Highlights
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In eyes with axial length (AL) ≥ 30.0 mm, we systematically evaluated modern IOL formulas and the impact of biometric parameters, including keratometry and the AL–to–corneal radius (AL/R) ratio, on refractive accuracy.
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Holladay 1 combined with the nonlinear polynomial Wang-Koch axial length adjustment (H1-PWK) achieved the most robust overall performance, while extreme AL and steep corneas were major drivers of hyperopic prediction error.
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The AL/R ratio outperformed AL alone for biometric stratification, demonstrating a significant positive correlation with prediction error (PE) in the Ladas Super formula, Barrett Universal II, EVO, PEARL-DGS, and Hoffer QST formulas, with the transition point from myopic to hyperopic PE varying across these formulas.
Purpose
To evaluate the accuracy of modern intraocular lens (IOL) power calculation formulas and axial length (AL) adjustment methods in eyes with AL ≥ 30.0 mm.
Design
Retrospective consecutive cross-sectional study.
Participants and Controls
A total of 308 eyes (308 patients) with AL ≥ 30.00 mm were included.
Methods
Accuracy of modern online formulas, alone or with established AL adjustments methods, was analyzed. Subgroup analyses were performed based on AL, keratometry (K), anterior chamber depth (ACD), lens thickness (LT), and AL–to–corneal radius (AL/R) ratio.
Main outcome measures
Predictive accuracy was evaluated using the formula performance index (FPI), root mean square absolute prediction error (RMSAE), standard deviation (SD) of prediction error (PE), and percentage of eyes within ±0.25 and ±0.50 diopters (D).
Results
Overall, Holladay 1 combined with the nonlinear polynomial Wang-Koch axial length adjustment (H1-PWK) demonstrated the best overall performance, achieving the lowest SD (0.40), RMSAE (0.40), and highest FPI (0.494). A tendency toward hyperopic error was observed in eyes with AL ≥ 32.0 mm, K ≥ 46.0 D. The AL/R ratio showed a significant positive correlation with PE in the Ladas Super formula, Barrett Universal II, EVO, PEARL-DGS, and Hoffer QST formulas. Spline-based regression analysis indicated that the transition point of AL/R from myopic to hyperopic PE varied across different formulas.
Conclusions
H1-PWK provides robust refractive accuracy in extremely long eyes. The AL/R ratio may provide a useful composite biometric stratification parameter compared to AL alone.
INTRODUCTION
A ccurate intraocular lens (IOL) power calculation remains a cornerstone of successful cataract surgery, yet it continues to be particularly challenging in eyes with extreme axial length (AL). ,,, With the global rise in myopia—especially in Asia—it is projected that by 2050 nearly half of the world’s population will be myopic, and approximately 10% will develop high myopia. Consequently, cataract surgeons are increasingly confronted with highly myopic eyes characterized by markedly elongated ALs.
Over the past decades, IOL power calculation has evolved from early regression formulas (e.g., SRK II) to thin-lens formulas (e.g., SRK/T, Holladay I), thick-lens formulas (e.g., Barrett Universal II and Kane), and more recently, pure AI-based approaches such as the RBF formula. Contemporary formulas incorporate multiple biometric parameters—including keratometry, axial length (AL), anterior chamber depth (ACD), lens thickness (LT), and white to white (WTW)—to improve effective lens position (ELP) prediction and refractive accuracy. Although large-scale studies have shown that these modern formulas outperform earlier generations in routine clinical populations, their performance remains less reliable in eyes with extreme biometric values, particularly extreme AL. ,, To address this issue, several axial length adjustment strategies—such as the Wang–Koch correction and its subsequent refinements, as well as the Cooke-modified axial length (CMAL) —have been proposed and shown to improve refractive accuracy in long eyes. ,
However, refractive prediction error reflects the combined influence of multiple biometric parameters (e.g., keratometry, ACD, LT, CCT, and WTW), leading to nonuniform formula performance across biometric profiles, yet evidence in extremely long eyes remains limited. ,, This study evaluated the predictive accuracy of contemporary online IOL power calculation formulas in eyes with an axial length of 30.0 mm or greater, with emphasis on axial length adjustment methods and biometric stratification to support more individualized formula selection in this challenging population.
METHODS
PARTICIPANTS
This retrospective study strictly adhered to the principles of the Declaration of Helsinki and its amendments. The study protocol was reviewed and approved by the Medical Ethics Committee of Zhongshan Ophthalmic Center (Ethics approval number: 2019KYPJ124).
A total of 308 eyes (308 patients) with AL ≥ 30.00 mm who underwent phacoemulsification with IOL implantation in Zhongshan Ophthalmic Center of Sun Yat-sen University from January 2019 to October 2024 were included in this study. Eyes were included if they had an axial length of 30.0 mm or greater measured with the IOL Master 700 (Version 1.80, Carl Zeiss Meditec AG, Jena, Germany), underwent uncomplicated phacoemulsification with intraocular lens implantation, and completed a postoperative follow-up of at least 1 month with available subjective refraction results. For cases in which both eyes were eligible, only 1 eye was included: the eye with better postoperative visual acuity was selected, or, if both eyes had the same visual acuity, the first-operated eye was included. Eyes were excluded if they had coexisting ocular pathologies, a history of ocular trauma or prior ocular surgery, or a postoperative best-corrected visual acuity of 20/50 or worse.
IOL POWER CALCULATION
The Holladay 1 formulas were evaluated in combination with the AL adjustment methods, including the modified Wang-Koch axial length adjustment (MWK), nonlinear polynomial Wang-Koch axial length adjustment (PWK), and the Cooke-modified axial length (CMAL).
Modern IOL power calculation formulas—including Barrett Universal II (BUII), K6, Emmetropia Verifying Optical 2.0 (EVO), Hoffer QST (QST), Kane, Ladas Super Formula (LSF), and PEARL-DGS (PEARL)—were evaluated using publicly available online platforms, with and without application of the CMAL. LSF, a hybrid formula that integrates components of Hoffer Q, Holladay 1, and SRK/T using a data-driven ensemble approach, was additionally evaluated in combination with CMAL and the nonlinear polynomial Wang-Koch axial length adjustment, given its incorporation of the Holladay 1 formula. Because many modern formulas already incorporate proprietary axial length adjustments, additional external AL correction may result in double correction; therefore, these analyses were considered exploratory.
Biometric parameter measurements, including AL, ACD, LT, keratometry (K), WTW, and CCT were obtained using the IOL master 700. For each intraocular lens model, A-constants were obtained from the IOLCon database ( www.iolcon.org ). Predictive accuracy was evaluated using the mean prediction error (PE), standard deviation (SD), mean absolute error (MAE), median absolute error (MedAE), root mean square absolute prediction error (RMSAE), and formula performance index (FPI). The spherical equivalent (SE) prediction error was defined as the difference between the postoperative subjective refraction SE and the predicted postoperative SE. In addition, the proportions of eyes with prediction errors within ± 0.25 diopters (D), ±0.50 D, ±0.75 D, and ± 1.00 D were calculated for each formula.
STATISTICAL ANALYSIS
Statistical analyses were performed using RStudio (version 2026.01.2 + 418). Differences in the variability of prediction errors among formulas were assessed using a heteroscedasticity test to compare SDs. Adjustment for multiple comparisons was performed using the Holm method. All analyses were conducted using a publicly available R script (Rallfun v45.txt, https://osf.io/xhe8u/ ). Statistical tests were two-sided, and a P value <.05 was considered statistically significant.
Univariate linear regression was first performed to assess the contribution of individual biometric parameters (AL, K, ACD, LT, CCT, WTW) on PE, particularly due to collinearity issues between axial length–to–corneal radius (AL/R) ratio and other parameters. Subsequently, multivariate linear regression was used to evaluate the combined contribution of these parameters. To identify the transition point from myopic to hyperopic PE, spline-based regression models were fitted separately for each formula, with arithmetic PE as the dependent variable and the biometric parameter of interest as the independent variable.
RESULTS
Table 1 summarizes the ocular biometric characteristics and implanted IOL models of the study population. All eyes implanted monofocal IOLs.
TABLE 1
Clinical Characteristics of Patients.
| Parameter | Mean ± SD | Range |
|---|---|---|
| Axial length (mm) | 31.77 ± 1.27 | (30.03, 34.87) |
| K flat (D) | 43.03 ± 1.54 | (37.68, 46.93) |
| K steep (D) | 44.26 ± 1.59 | (38.98, 48.73) |
| Anterior chamber depth (mm) | 3.47 ± 0.38 | (2.33, 4.67) |
| Lens thickness (mm) | 4.50 ± 0.42 | (3.06, 5.64) |
| Central corneal thickness (mm) | 0.55 ± 0.04 | (0.45, 0.66) |
| White-to-white (mm) | 11.93 ± 0.45 | (10.34, 13.81) |
| IOL power (D) | 3.95 ± 3.32 | (−6.0, 14.5) |
| IOL model | Number | IOL Constants |
| 920H (Rayner) | 81 | 118.3 |
| MX60 (Bausch + Lomb) | 78 | 119.2 |
| ZCB00 (Johnson and Johnson Vision) | 54 | 119.3 |
| Sensar AR40e/AR40M (Johnson and Johnson Vision) | 52 | 118.7 |
| RAO600C (Rayner) | 43 | 118.6 |
Abbreviation: K = keratometry; SD = standard deviation; IOL = intraocular lens.
ACCURACY OF IOL POWER CALCULATION FORMULAS
The SD, MAEs, MedAEs, and RMSAE of the entire study cohort were calculated, as shown in Table 2 . Holladay 1 combined with the nonlinear polynomial Wang-Koch axial length adjustment (H1-PWK) achieved the lowest SD (0.40), RMSAE (0.40), and highest FPI (0.494). PEARL achieved the lowest MAE (0.31), followed by H1-PWK (0.32). EVO achieved the lowest MedAE (0.25), followed by PEARL (0.25) and H1-PWK (0.27).
TABLE 2
Performance of Intraocular Lens Calculation Formulas.
| Formula | Arithmetic PE (D) | Absolute PE(D) | Percentages of PE (%) | FPI | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Mean | SD | Mean | Median | RMSAE | ±0.25 D | ±0.50 D | ±0.75 D | ±1.0 D | ||
| H1-PWK | −0.05 | 0.40 | 0.32 | 0.27 | 0.40 | 48.53 | 80.78 | 94.46 | 98.70 | 0.494 |
| K6 | 0.21 | 0.40 | 0.35 b | 0.28 b | 0.45 a | 45.60 | 77.20 | 90.55 | 97.39 | 0.437 |
| PEARL | 0.12 | 0.40 | 0.31 | 0.25 | 0.42 | 50.49 | 80.78 | 91.86 | 97.72 | 0.405 |
| EVO | 0.18 | 0.40 | 0.33 b | 0.25 | 0.44 a | 51.14 | 78.83 | 90.55 | 97.07 | 0.381 |
| H1-MWK | −0.34 | 0.40 | 0.44 b | 0.45 b | 0.52 a | 30.62 c | 61.89 a | 87.30 a | 96.74 | 0.373 |
| Kane | −0.28 | 0.41 | 0.40 b | 0.36 b | 0.49 a | 36.81 c | 67.75 a | 88.60 a | 97.39 | 0.366 |
| QST | 0.07 | 0.49 a | 0.37 b | 0.29 b | 0.50 a | 43.00 c | 76.87 | 87.62 a | 93.81 a | 0.294 |
| LSF-CMAL | 0.16 | 0.50 a | 0.41 b | 0.32 b | 0.53 a | 38.44 c | 69.38 a | 85.99 a | 93.49 a | 0.254 |
| BUII | 0.20 | 0.48 a | 0.40 b | 0.31 b | 0.52 a | 40.72 c | 70.03 a | 88.93 a | 93.49 a | 0.248 |
| LSF-PWK | −0.70 | 0.49 a | 0.73 b | 0.73 b | 0.84 a | 14.98 c | 31.60 a | 53.75 a | 75.57 a | 0.203 |
| LSF | 0.61 | 0.55 a | 0.67 b | 0.61 b | 0.82 a | 20.85 c | 41.69 a | 60.91 a | 79.15 a | 0.178 |
| H1-CMAL | 0.84 | 0.42 a | 0.85 b | 0.82 b | 0.94 a | 7.17 c | 19.87 a | 43.00 a | 70.03 a | 0.138 |
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