Accuracy of intraocular lens power calculation formulas using a swept-source optical biometer.

PURPOSE: To compare the accuracy of the five commonly used intraocular lens (IOL) calculation formulas integrated to a swept-source optical biometer, the IOLMaster 700, and evaluate the extent of bias within each formula for different ocular biometric measurements.
METHODS: The study included patients undergoing cataract surgery with a ZCB00 IOL implant, using IOLMaster 700 optical biometry. A single eye per patient was included in the final analysis for a total of 324 cases. The SRK/T, Hoffer Q, Haigis, Holladay 2, and Barrett Universal II formulas were evaluated. The correlations between the refractive prediction errors calculated using the five formulas and ocular dimensions such as axial length (AL), anterior chamber depth (ACD), corneal power, and lens thickness (LT) were analyzed.
RESULTS: There were significant differences in the median absolute error predicted by the five formulas after the adjustment for mean refractive prediction errors to zero (P = 0.038). The Barrett Universal II formula had the lowest median absolute error (0.263) and resulted in a higher percentage of eyes with prediction errors within ±0.50 D, ±0.75 D, and ±1.00 D (all P < 0.050). The refractive errors predicted by only the Barrett formula showed no significant correlation with the ocular dimensions: AL, ACD, corneal power, and LT.
CONCLUSIONS: Overall, the Barrett Universal II formula, integrated to a swept-source optical biometer had the lowest prediction error and appeared to have the least bias for different ocular biometric measurements for the ZCB00 IOL.

Introduction

The development of optical biometry and intraocular lens (IOL) power calculation formulas has improved the refractive outcomes of cataract surgery. Advanced technologies related to optical biometry such as partial coherence interferometry (PCI), optical low-coherence reflectometry (OLCR), and swept-source optical coherence tomography (SS-OCT) have increased the precision of biometric measurements. [1-4] Modern IOL power calculation formulas have tried to improve the accuracy of their predictions of effective lens position (ELP). For the most part, this has been accomplished by increasing the number of variables—including preoperative anterior chamber depth (ACD, measured from epithelium to lens), lens thickness (LT), corneal diameter, preoperative refraction, and age—as well as basic variables such as axial length (AL) and corneal power (K).

The IOL calculation formulas show similarly accurate refractive results in eyes with normal AL. [5] However, the accuracy of these formulas differ in eyes with short and long AL. [5-7] The Hoffer Q formula provide the more accurate outcomes in eyes with a short AL [5,8,9] and the SRK/T and Haigis formulas are suitable in eyes with a long AL. [8,10-13] Nevertheless, accurately predicting the ELP remains a major source of error in IOL power calculations, and controversy persists about the accuracy of refractive predictions among many formulas. [14] Because there is no single highly accurate formula across a range of eye characteristics such as long or short AL, flat or steep cornea, and deep or shallow ACD, many cataract surgeons should consider and use several formulas in eyes with various ocular dimensions. [8,15,16]

The Barrett Universal II formula was recently introduced and its accuracy has been studied, and better refractive outcomes than those of other formulas have been reported. [14,16,17-19] The newly developed IOLMaster 700 (Carl Zeiss Meditec AG, Jena, Germany) adopted SS-OCT technology and recently integrated the latest-generation Barrett IOL power calculation formulas. Therefore, cataract surgeons can automatically apply this formula using this device.

The purpose of this study was to determine which of the commonly used IOL formulas integrated to the IOLMaster 700 swept-source optical biometer is the best predictor of actual postoperative refractive outcomes: SRK/T, Hoffer Q, Haigis, Holladay 2, and Barrett Universal II. We also evaluated the extent of bias within each formula for the different ocular biometric measurements (AL, corneal power, ACD, LT).

Materials and methods

This retrospective chart review comprised all cataract surgeries performed in 2018 and 2019 at a tertiary center. The study received approval from the institutional review board of Inha University Hospital (no. 2018-11-010), and the IRB waived the requirement for informed consent. All research and data collection followed the tenets of the Declaration of Helsinki. Confidentiality of the information was maintained thoroughly by excluding names as identification in data abstraction form and keeping their privacy during data collection. No one had access to the non-coded data except investigators, data collectors and supervisor due to responsibilities associated with the study. This retrospective cross-sectional study included consecutive Korean patients who underwent uncomplicated phacoemulsification with an implantation of the most commonly used IOL (TECNIS® ZCB00, Johnson & Johnson Vision, Santa Ana, CA, USA) at our institution. Two surgeons performed the surgery by clear corneal temporal incision phacoemulsification. All patients underwent preoperative measurements by the IOLMaster 700, a swept-source optical biometer.

Our selection criteria for the study subjects and methods followed the recommendations of recent studies regarding the protocols for studies of IOL formula accuracy. [20,21] The exclusion criteria were incomplete biometry, corneal astigmatism more than 2.0 diopters (D), LT measurement less than 2.50 mm, complicated cataract surgery (posterior capsular rupture), additional procedures during cataract surgery (combined vitrectomy or glaucoma surgery), postoperative corrected distance visual acuity (CDVA) worse than 20/40, refraction performed before 4 weeks postoperatively, postoperative complications, and incomplete documentation. Patients with a history of corneal disease or refractive surgery and phacomorphic glaucoma were excluded. If both eyes were eligible, the first eye was selected. Fig 1 shows an overview of the study’s selection criteria.

Fig 1

Overview of the study selection process.

The commonly used and more recent five IOL power calculation formulas built-in software of IOLMaster 700 (software version 1.8) were evaluated: SRK/T, Hoffer Q, Haigis, Holladay 2, and Barrett Universal II. Lens constant optimizations for the ZCB00 IOL were performed in collaboration with Carl Zeiss Meditec AG, which has licensed versions of the proprietary Barrett Universal II and Holladay 2 as well as implementations of the SRK/T, Hoffer Q, and Haigis formulas. [5, 22, 23] The A-constant for SRK/T was 119.3 and the pseudophakic ACD was 5.80 for the Hoffer Q formula. The a0, a1, and a2 constants were -1.302, 0.210, and 0.251, respectively, for the Haigis formula and the ACD was 5.786 for the Holladay 2. The lens factor was 2.04 for the Barrett Universal II. [24]

Postoperative subjective manifest refraction was measured at least 1 month after surgery, when the refraction is considered stable. The refractive prediction error was then calculated as the actual postoperative refraction minus the refractive result predicted by each formula for the IOL implanted. The mean refractive prediction errors for each formula were zeroed out by adjusting the refractive prediction error for each eye. After the adjustment of the mean refractive prediction error to zero, the standard deviation (SD) of prediction error, median absolute error (MedAE), and mean absolute error (MAE) for each formula were calculated. The percentages of eyes within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D of the refractive prediction error were calculated.

Statistical analysis

All statistical analyses were performed using SPSS for Windows (version 20.0; SPSS Inc., Chicago, IL, USA). To compare the accuracies of the five formulas, we used the Friedman non-parametric test of the MedAE. The post-hoc test of the Wilcoxon signed rank test was performed for multiple comparisons of the formulas. We used Cochran’s Q test to compare the percentage of eyes within a certain range of prediction errors between the five formulas. The post-hoc test of McNemar’s test was performed for multiple comparisons of the formulas. Bonferroni correction was applied for multiple comparisons. Linear regression analysis was used to evaluate the correlation between refractive errors predicted by each formula and preoperative biometric factor. Adjusted P values (by Bonferroni correction) less than 0.05 were considered statistically significant.

Results

Data from 324 eyes of 324 patients were evaluated. The majority (n = 179, 55.2%) of the samples were left eyes and more women (n = 193, 59.6%) than men underwent cataract surgery during the study period. The demographic and biometric characteristics of the patient populations are shown in Table 1. The mean axial length was 23.34 ± 1.10 mm, mean corneal power was 44.42 ± 1.65 diopter, and mean ACD was 3.06 ± 0.48 mm.

Table 1

Demographics and biometric data using a single optical biometry device (IOLMaster 700) in the patients who underwent cataract surgery (n = 324).

Parameter	Mean ± SD	Range
Age (years)	69.6 ± 9.9	39–90
AL (mm)	23.34 ± 1.10	20.93–27.35
Km (D)	44.42 ± 1.65	40.13–48.12
ACD (mm)	3.06 ± 0.48	2.02–4.66
LT (mm)	4.47 ± 0.45	2.70–5.42
IOL power (D)	21.56 ± 2.77	10.00–32.00
	Count (% of total)
AL subgroups
Short (<22.0 mm)	22 (6.8%)
Medium (22.0–26.0 mm)	296 (98.1%)
Long (>26.0 mm)	6 (1.9%)
Keratometry subgroups
Flat (<42.0 D)	23 (7.1%)
Medium (42.0–46.0 D)	244 (75.3%)
Steep (>46.0 D)	57 (17.6%)
ACD subgroups
Shallow (<2.5 mm)	38 (11.7%)
Medium (2.5–3.5 mm)	222 (68.5%)
Deep (>3.5 mm)	64 (19.8%)

AL, axial length; ACD, anterior chamber depth; Km, mean keratometry; LT, lens thickness; IOL, intraocular lens

Table 2 shows the mean refractive prediction errors, SD of prediction error, MedAE, and MAE determined by the five formulas in the 324 eyes after the prediction errors for each formula were zeroed out. The MedAEs with adjusting the refractive prediction error to zero are shown in Fig 2. The Friedman test confirmed that there were statistically significant differences among the absolute prediction errors of the five formulas (P = 0.038). Post hoc analysis using Wilcoxon signed-rank pairwise comparisons for nonparametric samples with Bonferroni correction showed that the Barrett had a significantly smaller MedAE than the other formulas; SRK/T (P = 0.020), Hoffer Q (P = 0.048), Haigis (P = 0.012), and Holladay 2 (P = 0.024).

Table 2

Clinical outcomes of refractive prediction error and absolute error and among the five IOL formulas after adjusting the mean refractive prediction error to zero (n = 324).

Formula	Mean RE	SD	MedAE	MAE	Percentage of eyes within diopter range indicated (%)
					±0.25D	±0.50D	±0.75D	±1.00D	>±2.00D
SRK/T	0.000	0.472	0.310	0.376	41.0%	73.9%	87.3%	96.3%	0%
Hoffer Q	0.000	0.520	0.290	0.396	44.8%	67.8%	86.1%	94.3%	0%
Haigis	0.000	0.512	0.314	0.394	38.6%	72.6%	86.6%	94.4%	0%
Holladay 2	0.000	0.518	0.316	0.390	43.5%	72.4%	87.0%	92.2%	0%
Barrett Universal II	0.000	0.426	0.263	0.334	42.7%	79.4%	92.4%	97.2%	0%

SRK/T, Sanders-Retzlaff-Kraff/Theoretical; RE, refractive prediction errors; SD, standard deviation; MAE, mean absolute error; MedAE, median absolute error

Fig 2

Box plot of the absolute error (in diopters) of the five intraocular lens (IOL) calculation formulas for the ZCB00 model.

Dark gray boxes represent the second quartile, and white boxes represent the third quartile.

The percentage of eyes within a certain range of prediction errors is shown in Table 2 and Fig 3. The percentages of eyes within ±0.50 D, ±0.75 D, and ±1.00 D of error were significantly different among the five formulas using the Cochran’s Q test (all P < 0.050). Post hoc analysis using McNemar’s test with Bonferroni correction was performed. The Barrett formula produced a higher percentage of eyes within ± 0.50 D of error than the Hoffer Q and Holladay 2 formulas (P < 0.001 and P = 0.016). The Barrett formula produced a higher percentage of eyes within ± 0.75 D of error than the other formulas; SRK/T (P = 0.048), Hoffer Q (P = 0.008), Haigis (P = 0.020), and Holladay 2 (P = 0.004). The Barrett also produced a higher percentage of eyes within ± 1.00 D of error than the Holladay 2 (P = 0.016).

Fig 3

Stacked histogram comparing the percentage of cases within a given diopter range of predicted refraction outcome of the five intraocular lens (IOL) calculation formulas for the ZCB00 model.

The refractive errors predicted by all formulas except that by the Barrett Universal II were significantly correlated with the AL on linear regression analysis (all P < 0.050). The refractive errors predicted by the SRK/T formula showed a significant negative correlation with keratometry (P < 0.001), while the Hoffer Q and Haigis formula showed a significant positive correlation with keratometry (P = 0.023 and P < 0.001). The Hoffer Q and Haigis formulas showed a significant positive correlation with ACD (P < 0.001 and P = 0.027), and the refractive errors predicted by the Haigis and Holladay 2 formulas were correlated with LT (all P < 0.001; Fig 4).

Fig 4

Scatterplots showing the correlations between the refractive prediction error calculated using the five formulas and ocular dimensions including axial length (AL), anterior chamber depth (ACD), mean keratometry, and lens thickness (LT).

Discussion

To our knowledge, this is the first study to compare the accuracy of IOL power calculation formulas on one IOL type (TECNIS® ZCB00) using a swept-source optical biometer, the IOLMaster 700. We reported on five commonly used IOL calculation formulas: popular third-generation (SRK/T, Hoffer Q) and fourth-generation (Haigis, Holladay 2, and Barrett Universal II). These formulas were preinstalled on the IOLMaster 700. We followed the recently published protocols comparing their respective accuracies. [20,21]

Overall, the refractive outcomes and percentages of eyes with prediction errors within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D for each formula were similar to those in the recent study by Melles et al. using a Lenstar 900 optical biometer. [16] All five formulas achieved above 92% of eyes within ±1.00 D of the predicted refraction, much higher than the 85% suggested by Gale et al. [25] Recent studies reported that the Barrett Universal II formula was more accurate and showed the better refractive outcomes than the other formulas. [16,17-19,26] One large population study assessed the Barrett Universal II formula over the entire AL range and showed that this formula had the lowest MAE and SD of the prediction error and a higher percentage of eyes with prediction errors within ±0.25 D, ±0.50 D, and ±1.00 D, which was congruent with our findings. [18] In our study, the Barrett Universal II formula had the lowest median absolute error (0.263) and a higher percentage of eyes with prediction errors within ±0.50 D, ±0.75 D, and ±1.00 D compared to the other formulas. Cooke and Cooke [17] found that the same formula could give different results depending on the optical biometer (OLCR and PCI) and the preinstalled version or not. Our results suggested that the Barrett Universal II formula was the most accurate among the commonly used and representative five formulas integrated to an advanced swept-source optical biometer in our study subjects, who had mostly normal ranges of ocular dimension.

Hoffer et al. [27] reported a similar accuracy of IOL power calculation using the Hoffer Q, Holladay 1, and SRK/T formulas using both SS-OCT and OLCR instruments. In their study, the MedAEs and the percentage of eyes with prediction errors within ±0.50 D for Hoffer Q using IOLMaster 700, were better than our results. They evaluated the outcomes of different IOL models (MX60 and SA60AT) and ocular dimensions of their subjects were relatively different from those of our subjects. These were estimated as the possible causes of this discrepancy.

Here we also evaluated the extent of bias within each formula for different ocular biometric measurements. The refractive errors predicted by all but the Barrett Universal II formula, was significantly correlated with the AL. The SRK/T and Haigis formulas have significant bias with varying corneal power in opposite directions. According to the ACD, Hoffer Q and Haigis formulas showed a significant positive correlation, and the refractive errors predicted by Haigis and Holladay 2 formulas were correlated with the LT. Overall, the Barrett formula appeared to have the least bias of the formulas as measured by prediction error with variations in AL, corneal power, ACD, and LT. These results were similar to those reported by Melles et al., [16] who found notable biases in the errors of all other formulas except the Barrett when plotted versus ocular dimensions using a Lenstar 900 biometer.

When cataract surgeons select the IOL power during cataract surgery, they mainly use the preferred formula such as the Hoffer Q or SRK/T because modern IOL formulas have similar accuracy in eyes with a normal range. [6,28] However, surgeons should cross-check different IOL formulas in eyes with an unusual range of ocular dimensions such as a short or long AL, flat or steep cornea, or a recently shallow ACD. A swept-source optical biometer, the IOLMaster 700, integrated the various IOL formulas including the latest-generation Barrett IOL power calculation formula, and we can automatically apply these formulas and compare the predicted results without using a separate program. Because the formulas gave different results depending on which optical biometry measurements were used and the preinstalled version, [17] we first compared the accuracy of various IOL formulas integrated to a device and confirmed the bias of these formulas as measured by prediction error with variations in ocular dimensions.

The present study has some limitations. First, because we evaluated one popular IOL model, we caution that these results may not be generalizable to other IOL models. Second, the sample size of eyes with unusual ranges of ocular dimensions was relatively small; therefore, further studies with larger sample size are needed in these subgroups.

In conclusion, we found statistically significant differences in the MedAEs for the five formulas after the adjustment for mean refractive prediction errors to zero. Overall, the Barrett Universal II formula, integrated to a swept-source optical biometer, had the lowest prediction error for ZCB00 IOL model. The Barrett Universal II formula also appeared to have the least bias as measured by prediction error with variations in different biometric ocular dimensions including AL, corneal power, ACD, and LT.

16 Aug 2019

PONE-D-19-21173

Accuracy of intraocular lens power calculation formulas using a swept-source optical biometer

PLOS ONE

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Reviewer #1: This is an interesting study. Although it does not add significant information to the recently published studies on much larger samples, it is the one of the first multiformula comparisons carried out with measurements by the IOLMaster 700.

Please find below some suggestions to improve the paper.

METHODS

• Subgroup analysis: short eyes are usually defined as those with AL <22.0 mm (not 22.5 mm). Please correct and repeat analysis.

• Statistical analysis: in addition to Friedman’s test (to analyze the absolute prediction errors), I would include Repeated Measures ANOVA to compare the arithmetical prediction errors and their variance. This can be useful for both the whole sample and the different subgroups (shallow, medium and deep ACD, etc.), where it may reveal statistically significant differences among the 5 formulas.

• Statistical analysis: since you correctly used it, please cite Cochran’s Q test in the Methods section too.

• Please include errata for the Hoffer Q formula in the references (J Cataract Refract Surg 1993;19:700-712; errata, 1994;20:677; 2007;33:2-3.)

RESULTS

• It is quite hard to believe the Cochran’s Q test was not able to detect any statistically significant difference among the 5 formulas, as – for example – the Hoffer Q achieved only 69.6% of eyes within 0.5D, whereas the Barrett achieved 78.1% with the same prediction error. Please check carefully the statistical analysis once more.

DISCUSSION

• Barrett formula does not belong to 5th generation formulas. Although unpublished and thus largely unknown, it should be classified among 4th generation ones.

• Please compare your results with those reported by Hoffer Q when comparing the IOLMaster 700 to the Lenstar (JCRS 2016;42:1165-1172). They included the Hoffer Q, Holladay 1 and SRK/T formulas and achieved better results. It would be opportune to elaborate on the possible causes of this discrepancy.

• The whole discussion should be reviewed after ANOVA has been applied to the arithmetic prediction errors, as statistically significant differences may arise.

Reviewer #2: Good results that support the conclusion. Reasonable statistical analysis. Correct terminology used. The ideas are clearly expressed in English. A bigger sample size is suggested in future research.

Reviewer #3: I have read the article by Kim et al. The authors have analyzed the accuracy of IOL power calculation formulas using the IOL Master 700.

Comments:

- P3 L53 - what about LCOR?

- P3 L56 - some formulas also use preoperative refraction and age. Moreover, you should state that increasing the number, from the basic which is AL and K

- P3 L63 - be more precise, what formulas in what axial lengths? Is it concordant with the results of your study?

- P5 L108 - short eyes were determined as those having AL<22.5 mm, while long as those having 25.0 mm. As several studies used different cut-off values i.e. 22.0 mm or 26.0 mm choosing these values should be thoroughly explained.

- the group size for some subgroups (e.g. long eyes=16, flat keratometry=16, shallow ACD=20) very small, making an appropriate analysis difficult.

- in the results section you state: "The percentages of eyes within the prediction errors of ±0.25, ±0.50, ±0.75 D, and ±1.00 D were not significantly different among the five formulas using the Cochran Q test (P > 0.050)". However, in the abstract one can find "The Barrett Universal II formula resulted ... in a higher percentage of eyes with prediction errors within ±0.50 D, ±0.75 D, and ±1.00 D." The same in P8 L163

- P8 L164 - present what test was used and the p values.

- P12 L238 as 20 eyes had a shallow ACD, how is it possible that 36.8% eyes (and not 35% or 40%) in this group had a prediction error of ±0.50 D with the Hoffer Q formula

- Figure 3 is difficult analyze. Please consider a more various grayshade scheme or preferably adding colours...

The main limitation of the study is the group size, which is 219 eyes, compared to e.g., 18 501 in the study by Melles et al. Moreover, the novelty of this study is limited. Finally, the conclusions do not reflect the actual findings of the study (low difference between formulas, limited statistical significance)

I would consider publication after the revision.

Reviewer #4: This study evaluated the accuracy of the five intraocular lens (IOL) formulas integrated to a swept-source optical biometer. The manuscript was well written. I would like to add some comments.

1. Page 5, Line 108-111

Provide a reference for the criteria of subgroup classification as follows:

For the subgroup analysis, the AL, preoperative mean keratometry, and ACD (measured

from epithelium to lens) were divided into three subgroups: short (<22.5 mm), medium

(22.5–25.0 mm), and long (>25.0 mm); flat (<42.0 D), medium (42.0–45.0 D), and steep

(>45.0D); shallow (<2.50 mm), medium (2.5–3.5 mm), and deep (>3.5 mm).

2. Page 7, Line 150, Table 1

Please present the mean±SD of each subgroup in AL, K, and ACD.

3. Page 21, Fig.2.

For the MAE, we recommend the box whiskers plot instead of the line. The box whiskers plot can provide more information to the reader.

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Reviewer #1: Yes: Giacomo Savini, MD

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Reviewer #3: Yes: Piotr Kanclerz, MD, PhD

Reviewer #4: No

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29 Oct 2019

September 30, 2019

Editor in Chief

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Thank you very much for your letter regarding our revised manuscript. We revised the manuscript as recommended by the editor and reviewer. Each of the coauthors has seen and agrees with each of the changes made to the manuscript. Our responses to the comments of the editor and reviewer, including the changes made in the manuscript, are provided in a point-by-point manner in the following pages.

We hope that you will find the manuscript suitable for publication in your esteemed journal.

Yours sincerely,

Ji Won Jung, MD, PhD

Department of Ophthalmology, Inha University Hospital, 7-206, 3-ga,

Shinheung-dong, Jung-gu, Incheon 400-711, South Korea

Tel.: 82-32-890-2400, Fax: 82-32-890-2403, E-mail: panch325@gmail.com

Reviewer Comments:

Reviewer #1: This is an interesting study. Although it does not add significant information to the recently published studies on much larger samples, it is the one of the first multiformula comparisons carried out with measurements by the IOLMaster 700.

Please find below some suggestions to improve the paper.

� Thank you for your comments. We have revised this manuscript according to your suggestions.

METHODS

• Subgroup analysis: short eyes are usually defined as those with AL <22.0 mm (not 22.5 mm). Please correct and repeat analysis.

� We agree with the reviewer’s opinion and we added the samples (from 219 eyes to 324 eyes) and repeated the analysis. The results revealed statistically significant differences, unlike previous version with borderline statistical significance.

We also re-defined the subgroup classification. However, some of the subgroups contained only few subjects; therefore, we removed the subgroup analysis.

• Statistical analysis: in addition to Friedman’s test (to analyze the absolute prediction errors), I would include Repeated Measures ANOVA to compare the arithmetical prediction errors and their variance. This can be useful for both the whole sample and the different subgroups (shallow, medium and deep ACD, etc.), where it may reveal statistically significant differences among the 5 formulas.

� We agree with the reviewer’s opinion. We added the samples (from 219 eyes to 324 eyes) and repeated the analysis. Friedman’s and Cochran’s Q test results revealed statistically significant differences among the five formulae, unlike previous version with borderline statistical significance.

• Statistical analysis: since you correctly used it, please cite Cochran’s Q test in the Methods section too.

� We added Cochran’s Q test to the Methods section.

• Please include errata for the Hoffer Q formula in the references (J Cataract Refract Surg 1993;19:700-712; errata, 1994;20:677; 2007;33:2-3.)

� We added the errata in the reference 5.

RESULTS

• It is quite hard to believe the Cochran’s Q test was not able to detect any statistically significant difference among the 5 formulas, as – for example – the Hoffer Q achieved only 69.6% of eyes within 0.5D, whereas the Barrett achieved 78.1% with the same prediction error. Please check carefully the statistical analysis once more.

� We agree with the reviewer’s opinion. We added the samples and repeated the analysis. Cochran’s Q test results revealed statistically significant differences in the percentages of eyes within ±0.50, ±0.75 D, and ±1.00 D of the prediction errors among the five formulae.

DISCUSSION

• Barrett formula does not belong to 5th generation formulas. Although unpublished and thus largely unknown, it should be classified among 4th generation ones.

� We agree with the reviewer’s opinion and have made the recommended correction.

• Please compare your results with those reported by Hoffer Q when comparing the IOLMaster 700 to the Lenstar (JCRS 2016;42:1165-1172). They included the Hoffer Q, Holladay 1 and SRK/T formulas and achieved better results. It would be opportune to elaborate on the possible causes of this discrepancy.

� As you suggested, we added this contents in Discussion section.

• The whole discussion should be reviewed after ANOVA has been applied to the arithmetic prediction errors, as statistically significant differences may arise.

� We agree with the reviewer’s opinion. We added the samples and repeated the analysis.

Friedman’s and Cochran’s Q test results revealed statistically significant differences among the five formulae. We have reviewed these results in the Discussion section.

Reviewer #2: Good results that support the conclusion. Reasonable statistical analysis. Correct terminology used. The ideas are clearly expressed in English. A bigger sample size is suggested in future research.

� We agree with the reviewer’s opinion. We added the samples and repeated the analysis.

Reviewer #3: I have read the article by Kim et al. The authors have analyzed the accuracy of IOL power calculation formulas using the IOL Master 700.

Comments:

- P3 L53 - what about LCOR?

� We agree with the reviewer’s opinion and we added the optical low-coherence reflectometry in P3 L53.

- P3 L56 - some formulas also use preoperative refraction and age. Moreover, you should state that increasing the number, from the basic which is AL and K

� We agree with the reviewer’s opinion and have made the suggested correction in P3 L56.

- P3 L63 - be more precise, what formulas in what axial lengths? Is it concordant with the results of your study?

� We agree with the reviewer’s opinion and we added these contents in P3. However, our data could not conclude because of the limited number of subjects in each subgroup. We plan to further evaluate in short or long AL subgroups.

- P5 L108 - short eyes were determined as those having AL<22.5 mm, while long as those having 25.0 mm. As several studies used different cut-off values i.e. 22.0 mm or 26.0 mm choosing these values should be thoroughly explained.

- the group size for some subgroups (e.g. long eyes=16, flat keratometry=16, shallow ACD=20) very small, making an appropriate analysis difficult.

� We agree with the reviewer’s opinion and we re-defined subgroup criteria. We reported the proportion of subgroup in order to understand our subjects in Table 1. However, because the sample sizes of new subgroups were small, therefore we have removed the subgroup analysis. The results of the entire group were similar to those of normal range subgroup, and the results of some subgroups with unusual range of ocular dimensions were difficult to draw conclusion because of small sample size.

- in the results section you state: "The percentages of eyes within the prediction errors of ±0.25, ±0.50, ±0.75 D, and ±1.00 D were not significantly different among the five formulas using the Cochran Q test (P > 0.050)". However, in the abstract one can find "The Barrett Universal II formula resulted ... in a higher percentage of eyes with prediction errors within ±0.50 D, ±0.75 D, and ±1.00 D." The same in P8 L163

- P8 L164 - present what test was used and the p values.

� We agree with the reviewer’s opinion. We added the samples and repeated the analysis.

Cochran’s Q test revealed statistically significant differences among the five formulae. We revised these results in the Results and Discussion sections.

- P12 L238 as 20 eyes had a shallow ACD, how is it possible that 36.8% eyes (and not 35% or 40%) in this group had a prediction error of ±0.50 D with the Hoffer Q formula

� This calculation was in error and has been corrected in the revised manuscript.

- Figure 3 is difficult analyze. Please consider a more various grayshade scheme or preferably adding colours...

� We corrected the figure by adding the colors.

The main limitation of the study is the group size, which is 219 eyes, compared to e.g., 18 501 in the study by Melles et al. Moreover, the novelty of this study is limited. Finally, the conclusions do not reflect the actual findings of the study (low difference between formulas, limited statistical significance)

I would consider publication after the revision.

� We agree with the reviewer’s opinion. We added the samples and repeated the analysis. Friedman’s and Cochran’s Q test results revealed statistically significant differences among the five formulae, unlike previous version with borderline statistical significance. We reviewed these results in Results and Discussion section. Our study had much smaller sample size than that of study by Melles et al. However, our study may be meaningful to compare the accuracy of various IOL formulae integrated to a swept-source optical biometer, the IOLMaster 700 for one popular IOL type (ZCB00). Please consider the revision of our manuscript.

Reviewer #4: This study evaluated the accuracy of the five intraocular lens (IOL) formulas integrated to a swept-source optical biometer. The manuscript was well written. I would like to add some comments.

1. Page 5, Line 108-111

Provide a reference for the criteria of subgroup classification as follows:

For the subgroup analysis, the AL, preoperative mean keratometry, and ACD (measured

from epithelium to lens) were divided into three subgroups: short (<22.5 mm), medium

(22.5–25.0 mm), and long (>25.0 mm); flat (<42.0 D), medium (42.0–45.0 D), and steep

(>45.0D); shallow (<2.50 mm), medium (2.5–3.5 mm), and deep (>3.5 mm).

2. Page 7, Line 150, Table 1

Please present the mean±SD of each subgroup in AL, K, and ACD.

� We agree with the reviewer’s opinion and have re-defined the subgroup criteria according to other references. However, because some subgroups were so small in size, we removed the subgroup analysis.

3. Page 21, Fig.2.

For the MAE, we recommend the box whiskers plot instead of the line. The box whiskers plot can provide more information to the reader.

� We agree with the reviewer’s opinion and we revised the figure as a box plot.

Submitted filename: Respond to reviewers.docx

Click here for additional data file.

26 Nov 2019

PONE-D-19-21173R1

Accuracy of intraocular lens power calculation formulas using a swept-source optical biometer

PLOS ONE

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Additional Editor Comments (if provided):

Some minor editing of the plot needed as given by the Reviewer 4

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Reviewers' comments:

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Comments to the Author

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Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #4: All comments have been addressed

**********

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**********

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Reviewer #2: Yes

Reviewer #4: Yes

**********

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #4: Yes

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Reviewer #2: (No Response)

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Reviewer #1: Just a minor comment: in table 1, medium axial length is still defined as between 22.5 and 26 mm. Please correct 22.5 and change it into 22

Reviewer #2: Good results that support the conclusion. Reasonable statistical analysis. Correct terminology used. The ideas are clearly expressed in English. A bigger sample size is suggested in future research.

Reviewer #4: We have confirmed the corrections in the manuscript.

Please indicate the minimum and maximum values ​​for the box & whisker plots.

**********

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Reviewer #1: No

Reviewer #2: No

Reviewer #4: No

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29 Nov 2019

Reviewer Comments:

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Just a minor comment: in table 1, medium axial length is still defined as between 22.5 and 26 mm. Please correct 22.5 and change it into 22

� Thank you for your comment. We corrected it.

Reviewer #2: Good results that support the conclusion. Reasonable statistical analysis. Correct terminology used. The ideas are clearly expressed in English. A bigger sample size is suggested in future research.

� Thank you for your comment. We added the need of bigger sample size in future research in Discussion section.

Reviewer #4: We have confirmed the corrections in the manuscript.

Please indicate the minimum and maximum values for the box & whisker plots.

� Thank you for your comment. We added the minimum and maximum values in Fig2.

Submitted filename: Respond to reviewers_191128.docx

Click here for additional data file.

26 Dec 2019

Accuracy of intraocular lens power calculation formulas using a swept-source optical biometer

PONE-D-19-21173R2

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Comments to the Author

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Reviewer #4: All comments have been addressed

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**********

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Reviewer #4: Yes

**********

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Reviewer #4: Yes

**********

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30 Dec 2019

PONE-D-19-21173R2

Accuracy of intraocular lens power calculation formulas using a swept-source optical biometer

Dear Dr. Jung:

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