**3. Results**

#### *3.1. Population Demographics*

The study comprised 35 eyes of 25 patients. The mean age of the study was 56.94 ± 9.56 years and 60% of the patients were female. The mean axial length was 28.71 ± 0.87 mm (range: 28.01 mm to 31.10 mm). The mean corneal power was 43.30 ± 1.61 D, with the majority of patients' average keratometry (65.7%) falling between 42.0 D and 46.0 D. The average ACD was 3.66 ± 0.38 mm and the average LT of the patients was 4.25 ± 0.52 mm. Table 1 summarizes all the biometrics, refractive outcomes, and demographics of the study population.

**Table 1.** Demographics, biometrics, and refractive outcomes (*n* = 35).


D = diopters; F = female; IOL = intraocular; M = male; mm = millimeters; OD = right eye; OS = left eye; SD = standard deviation.

The refractive measurements show a marked improvement in refractive error following phacoemulsification surgery. The mean CDVA before the procedure was 0.22 ± 0.17 (LogMAR) and improved to 0.01 ± 0.07 (LogMAR) after the procedure. After surgery, the mean SE approached emmetropia at –0.58 ± 0.79 compared to a mean preoperative SE that was highly myopic at –11.28 ± 4.29. The implanted IOLs had a mean power

of 7.76 ± 3.06 D (range: –1.00 to +12.00 D) with only one (2.86%) implanted lens with a minus power diopter (Table 1).

#### *3.2. Accuracy of the Six Formulas*

Figure 1A shows the distribution and interquartile ranges of the PEs for each formula, and Table 2 shows the MPE of each formula to illustrate the tendency of each formula to lead to either myopic or hyperopic surprises. The four newer formulas tended to result in hyperopic surprises as compared with the older SRK/T and Holladay 1 formulas. The WK AL adjustment tended to lead to a myopic surprise for both SRK/T and Holladay 1. In contrast, the CMAL adjustment tended towards a hyperopic shift for Holladay 1. Interestingly, the median value of PE closest to zero was the SRK/T formula with CMAL adjustment, and this formula's MPE is also closest to zero. Kane's formula had the lowest MedAE (0.270), with the three newer formulas (BU-II, EVO, and Hill-RBF) following closely behind (Table 2). The WK adjustment, with either SRK/T or Holladay 1, had the highest MedAE values. The WK adjustment for SRK/T had the highest MedAE of all the formulas, but the CMAL adjustment with SRK/T was not far from the BU-II formula. The Wilcoxon signedrank test revealed a statistically significant difference (*p* < 0.05) of the WK adjustment to either SRK/T and Holladay 1 compared to the CMAL adjustment of SRK/T, indicating that the WK adjustment, with either formula, had lower accuracy (Table 3). Figure 1B shows a boxplot of the AEs for each formula. The Holladay 1 with WK adjustment and SRK/T with WK adjustment had the widest range and highest MedAE compared with the CMAL adjustments or the four newer formulas.

**Figure 1.** Boxplots showing the prediction errors of intraocular lens calculation formulas. ( **A**) The numerical prediction errors were calculated by subtracting the predicted spherical equivalent (SE) from the postoperative SE. (**B**) The absolute prediction errors were then taken from the numerical prediction errors. BU-II = Barrett Universal II; CMAL = Cooke-modified axial length; EVO = Emmetropia Verifying Optical; H1 = Holladay 1; WK = Wang–Koch AL adjustment. \* significant *p* < 0.05.


**Table2.** Comparisonofpredictiveoutcomes.

AE = absolute prediction error; BU-II = Barrett Universal II; CMAL = Cooke-modified axial length; D = diopters; EVO = Emmetropia Verifying Optical; H1 = Holladay 1; MAE = mean absolute prediction error; MedAE = median absolute prediction error; MPE = mean numerical prediction error; Max AE = maximum absolute prediction error SD = standard deviation; WK = Wang–Koch axial length adjustment. a = % of patients with refractive prediction errors within 0.25 D, 0.50 D, 0.75 D, or 1.00 D.

**Table 3.** Statistical analysis comparison of AE.


AE = absolute prediction errors; BU-II = Barrett Universal II; CMAL = Cooke-modified axial length; EVO = Emmetropia Verifying Optical; H1 = Holladay 1; WK = Wang–Koch axial length adjustment. † = *p* < 0.05.

Cochran's Q test evaluated the percentage of eyes within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D. The percentages for each formula are stated in Table 2 and graphically represented in Figure 2. The only significant difference among the formulas was found between the percentage of eyes within ±0.50 D and ±0.75 D. Further testing identified that the statistically significant difference was between the SRK/T-CMAL formula compared to the SRK/T-WK, Holladay 1-CMAL, and Holladay 1-WK formulas for the percentage of eyes within ±0.50 D (*p* < 0.05) with SRK/T-CMAL having the highest percentage of eyes with predicted SE within ±0.50 D. The Hill-RBF formula had more accuracy in predicting eyes within ±0.50 D compared with the Holladay 1 with CMAL adjustment (*p* = 0.0143). When assessing the percentage of eyes that achieved postoperative refraction within 0.75 D of the predicted SE, the SRK/T with WK adjustment did significantly worse than the remaining formulas (*p* < 0.05) with only the exception of the Holladay 1 with WK adjustment formula, which performed as poorly as the SRK/T-WK. The BU-II, Hill-RBF, and Kane formulas could predict the postoperative manifest refraction within 1.00 D for all 35 eyes.

**Figure 2.** Stacked histogram comparing the percentage of eyes within ±0.25 diopters (D), ±0.50 D, ±0.75 D, and ±1.00 D of predicted spherical equivalent for various intraocular lens calculation formulas. BU-II = Barrett Universal II; CMAL = Cooke-modified axial length; EVO = Emmetropia verifying optical; H1 = Holladay 1; WK = Wang–Koch AL adjustment.

## **4. Discussion**

In this study, we assessed the accuracy of BU-II, EVO, Hill-RBF, Holladay 1, Kane, and SRK/T in long eyes in a predominantly Caucasian population. Despite advances in formulas, surgeons are still faced with the difficulty of accurately achieving desired refractive outcomes for high myopes. In our study, the newer-generation BU-II, EVO, Hill-RBF 3.0, and Kane formulas had greater accuracy than the third-generation Holladay 1 formula with either the WK or CMAL adjustment. The SRK/T with CMAL adjustment was comparable to the newer IOL formulas. The WK axial length adjustment for SRK/T did not prove to be as accurate as the CMAL adjustment and was comparable to the accuracy of Holladay 1 (Figure 1 and Table 2).

Asians have a higher percentage of high myopia as compared with Caucasians [16,17]. As a result, most studies assessing IOL calculation accuracy within high AL have been performed in predominantly Asian study populations [14,23–32]. While our study did not have ethnicity data readily available in the paper charts, the population demographics of the study site (Draper, UT) are 91.1% white and 3.5% Asian (US Census Data for Draper, UT, available at https://www.census.gov/quickfacts/drapercityutah, accessed 27 June 2021). To the surgeon's knowledge, only one patient was of Asian descent in the study. There have been fewer studies assessing IOL formula accuracy evaluating AL greater than 25.0 mm in predominantly Caucasian populations, and even fewer evaluating the newer vergence or artificial intelligence formulas [33–35]. The criteria for these studies were AL >25.0, 26.0, or 26.5 mm, whereas the current study evaluated much longer eyes. In addition to having a higher percentage of eyes with longer ALs, some studies have shown that Asians have flatter corneal shapes as compared with Caucasians [18,19]. Axial length and corneal shape are two variables known to heavily influence the predictive capabilities of IOL formulas [27].

Assessing the accuracy of the formulas, the MedAE of the four newer formulas, Hill-RBF, Kane, EVO, and BU-II, had the lowest prediction errors, with Kane having the lowest of all the formulas and BU-II coming in fourth. The only significant difference in MedAE identified between formulas was the Holladay 1 formula with the CMAL adjustment, which

performed significantly worse than any of the four newer formulas or the SRK/T with CMAL adjustment (Table 2 and Figure 1). Similarly, in assessing the percentage of eyes that achieved a prediction error of ±0.25 D, ±0.50 D, ±0.75 D, or ±1.00 D, BU-II, Hill-RBF, EVO, Kane, and SRK/T-CMAL had the highest percentage of eyes within 0.25 D. The statistical difference showed that SRK/T-CMAL had a higher accuracy of predicting SE within 0.50 D than the Holladay 1 formulas and the WK adjustment of SRK/T. The Holladay 1 formula with WK adjustment did worse than the other remaining formulas in predicting the SE ±0.75 D (Table 2). The four new formulas also tended to predict postoperative hyperopic shift compared with the older formulas, which tended to predict a postoperative myopic shift. This result is consistent with the previous studies that have documented the tendency for newer fourth-generation formulas to lead to postoperative hyperopia as compared with older-generation formulas, which tend to have greater postoperative myopia [11].

A similar study compared the same formulas as the current study, except that they used version 2.0 of the Hill-RBF formula and looked at a population of 370 high-AL eyes of a predominantly Asian population [32]. Their study showed that the Holladay 1 with WK adjustment and Kane formulas had higher accuracy in extremely high myopes. Of note, their study defined extreme myopia as AL ≥ 30.0 mm, while the current study only had four patients that fit this criterion. However, Fuest et al. in Germany looked at eyes with long axial lengths and compared the BU-II and Hill-RBF 2.0 with Holladay 1 and SRK/T formulas and found that the BU-II and Hill-RBF 2.0 performed better than the Holladay 1 and SRK/T formulas, which was consistent with other studies, including studies consisting of Asian populations [1,34–37]. Our data support previous reports that the BU-II and Hill-RBF perform more accurately than Holladay 1 and SRK/T in long eyes. This study was able to add that the Kane, EVO, and SRK/T-CMAL formulas performed similarly to BU-II and Hill-RBF in predominately Caucasian eyes. Similar studies in four Asian populations and one European population also found newer-generation formulas such as the Kane, EVO, and BU-II to be most accurate in long eyes [38–42].

Our study did have some limitations: (1) Because very high axial lengths are less frequent in the population and even less so in Caucasian populations, our study sample size was not as robust as other Asian studies, and we included bilateral eyes as a result of the small size. The use of bilateral eyes can potentially compound data. (2) The chart data did not include the patient's self-reported ethnicity, and therefore assumptions were made based on the demographics of the location of the surgical center and the physician's recollection of presumed ethnicity. (3) The study was retrospective and we had limitations in standardization and follow-up periods. Future studies on larger sample sizes of Caucasian populations or a single-site comparison of Asian to Caucasian would be warranted.

In conclusion, our results show that for axial lengths greater than or equal to 28.0 mm, the Barrett Universal II, Emmetropia Verifying Optical, Hill-RBF version 3.0, and Kane formulas were comparable in accuracy. Additionally, the Cooke-modified axial length adjustment was better than the Wang–Koch axial length adjustment when used with the SRK/T formula. The Holladay 1 had the lowest predictive accuracy of the six formulas we tested. The most accurate prediction of high axial lengths in Caucasian eyes may be achieved with Barrett Universal II, Emmetropia Verifying Optical, Hill-RBF version 3.0, Kane, and SRK/T with the CMAL adjustment.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/jcm11195947/s1, **Figure S1**: Flow diagram illustrates the process by which patients were selected for the study to obtain the predicted postoperative spherical equivalent (SE) used to analyze the prediction accuracy of the six formulas. The axial lengths were modified with the Wang–Koch and Cooke-modified adjustment prior to their input in the Holladay 1 and SRK/T formulas. The Barrett Universal II, Kane, Emmetropia Verifying Optical (EVO), and Hill-RBF version 3.0 formulas are all unpublished, and the biometric data were input directly into their respective online calculators.

**Author Contributions:** Conceptualization, M.M.; methodology, M.M.; formal analysis, K.M.D. and D.P.B.; resources, P.C.H.; data curation, K.M.D., T.S.P. and I.M.D.; writing—original draft preparation, K.M.D., J.L.J., M.M., D.P.B. and T.S.P.; writing—review and editing, K.M.D., J.L.J., M.M. and Y.C.R.; supervision, M.M., Y.C.R. and P.C.H.; project administration, P.C.H.; funding acquisition, M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was funded by an unrestricted gran<sup>t</sup> from Research to Prevent Blindness (RPB), 360 Lexington Avenue, 22nd Floor New York, NY 10017. No support was received for the publication of this article.

**Institutional Review Board Statement:** The study was conducted in accordance with the Declaration of Helsinki and approved by the Institutional Review Board of the Biomedical Research Alliance of New York (BRANY, protocol 20-12-547-823). This study was approved by the Hoopes Vision Ethics Board and was HIPAA-compliant.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented are available upon request to the corresponding author. The data are not publicly available due to patient privacy.

**Acknowledgments:** We thank Shannon McCabe who provided guidance, expertise, and constructive criticism of the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
