Myopia is increasingly recognized as a major global public health issue, contributing substantially to visual impairment and serving as a significant risk factor for a range of serious ocular pathologies. ^, Myopia is commonly defined as a spherical equivalent refractive error of ≤–0.5 diopters (D) under the condition of relaxed accommodation, whereas high myopia means a spherical equivalent refractive error of ≤ −6.0 D, or axial length (AL) ≥ 26.0 mm. Currently, the prevalence of myopia is rising worldwide. In Europe, myopia affects approximately 23.5% of the population, with high myopia reported in about 0.8%. In contrast, in East Asia, as many as 80% to 90% of 18-year-olds are affected, and 10% to 20% present with high myopia. ^, If current trends persist, it is estimated that by the year 2050, approximately 4.76 billion people worldwide will be myopic, with 0.94 billion classified as having high myopia.

Myopia is recognized as a risk factor for age-related cataract, particularly the nuclear and posterior subcapsular subtypes. ^, Cataract surgery in myopic eyes presents distinct clinical challenges due to a higher incidence of phacoemulsification-related complications and postoperative suboptimal visual outcomes. In myopic eyes, major sources of postoperative refractive error include inaccuracies in measuring anterior chamber depth (ACD) and AL, as well as in predicting the effective lens position (ELP)—particularly when an inappropriate IOL power calculation formula is selected. Consequently, several theoretical corrections and regression-based modifications have been proposed to enhance IOL power calculation accuracy in long eyes, such as Wang-Koch adjustment or Cooke modified AL. ^,

Currently, artificial intelligence (AI) plays a dominant role in the development of IOL power calculation formulas. ^,,,,,,,, Among the most recently introduced formulas, the majority are AI-based. ^,,,,, Some of these formulas rely entirely on AI methodologies, ^,, while others incorporate AI components to enhance traditional vergence-based approaches—whether thin-lens, ^,, paraxial, or thick-lens models. The fundamental principles underlying AI-based formulas are summarized in Table 1 . Despite the growing number of available formulas, no universally accepted gold standard has yet emerged for selecting the optimal IOL power calculation method. ^,,,,,,,,

This study aimed to cf the performance of nine AI-based IOL power calculation formulas in eyes with an AL exceeding 26.00 mm. To the best of our knowledge, this is the first study to evaluate as many as nine AI-based formulas in this context. An additional strength of this study is the relatively large sample size—321 eyes from Caucasian patients—which is particularly valuable given that most previous studies have focused on Asian populations, where the prevalence of myopia is highest. ^,

Data from consecutive patients with Wisconsin grade 3 or 4 cataracts who underwent uneventful phacoemulsification with in-the-bag implantation of a monofocal IOL between May 2019 and September 2024 were retrospectively reviewed. The following inclusion criteria were applied: age over 18 years, AL exceeding 26.00 mm, implantation of a non-toric, PARTIAL − RoF narrow IOL, ie, an AcrySof IQ SN60WF (Alcon Laboratories), and detailed postoperative refraction recorded 3 months after surgery, with a best-corrected visual acuity (BCVA) of at least 0.8 on the Snellen chart. Exclusion criteria included any history of ocular surgery, vision-threatening corneal pathology, intraoperative or postoperative complications, and corneal astigmatism greater than 2.0 diopters.

The study was conducted in accordance with the tenets of the Declaration of Helsinki and received approval from the Institutional Review Board of the Foundation for the Advancement of Ophthalmology “Ophthalmology 21” on May 29, 2025 (approval number: 02/2025). Written informed consent was obtained from each patient prior to routine cataract surgery. The study is compliant with the Health Insurance Portability and Accountability Act, and all patient data were anonymized to ensure confidentiality. For each patient, preoperative biometric data such as AL, keratometry (K), ACD, lens thickness (LT) and white to white (WTW) distance were obtained using a Zeiss IOL Master 700 with Standard K value, software version 1.88 (Carl Zeiss Meditec AG), while central corneal thickness (CCT) value was achieved utilizing auto kerato-refracto tonometer TRK-2P (Topcon Corporation). Prior to cataract surgery, the IOL power was calculated using IOLMaster 700. The power of the implanted IOL was selected from calculations based on the SRK/T, Holladay 2, or Barrett Universal II formulas according to institutional or surgeons’ preferences. The refractive target was chosen according to patient preference following a detailed preoperative discussion. Two experienced eye surgeons (W.S., O.V.) performed all cataract surgeries.

Postoperative refraction was measured 3 months after cataract surgery. Manifest refraction performed by appropriately trained medical personnel was assessed at a distance of 6 meters, in accordance with the recommendations of Simpson and Charman. Postoperative IOL power predictions were calculated using nine AI-based formulas: Hill-RBF 3.0, Ladas Super Formula AI (LSF AI), Kane, Hoffer QST, PEARL-DGS, Karmona, Nallasamy, Zhu-Lu, and 3C 2.0. Other available AI-based formulas were excluded due to limited accessibility—specifically, FullMonte, which currently lacks an active online calculator, and Zeiss AI, which is restricted to users in the United States. Lens constants for the AcrySof IQ SN60WF IOL (A-constant: 119.00) were obtained from the ULIB and IOLCon databases. Further optimization to achieve a zero mean prediction error was not performed, as the SN60WF IOL is a well-established lens with thoroughly validated constants derived from large datasets (>5000 eyes). For the Zhu-Lu formula, the recommended constants for the SN60WF IOL were adopted from the official website ( https://hm-zlf.com/ ). The pACD value of 5.670, as advised on the Hoffer QST platform ( https://hofferqst.com/ ), was used for calculations with that formula. The following online platforms were used for IOL power prediction: Hill-RBF 3.0 ( https://rbfcalculator.com/online/index.html ), LSF AI ( https://www.iolcalc.com/ ), Karmona ( https://karmona-iol.com/ ), Kane (

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), and Nallasamy ( https://lenscalc.com/ ), all using an A-constant of 119.00. For the 3C 2.0 and PEARL-DGS formulas, calculations and data analysis were carried out by the original developers via personal communication (Camellin U. and Debellemanière G., respectively). A keratometric index of 1.3375 was uniformly applied across all formulas.

The accuracy of IOL power calculation formulas can be evaluated using various metrics. In this study the comparison was based on root mean square absolute error (RMSAE), median absolute error (MedAE), and the percentage of eyes with a prediction error (PE) within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D. Among the most commonly reported are the percentage of eyes with a PE within ± 0.50 D and the mean absolute error (MAE). ^,,,,,,,,,,, Hoffer and associates have recommended the use of the MedAE as a primary outcome measure, due to the non-normal distribution of absolute refractive PE. Holladay and associates advocated for the RMSAE, especially when comparing formulas using the bootstrap-t method with Holm sequential correction. RMSAE is a valuable alternative to SD for representing the distribution of PEs in subgroups with non-zero predicted errors, such as eyes with short or long ALs, or those that have undergone corneal refractive surgery.

PE was specified as the difference between the actual postoperative refractive outcome expressed as spherical equivalent (ie, the sum of the spherical power and half the cylindrical power) and the predicted refraction from each formula. A positive PE indicated a more hyperopic outcome than predicted, while a negative value signified a more myopic result compared to the predicted refraction. In turn, absolute error (AE) was calculated as the absolute value of PE. Using AE, the percentage of patients with a PE within ±0.25D, ±0.50D, ±0.75D, and ±1.00D was determined.

STATISTICAL ANALYSIS

Data were analyzed in IBM SPSS Statistics for Windows, Version 22.0 (IBM Corp) and R Project 4.4.1 for Statistical Computing ( https://www.r-project.org/ ). An adjusted P -value of less than.05 was considered statistically significant. The normality of PE distribution was assessed with the Shapiro-Wilk test. The RMSAE and mean of PE were chosen as primary outcomes. The RMSAE was compared between formulas using the bootstrap-t method with Holm sequential correction. Mean PEs were compared to zero using the Wilcoxon signed-rank test. A nonparametric McNemar’s χ ² test with continuity correction to determine P values for every pair of formulas and the adjusted P values using Holm’s correction were used to cf the percentage of eyes with a PE within ±0.50 D. Additionally, MedAE was considered, utilizing Friedman ANOVA with Dunn post hoc test. A minimum sample size of 176 eyes was required to achieve a 95% confidence level, ensuring that the true value lies within ±5% of the measured value, as calculated using the PS Power and Sample Size Program, Version 3.0.12 (Dupont WD, 2012).

A total of 321 (120 male and 201 female) were included in the study. Only one of each patient was considered in the study, in accordance with Hoffer’s recommendations. In patients who underwent bilateral cataract surgery, only the right eye was enrolled in the analysis. The AL of the examined eyes ranged from 26.00 mm to 32.51 mm. Demographic details of enrolled patients and biometric data of studied eyes are listed in Table 2 .

The Karmona, LSF AI, Nallasamy, Zhu-Lu, and 3C 2.0 formulas showed a statistically significant hyperopic PE ( P <.05). In contrast, the Kane, Hill-RBF 3.0, Pearl-DGS, and Hoffer QST formulas demonstrated PE values that were not significantly different from zero ( P >.05). The RMSAE results of the analyzed formulas ranged from 0.418 (Pearl-DGS) to 0.532 (Zhu-Lu). Details are summarized in Figure 1 . Statistical comparison of the RMSAE was performed using the Bootstrap-t method with the Holm correction. P -value less than.05 was considered statistically significant. PEARL-DGS and Hill-RBF 3.0 demonstrated significantly lower RMSAE compared to Zhu-Lu, 3C 2.0, and Karmona. For LSF AI, Hoffer QST, Kane, and Nallasamy, significantly lower RMSAE values were observed relative to Zhu-Lu and 3C 2.0. Moreover, Karmona achieved a statistically lower RMSAE than Zhu-Lu. Detailed outcomes of P -value are presented in Table 3 .

In terms of the MedAE, outcomes ranged from 0.260 (Hill-RBF 3.0) to 0.371 (Zhu-Lu). Figure 2 provides a comprehensive overview of the detailed results for all the analyzed formulas. Statistical comparison of MedAE utilizing Friedman ANOVA with Dunn post hoc test showed that Zhu-Lu was less accurate than Hill-RBF 3.0, Nallasamy, PEARL-DGS, and Kane, whereas 3C 2.0 was less accurate than Hill-RBF 3.0, Kane, and PEARL-DGS ( Figure 3 ).

Analysis of the percentage of eyes with PE within ≤0.50 D revealed values ranging from 66.67% (Zhu-Lu) to 80.06% (Pearl-DGS). Multiple comparisons of the formulas according to McNemar’s χ ² test with continuity correction to determine P values for every pair of formulas and the adjusted P values using Holm’s correction are summarized in Table 4 . The second column shows each formula for which the differences were statistically significant with the other formulas. Statistical significance was found for Hill-RBF 3.0, Hoffer QST, Kane, LSF AI, PEARL-DGS, and Nallasamy vs Zhu-Lu and 3C 2.0.

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