes within ± 0.25, ± 0.50, ± 0.75 and ± 1.00 D of PE between formulas. The post-hoc Bonferroni correction was used for multiple comparisons. A P value of less than 0.05 was considered statistically significant.
A priori power analysis (Wilcoxon signed-rank test, Cohen’s effect size = 0.4, power = 0.8, α = 0.05) determined a minimum sample size of 98 eyes for each group.
Results
This study enrolled 200 eyes from 200 patients, with 100 cases each in the Vivity and Symfony groups. The mean age of patients in the Vivity group was 63.86 ± 11.18 years (30 males, 70 females), while in the Symfony group, it was 63.27 ± 8.62 years (37 males, 63 females). No statistically significant difference was found in demographic and biometric parameters between Vivity group and Symfony group, detailed characteristics are presented in Table 1.
Table 1.
Preoperative and postoperative data of enrolled eyes
| Parameter | Vivity Group | Symfony Group | P value |
|---|---|---|---|
| Age, years |
63.86 ± 11.18 range: 31–85 |
63.27 ± 8.62 range: 33–81 |
0.677 |
| Gender, no. (%) | 0.369 | ||
| Male | 30 | 37 | |
| Female | 70 | 63 | |
| AL, mm |
23.37 ± 0.87 range: 21.50-25.44 |
23.24 ± 0.82 range: 21.52–25.55 |
0.285 |
| LT, mm |
4.37 ± 0.48 range: 2.90–5.32 |
4.49 ± 0.38 range: 3.02–5.24 |
0.057 |
| ACD, mm |
2.99 ± 0.38 range: 2.10–4.13 |
2.98 ± 0.35 range: 2.15–4.03 |
0.977 |
| Km, D |
43.99 ± 1.54 range: 40.52–47.91 |
44.02 ± 1.30 range: 41.37–47.10 |
0.878 |
| CD, mm |
11.83 ± 0.41 range: 10.8–12.9 |
11.86 ± 0.40 range: 10.5–12.8 |
0.340 |
| CCT, µm |
537.22 ± 33.19 range: 466–641 |
533.61 ± 31.16 range: 465–613 |
0.756 |
| Postoperative UDVA, logMAR |
0.11 ± 0.10 range: 0.30-0.00 |
0.09 ± 0.11 range: 0.52-0.00 |
0.180 |
| Postoperative CDVA, logMAR |
0.02 ± 0.05 range: 0.15-0.00 |
0.02 ± 0.04 range: 0.20-0.00 |
0.152 |
ACD = anterior chamber depth; AL = axial length; CD = horizontal corneal diameter; CDVA = corrected distance visual acuity; CCT = central corneal thickness; D = diopter; Km = corneal keratometry; logMAR = logarithm of the minimum angle resolution; LT = lens thickness; UDVA = uncorrected distance visual acuity
Accuracy of formulas
All results are reflected in Table 2. The FPI served as a primary outcome measure, as illustrated in Fig. 1. In the Vivity group, the FPI values in descending order were: Cooke K6 (0.613), Kane (0.496), Hill-RBF 3.0 (0.478), Pearl DGS (0.474), BUII (0.430), EVO 2.0 (0.405), and Hoffer QST (0.341). For the Symfony group, the FPI ranked as follows: Cooke K6 (0.495), Pearl DGS (0.473), Hill-RBF 3.0 (0.428), BUII (0.403), Kane (0.385), EVO 2.0 (0.352), and Hoffer QST (0.310).
Table 2.
Accuracy of IOL calculation formula after constant optimization
| Formula | % of Eyes with PE Range | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| FPI | RMSAE | SD | ME* | MAE | MedAE | ± 0.25D | ± 0.50D | ± 0.75D | ± 1.00D | |
| Vivity Group | ||||||||||
| BUII | 0.430 | 0.349 | 0.350 | 0.010 | 0.276 | 0.215 | 58 | 86 | 97 | 99 |
| Cooke K6 | 0.613 | 0.333 | 0.334 | 0.003 | 0.263 | 0.210 | 58 | 86 | 98 | 100 |
| EVO 2.0 | 0.405 | 0.344 | 0.346 | 0.003 | 0.274 | 0.203 | 56 | 85 | 97 | 100 |
| Hill-RBF 3.0 | 0.478 | 0.336 | 0.338 | -0.003 | 0.264 | 0.223 | 56 | 88 | 98 | 99 |
| Hoffer QST | 0.341 | 0.352 | 0.354 | 0.007 | 0.279 | 0.240 | 54 | 87 | 96 | 99 |
| Kane | 0.496 | 0.330 | 0.332 | -0.007 | 0.264 | 0.213 | 53 | 86 | 98 | 100 |
| Pearl DGS | 0.474 | 0.337 | 0.339 | 0.001 | 0.268 | 0.238 | 54 | 90 | 98 | 98 |
| Symfony Group | ||||||||||
| BUII | 0.403 | 0.387 | 0.389 | -0.006 | 0.299 | 0.210 | 55 | 82 | 93 | 98 |
| Cooke K6 | 0.495 | 0.385 | 0.387 | -0.007 | 0.298 | 0.240 | 52 | 82 | 92 | 99 |
| EVO 2.0 | 0.352 | 0.405 | 0.407 | -0.004 | 0.304 | 0.220 | 55 | 77 | 92 | 98 |
| Hill-RBF 3.0 | 0.428 | 0.397 | 0.399 | -0.004 | 0.298 | 0.220 | 57 | 81 | 91 | 97 |
| Hoffer QST | 0.310 | 0.430 | 0.432 | -0.008 | 0.333 | 0.280 | 49 | 81 | 91 | 95 |
| Kane | 0.385 | 0.399 | 0.401 | -0.011 | 0.304 | 0.210 | 54 | 81 | 91 | 97 |
| Pearl DGS | 0.473 | 0.401 | 0.403 | -0.012 | 0.313 | 0.243 | 53 | 79 | 91 | 99 |
* ME of all formulas has no significantly different from zero
D = diopter; FPI = formula performance index; MAE = mean absolute prediction error; ME = mean refractive prediction error; MedAE = median absolute prediction error; PE = prediction error; SD = standard deviation
Fig. 1.
IOL Formula Performance Index (FPI) of the Vivity and Symfony groups
Another key metric for formula accuracy evaluation was the RMSAE and SD of PE, as proposed by Holladay and Wilcox et al. [16], presented in Fig. 2 and detailed in Table A and Table B (see Additional file 1). In the Vivity group, the ascending order of RMSAE and SD was: Kane (RMSAE = 0.330 D; SD = 0.332 D), Cooke K6 (RMSAE = 0.333 D; SD = 0.334 D), Hill-RBF 3.0 (RMSAE = 0.336 D; SD = 0.338 D), Pearl DGS (RMSAE = 0.337 D; SD = 0.339 D), EVO 2.0 (RMSAE = 0.344 D; SD = 0.346 D), BUII (RMSAE = 0.349 D; SD = 0.350 D), and Hoffer QST (RMSAE = 0.352 D; SD = 0.354 D). No statistically significant differences were observed in RMSAE values; however, the SD of Kane was significantly lower than that of Cooke K6 (P = 0.046).
Fig. 2.
Root-mean-square absolute prediction error (RMSAE) and SD of prediction errors in the Vivity and Symfony groups
For the Symfony group, the ascending order of RMSAE and SD was: Cooke K6 (RMSAE = 0.385 D; SD = 0.387 D), BUII (RMSAE = 0.387 D; SD = 0.389 D), Hill-RBF 3.0 (RMSAE = 0.397 D; SD = 0.399 D), Kane (RMSAE = 0.399 D; SD = 0.401 D), Pearl DGS (RMSAE = 0.401 D; SD = 0.403 D), EVO 2.0 (RMSAE = 0.405 D; SD = 0.407 D), and Hoffer QST (RMSAE = 0.430 D; SD = 0.432 D). No statistically significant differences were noted in RMSAE. However, the SD of Cooke K6 was significantly lower than that of Pearl DGS (P = 0.027), while the SD of Hoffer QST was significantly higher than BUII (P < 0.001), Cooke K6 (P = 0.032), and Hill-RBF 3.0 (P = 0.001).
Figure 3 present the percentages of eyes with PEs within ± 0.25 D, ± 0.50 D, ± 0.75 D, and ± 1.00 D for both groups. In the Vivity group, all formulas achieved > 50.0% of eyes within ± 0.25 D and > 80.0% within ± 0.50 D. In the Symfony group, most formulas exceeded 50.0% for PEs within ± 0.25 D, except for Hoffer QST (49.0%). The percentages within ± 0.50 D were 77.0% for EVO 2.0 and 79.0% for Pearl DGS, while other formulas surpassed 80.0%. No statistically significant differences were observed among formulas for any PE range in either group.
Fig. 3.
Percentage of eyes with prediction error within ± 0.25, ± 0.50, ± 0.75 and ± 1.00 diopters (D) in the Vivity and Symfony groups
Constant optimization
In the Vivity group, a mean IOL power was 21.60 ± 1.89 D (range: 17.5D-26.5D). In the Symfony group, a mean IOL power was 22.15 ± 2.27 D (range: 16.0D-26.5D). The baseline constants, original PEs, and results of the TVO for both groups are summarized in Table 3. Following constant optimization, all formulas in the Vivity group demonstrated mean PEs within ± 0.01 D, while in the Symfony group, mean PEs ranged between 0 and − 0.012 D.
Discussion
This study evaluated the performance of modern IOL power calculation formulas in two different PARTIAL-RoF extend IOL designs implantation. While all formulas demonstrated high accuracy in calculation outcomes, their performance varied between the Vivity and Symfony IOL models. Optimizing lens constants for each formula is essential, and the TVO method proved to be an effective and convenient tool for this purpose.
To our knowledge, no consensus exists regarding the optimal IOL power calculation formula for PARTIAL-RoF extend IOL implantation. Previous studies on the Tecnis Symfony IOL (Johnson & Johnson Vision) primarily evaluated traditional formulas such as SRK/T, Haigis, and Hoffer Q [2, 17], with limited data on modern formulas. Jeon et al. [6] assessed the accuracy of Kane, BUII, EVO 2.0, Hill-RBF 3.0, Olsen, SRK/T, Haigis, Hoffer Q, and Holladay 1 in 101 eyes implanted with the Acrysof IQ Vivity IOL (Alcon Laboratories, Inc.). Their findings revealed no significant differences between Kane (SD = 0.373 D), BUII (SD = 0.394 D), EVO 2.0 (SD = 0.381 D), and Hill-RBF 3.0 (SD = 0.396 D), with all formulas achieving a PE within ± 0.50 D in over 80% of eyes. These results align with our study, confirming the high accuracy of modern IOL calculation formulas for PARTIAL-RoF extend IOLs.
Modern IOL power calculation formulas have significantly improved refractive outcomes. Prior studies have demonstrated their accuracy for monofocal IOLs, with Yoon et al. reporting comparable performance among BUII, EVO 2.0, Hill-RBF 3.0, Hoffer QST, Kane, and Pearl DGS [18]. Skrzypecki et al. included Cooke K6 in their analysis and found it yielded the lowest SD among the evaluated formulas [19]. The performance of IOL power calculation formulas was different between caucasian and asian eyes. In this study, the seven modern IOL calculation formulas exhibited similarly high accuracy for PARTIAL-RoF extend IOLs. A comparison revealed no statistically significant differences in RMSAE and SD among formulas for Vivity IOL calculation. For Symfony IOL calculation, while RMSAE showed no significant inter-formula differences, Cooke K6 yielded a significantly lower SD than Hoffer QST and Pearl DGS.
IOL design influences the accuracy of IOL power calculation formulas [20, 21]. Such as the refractive index, the central optic thickness, the anterior and posterior curvature radii, and haptic angulation would influence the IOL power formula calculation outcomes. Jiang et at. reported that IOL power calculation formula performed differently for AcrySof SN60WF or Tecnis ZCB00 [22]. In our study, despite comparable preoperative demographics and biometrics between the Vivity and Symfony groups, a disparity in formula performance was observed between these IOL models. This finding underscores that IOL power calculation accuracy is influenced by factors inherent to the specific IOL model.
IOL power calculation accuracy is dependent on precise constant optimization. Manufacturer-provided constants, typically based on the SRK/T formula, are not universally applicable. IOL constants must be adjusted for IOL type, material, surgeon, and biometer. However, optimizing constants for modern IOL calculation formulas is challenging due to their unpublished content, requiring biometric data, postoperative refractions, and collaboration with formula authors [12]. The TVO method, introduced by Buonsanti et al. [11], simplifies this process by enabling online optimization using only the initial constant, average IOL power, and average PE. In our study, all formulas achieved a ME of < 0.012 D after a single optimization.
This study has several limitations. First, its retrospective design carries inherent risks of selection bias and unmeasured confounding, and the sample size, while adequate for analysis, remains limited. Second, the exclusion of eyes with poorer visual acuity improves the accuracy of postoperative refractive error assessment but may potentially inflate performance estimates compared to real-world settings. Third, due to the limited sample size, the outcomes of TVO lack external validation within this specific cohort. Fourth, only two PARTIAL-RoF extend IOL models (Acrysof IQ Vivity and Tecnis Symfony) were included, restricting the applicability of the findings to other PARTIAL-RoF extend designs. Finally, the exclusion of traditional formulas and ocular parameters (e.g., AL, K, ACD, LT) from accuracy evaluations warrants further investigation.
Conclusions
Modern IOL power calculation formulas exhibit high accuracy for PARTIAL-RoF extend IOLs, inter formula differences are statistically small, with performance varying by IOL model. The TVO method provides a practical, accessible tool for constant optimization across modern IOL calculation formulas, offering surgeons a streamlined approach to achieving precise refractive outcomes.
Supplementary Information
Below is the link to the electronic supplementary material.
Acknowledgements
None.
Abbreviations
- ACD
Anterior chamber depth
- AL
Axial length
- CCT
Central corneal thickness
- CD
Horizontal corneal diameter
- CDVA
Corrected distance visual acuity
- D
Diopter
- FPI
Formula Performance Index
- IOL
Intraocular lens
- LT
Lens thickness
- MAE
Mean absolute prediction error
- ME
Mean prediction error
- MedAE
Median absolute prediction error
- PARTIAL-RoF
PARTIAL-Range of Field
- PE
Prediction error
- RMSAE
Root-mean-square absolute prediction error
- SE
Spherical equivalent
- Sim K
Corneal keratometry
- TVO
Three variable optimization
- UDVA
Uncorrected distance visual acuity
Author contributions
Conceptualization: Meiyi Zhu, Zongsheng Zeng, and Guangbin Zhang; Methodology: Meiyi Zhu and Ziling Zhang; Formal analysis and investigation: Meiyi Zhu and Ziling Zhang; Writing - original draft preparation: Meiyi Zhu; Writing - review and editing: Meiyi Zhu and Zongsheng Zeng; Funding acquisition: Guangbin Zhang; Resources: Guangbin Zhang; Supervision: Guangbin Zhang.
Funding
Partial financial support was received from the Fujian Provincial Natural Science Foundation (2023J011590). The funding organization had no role in the design or conduct of this research.
Data availability
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Declarations
Ethics approval and consent to participate
This study adhered to the tenets of the Declaration of Helsinki and approved by the Institutional Ethics Committee of Xiamen Eye Center, Xiamen University. As the study utilized data obtained from routine clinical practice and did not involve any interventions, human biological specimens, or sensitive personal information, individual informed consent was waived in accordance with the Ethical Guidelines of the Ethics Committee of the Xiamen Eye Center, Xiamen University.
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Meiyi Zhu, Zongsheng Zeng and Ziling Zhang contributed equally to this work.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.