January-February 2020


EyeWorld Journal Club
Review of “Assessment of the accuracy of new and updated IOL power calculation formulas in 10,930 eyes from the UK National Health Service”

by Caroline Wilson, MD, Austin Fox, MD, Lauren Hock, MD, Tony Chung, MD, Thomas Oetting, MD, residency program director, and the ophthalmology residents of the Department of Ophthalmology and Visual Sciences, University of Iowa Hospitals and Clinics

Caroline Wilson, MD
Ophthalmology resident and
first author on the review
University of Iowa
Iowa City, Iowa

Dr. Jack Kane met with the University of Iowa ophthalmology residents over Skype to discuss his article. From left: Tony Chung, MD, Karam Alawa, MD, Dr. Kane on screen, Caroline Wilson, MD, and Austin Fox, MD
Source: University of Iowa

Several new IOL formulas have been introduced, including some that incorporate artificial intelligence. I asked the Iowa residents to review this study from the January JCRS that compares their performance to other leading formulas, including the Barrett Universal.

—David F. Chang, MD, EyeWorld Journal
Club Editor

While everything else seems to get more complicated, intraocular lens (IOL) calculations are becoming simpler. In the past, we have used a different IOL calculation formula depending on whether the eye undergoing cataract surgery was short, medium, or long. Here we review an impressive paper by Darcy et al. that demonstrates that the Kane formula is superior to other formulas in a huge data set across all axial eye lengths. The Kane formula is based on both theoretical models of the eye and on machine learning. Dr. Jack Kane has generously provided this formula online as a service to the ophthalmology community. During our review of this paper we had the opportunity to meet Dr. Kane virtually and were very appreciative of the time he spent with us.


Dr. Kane’s group retrospectively analyzed two large National Health Service (NHS) datasets in the United Kingdom. Uncomplicated phacoemulsification cataract surgeries performed between May 2008 and November 2017 that included insertion of one of four IOL types (Alcon SA60AT, Rayner Superflex 920H, Rayner C-Flex 970C, or Bausch + Lomb Akreos Adapt AO) and had preoperative biometry performed using partial coherence interferometry (IOLMaster, Carl Zeiss Meditec) were included. Cases with incomplete biometry, corneal astigmatism >4 diopters (D), other corneal disease, previous vitrectomy, complicated cataract surgery, postoperative corrected distance visual acuity worse than 20/40, or postoperative complications were excluded. If patients underwent bilateral phacoemulsification cataract extraction, a single eye was randomly selected for study inclusion. Formal pre- and postoperative manifest refractions were required for study inclusion. Data on lens thickness, central corneal thickness, and white-to-white values were not used.
The authors compared refractive calculations from the following IOL formulas: Hoffer Q, Holladay 1, Haigis, SRK/T, Kane, Holladay 2-AL, Olsen, Hill 2.0, and Barrett II. Lens constant optimization was performed for each formula. Prediction error (PE), including mean absolute prediction error (MAE), was calculated as the postoperative refraction by an optometrist minus the formula-predicted refractive outcome. The percentages of eyes that had a PE of ±0.25, ±0.50, and ±1 D were calculated for each formula. Sub-group analyses were performed based on axial eye length (short AL ≤22 mm, medium AL >22 mm to <26 mm, long AL ≥26 mm) and IOL type. Mean rank scores were calculated for each subgroup analysis. The differences in absolute prediction error between formulas was analyzed using the Friedman test. A p-value <0.05 was considered statistically significant.


In the analysis of 10,930 eyes, the Kane formula had the lowest MAE compared to the other formulas (p<0.001). Using the Kane formula, the highest percentage of eyes (72%) had an actual refractive outcome within ±0.5 D of the predicted refractive outcome (71.2% for the Hill 2.0, 70.6% for the Olsen, 71% for the Holladay 2, 70.7% the Barrett II, 69.1% the SRK/T, 69% the Haigis, and 68.1% for the Hoffer Q). This was also the case for actual refractive outcome within ±0.25 and ±1 D of the predicted refractive outcome. Not surprisingly, the other newer generation formulas (Hill 2.0, Olsen, Holladay 2-AL adjusted, and Barrett) outperformed the third generation formulas with lower MAEs (p<0.05).
When analyzing the axial length subgroups, the Kane formula also had the lowest mean absolute prediction error at all axial lengths: short (p<0.01), medium (p<0.001), and long (p<0.05 Barrett; p<0.001 other formulas). In addition, the formulas were compared among the IOL types used. The Kane formula had the lowest mean absolute prediction error for the SA60AT (p<0.001), C-Flex (p<0.001), and Akreos Adapt (p<0.05); however, the Barrett (p=0.4) and Hill 2.0 (p=0.06) formulas resulted in a lower mean absolute prediction error for the Superflex IOL.


Accurate postoperative refractive outcomes are fundamental to surgical success in modern cataract surgery. Refractive accuracy continues to improve with advancements in IOL technologies, surgical techniques, and newer generation IOL formulas. Choosing which IOL formula to use is not always a straightforward process, however, as previous comparison studies have shown varying superiority of the formulas at different axial eye lengths, in post-refractive surgery eyes, and with different IOLs.1–5 In this paper, Darcy et al. provide a performance comparison of available IOL formulas in a large U.K. dataset. What stands out most from this work is that the new Kane formula, based on theoretical optics and artificial intelligence, provided the most accurate refractive outcomes across all axial eye lengths and with the four IOLs included in the study. The importance of this result is that access to a single, ubiquitously accurate formula could simplify the busy cataract surgeon’s IOL selection process.
A major strength of this study was its large-scale nature. The dataset used in the IOL formula analysis included >10,000 eyes over a 10-year period, obtained from two large NHS trusts. Of note, there were large numbers of all axial eye lengths including short (<22 mm) and long (>26 mm) eyes, strengthening the accuracy of the analysis at these eye lengths. Further, there were strong numbers of each of the four IOLs used.
One question our readers had when reviewing this paper was how the outcomes might be stratified across varying demographics. Dr. Kane did not include detailed demographic data in the study aside from gender and age, making it unclear how the formulas would perform in different populations. Also, the study was limited to uncomplicated cataract surgery cases and did not assess how the different IOL formulas might perform in complicated situations, such as post-refractive eyes, with premium IOLs, or in secondary IOL cases.
For uncomplicated surgical cases, there are a number of notable perks to the Kane formula aside from its validated accuracy. First, it is easily accessible at IOLformula.com and is free to use. Second, although it is recommended that central corneal thickness (CCT) and lens thickness (LT) be included in IOL calculations for the most accurate results, the Kane team showed that the formula remains significantly accurate even when these parameters are not available, as may be the case for surgeons who do not have access to newer biometers. Third, the formula remained accurate across multiple IOL types and materials, which makes its use applicable to a wide range of IOLs. The main limitation of the Kane formula is that it is not yet integrated into current biometers for ease of use.
Further studies are needed to show how the Kane formula compares to the other new generation formulas when applied to IOL selection in complicated or premium cataract surgical cases. Also, more data is needed to address which formulas are most accurate at extreme refractive values, such as in extremely myopic or hyperopic eyes. Though in all cases, accuracy will continue to be limited by the lack of manufacturer precision in the making of IOLs, especially at extreme degrees of ametropia.


1. Abulafia A, et al. Intraocular lens power calculation for eyes with an axial length greater than 26.0 mm: comparison of formulas and methods. J Cataract Refract Surg. 2015;41:548–56.
2. Hamill EB, et al. Intraocular lens power calculations in eyes with previous hyperopic laser in situ keratomileusis or photorefractive keratectomy. J Cataract Refract Surg. 2017;43:189–194.
3. Gökce SE, et al. Intraocular lens power calculations in short eyes using 7 formulas. J Cataract Refract Surg. 2017;43:892–897.
4. Rong X, et al. Intraocular lens power calculation in eyes with extreme myopia: Comparison of Barrett Universal II, Haigis, and Olsen formulas. J Cataract Refract Surg. 2019;45:732–737.
5. Wang Q, et al. Meta-analysis of accuracy of intraocular lens power calculation formulas in short eyes. Clin Exp Ophthalmol. 2018;46:356–363.



Review of “Assessment of the accuracy of new and updated IOL power calculation formulas in 10,930 eyes from the UK National Health Service” Review of “Assessment of the accuracy of new and updated IOL power calculation formulas in 10,930 eyes from
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