Comparing the Accuracy of Four Intraocular Lens Formulas in Eyes with Two Types of Widely Used Monofocal Lens Implants

Abstract

The present study aimed to compare the accuracy of intraocular lens calculation formulas Barrett Universal II, Hoffer Q, Holladay 1, and SRK/T in the prediction of postoperative refraction for two widely used monofocal implants: SN60WF and ZCB00. All eyes were divided based on axial length (<22 mm, 22–24.5 mm, and >24.5 mm) and lens type. The mean and median of the absolute refractive error (AE) were calculated for all four formulas, using manufacturer-recommended lens constants as well as optimized constants. The subgroup analysis showed that the Barrett Universal II formula had the smallest mean absolute error in three groups (with short, medium, and long axial length) before and after lens factor optimization, and Holladay 1 had the best results in two groups (of medium and long axial length), and SRK/T in one short axial length group, as well as one medium AL group after A-constant optimization. This study hints at the versatility of the Barrett Universal II formula, a fourth-generation formula that is now widely available on most optical biometers and provides a useful tool of calculation for eyes of all axial lengths even without lens constant optimization.

1. Introduction

A cataract is the major cause of reversible vision loss, and cataract surgery is the most common surgical procedure in the world [1]. The progress of medical technology has allowed not only to restore vision but also to gain great refractive results. Good preoperative planning includes the selection of suitable lens power, a selection that has become easier and more accurate thanks to the new biometrical formulas. New optical biometers incorporate even the fourth-generation formulas [2,3,4,5]. Formula optimization allows the expansion of the axial length range for which the biometric formulae can be used optimally. Optimization can be time-consuming and can even require expertise. However, there is online available formula optimization software that allows accessible constant personalization. Many surgeons still base their decision when choosing the right intraocular lens diopter solely on formulas with provided constants and have a great interest in the development of a “universal” formula that can offer great refractive results on a wide range of axial lengths without optimization. This study aims to find an accessible method of choosing the right intraocular implant diopter in order to obtain the best refractive results.

2. Materials and Methods

2.1. Patients

This study included consecutive patients who underwent uncomplicated cataract surgery (1104 eyes) in our clinic, from 1 January 2018 to 31 December 2019, with implantation of monofocal IOLs from two different manufacturers: Acrysof^® IQ SN60WF IOL (Alcon, Fort Worth, TX, USA) 714 eyes and Tecnis^® ZCB00 IOL (Johnson & Johnson Vision, Santa Ana, CA, USA)—390 eyes.

The SN60WF monofocal lens is a hydrophobic UV and blue light filtering acrylic foldable single-piece posterior chamber intraocular lens with a power range from +6 to +30 diopters. It has a biconvex optic with a posterior aspheric surface. The index of refraction is 1.55 at 35 °C [6]. The ZCB00 monofocal lens is a hydrophobic UV filtering acrylic foldable single-piece posterior chamber intraocular lens with a power range from +5 to +34 diopters. It has a biconvex optic with an anterior aspheric surface. The index of refraction is 1.47 at 35 °C [7]. These are two widely used monofocal aspheric lenses that have been used successfully over the years and are still popular among surgeons. The older generation biometric formulas have aided the calculation of suitable implants depending on several variables, but there is a constant search for one universal formula well suited for every eye, regardless of the biometric variables [2,3,4,5].

The study was approved by “Prof. Dr. Agrippa Ionescu” Emergency Hospital’s Ethical Committee (Bucharest), and all patients signed an informed consent after being informed about the benefits and risks of the surgical procedure.

The patients were followed-up prospectively for one week and one month, as scheduled. Inclusion criteria for the study were: age 40 or over, endothelial cell count of more than 1500 cells/mm², no corneal opacities, no retinal diseases, no previous ocular surgery or ocular trauma, and normal central and peripheral retina. Exclusion criteria for the study were patients who did not fulfill the inclusion criteria, irregular astigmatism [8], postoperative best corrected visual acuity below 20/40 (at 6 m), silicone oil internal tamponade, and associated retinal pathology [9,10].

2.2. Preoperative Assessment

The preoperative ocular examination included best-corrected distance visual acuity, manifest refraction, keratometry, tonometry and corneal pachymetry measured with the autorefracto/kerato/tono/pachymeter Tonoref III (Nidek Co, Ltd., Tokyo, Japan), corneal endothelial cell count evaluated with the SP 3000P Specular Microscope (Topcon, Tokyo, Japan), optical coherence biometry measured with the Aladdin HW3.0 (Topcon, Tokyo, Japan), anterior segment slit-lamp biomicroscopy, mydriatic fundoscopy and optical coherence tomography performed with the Cirrus HD-OCT 4000 (Carl Zeiss Meditec AG, Jena, Germany).

The Aladdin low coherence interferometry biometer obtains the axial length (AL) using a superluminescent 820 nm diode. The anterior chamber depth (ACD) is measured using a blue light emitting diode horizontal slit projection across the anterior chamber, from the anterior surface of the cornea to the anterior surface of the crystalline lens [11].

2.3. Formula Calculations

Spherical equivalent formula predictions were performed with the Topcon Aladdin biometer.

For this study, the authors focused on the comparison between Barrett Universal II (BU II), Hoffer Q, Holladay 1, and SRK/T and formulas. The formulas used had lens constants provided by the lens manufacturers. Retrospectively we optimized the constants using the LCO V 5.1. Ref. [12] and obtained new constants, as illustrated in

Table 1. Constants used for each formula.

Implant	Formula	Constant	Manufacturer Constant	Optimized Constant
SN60WF	BU II	LF	1.884	1.962
	Hoffer Q	pACD	5.640	5.690
	Holladay 1	SF	1.840	1.910
	SRK/T	A Constant	119.0	119.15
ZCB00	BU II	LF	2.041	1.999
	Hoffer Q	pACD	5.800	5.710
	Holladay 1	SF	2.020	1.950
	SRK/T	A Constant	119.30	119.22
	LF—lens factor; pACD—predicted ACD; SF—surgeon factor.

. Barrett lens factor was recalculated according to the new A-constants-1.962 for SN60WF and 1.999 for ZCB00 (Table 1).

2.4. Surgical Procedure

All eyes were operated on by the same surgeon (HTS) using the same surgical protocol, under local peribulbar anesthesia with 2.5 mL Lidocaine 4% and 2.5 mL Marcaine 0.5%. The phaco-aspiration (222 eyes) and phacoemulsification (882 eyes) were performed using the INFINITI^® Vision System phacoemulsifier (Alcon, Fort Worth, TX, USA).

2.5. Postoperative Treatment and Evaluation

Immediately after surgery, there were the following topical eye drops prescribed: moxifloxacin 0.5%, four times a day. For one week, tobramycin/dexamethasone 0.3%/0.1% for 6 weeks (five times then four times a day, one week each, then three times a day for 3 weeks), tropicamide 0.5% one time a day for 3 weeks and dexpantenol 5% gel three times a day for 4 weeks.

Slit lamp examination and mydriatic fundoscopy were performed at the first appointment, on the first day postoperatively, after the eye bandage removal. The second and the third appointment, at one week and one month after surgery, consisted of uncorrected distance visual acuity, manifest refraction, keratometry, tonometry, corneal pachymetry, anterior segment slit-lamp biomicroscopy, and mydriatic fundoscopy.

All the measurements were performed by the same technician on the same devices, which were calibrated before each measurement.

2.6. Data Analysis and Statistics

Patient data were collected and centralized into an Excel^® database (ver. 1902, Microsoft Office 365 ProPlus. Microsoft Corp., Washington, DC, USA). Data analysis was performed on Statistical Package for the Social Sciences (SPSS) software (ver. 24, IBM^® SPSS^® Statistics, IBM Corp., Armonk, NY, USA).

Final postoperative manifest refraction was measured by the same technician on the same auto-kerato-refractometer one month after the surgery and was converted into its spherical equivalent. For the statistical analysis of the postoperative refractive data, we analyzed only the one-month manifest refraction.

All eyes were divided into groups for each lens based on the axial length (AL): SN60WF-Group 1.1: <22 mm (42 eyes), Group 1.2: 22–24.5 mm (354 eyes), and Group 1.3: >24.5 mm (318 eyes), ZCB00-Group 2.1: <22 mm (96 eyes), Group 2.2: 22–24.5 mm (234 eyes), and Group 2.3: >24.5 mm (60 eyes).

The mean absolute error (MAE) and the median absolute error (MedAE) were calculated for four different formulas: three third-generation formulas: Hoffer Q and Holladay 1 and SRK/T, and one fourth-generation formula: Barrett Universal II.

The statistical analysis aimed to evaluate the refractive results. After checking the normality of the distribution of continuous variables by the Shapiro–Wilk test, the differences in absolute error between formulas were assessed using the Friedman test (statistical significance at p < 0.05) and the Wilcoxon signed-rank post hoc analysis with the Bonferroni correction (statistical significance at p < 0.0125).

3. Results

The study included 1104 eyes (564 right and 540 left eyes) from 1100 patients, 452 (41.3%) males and 648 (58.7%) females with implant of SN60WF (714 eyes) and ZCB00 (390 eyes). The mean age was 73.157 ± 8.303 years (from 44 to 89 years). The ACD of the eyes included in the study was 3.180 ± 0.425 mm (from 2.23 to 4.06 mm), and the AL was 23.829 ± 1.574 mm (from 20.68 to 30.01 mm). The power of the implants ranged from 7.50 to 33.50 D (20.815 ± 4.173D).

Table 2. Descriptive data of all of eyes included in the study.

Parameter	Age (years)	ACD (mm)	AL (mm)	IOL Diopter
Mean ± SD	73.157 ± 8.303	3.180 ± 0.425	23.829 ± 1.574	20.815 ± 4.173
Minimum	44	2.23	20.68	7.50
Maximum	89	4.06	30.01	33.50

shows the descriptive data of all patients.

Table 3. Descriptive data of each group with Acrysof^® IQ SN60WF implant.

Acrysof® IQ SN60WF
Parameter	Age (years)	ACD (mm)	AL (mm)	IOL Diopter
Group 1.1. (AL < 22 mm, n:42)
Mean ± SD	77.714 ± 5.594	2.810 ± 0.325	21.767 ± 0.247	25.357 ± 1.610
Minimum	67	2.23	21.39	22.50
Maximum	84	3.29	21.99	27.50
Group 1.2. (AL 22–24.5 mm, n:354)
Mean ± SD	77.101 ± 6.269	3.083 ± 0.359	23.313 ± 0.595	21.669 ± 1.953
Minimum	65	2.24	22.03	16.00
Maximum	89	3.98	24.35	25.50
Group 1.3. (AL > 24.5 mm, n:318)
Mean ± SD	69.207 ± 10.578	3.476 ± 0.372	25.647 ± 1.176	16.452 ± 2.911
Minimum	44	2.44	24.52	7.50
Maximum	89	4.06	30.01	21.50
ACD—anterior chamber depth; AL—axial length; SD—standard deviation.

and

Table 4. Descriptive data of each group with Tecnis^® ZCB00 implant.

Tecnis® ZCB00
Parameter	Age (years)	ACD (mm)	AL (mm)	IOL Diopter
Group 2.1. (AL < 22 mm, n:96)
Mean ± SD	73.875 ± 6.020	2.688 ± 0.354	21.550 ± 0.423	27.718 ± 3.311
Minimum	61	2.27	20.68	23.00
Maximum	82	3.18	21.94	33.50
Group 2.2. (AL 22–24.5 mm, n:234)
Mean ± SD	71.692 ± 6.563	3.142 ± 0.312	23.122 ± 0.667	22.538 ± 1.988
Minimum	51	2.60	22.07	19.50
Maximum	87	3.96	24.44	26.50
Group 2.3. (AL > 24.5 mm, n:60)
Mean ± SD	72.200 ± 2.587	3.380 ± 0.393	25.095 ± 0.454	17.950 ± 1.856
Minimum	69	2.85	24.52	14.50
Maximum	77	4.04	25.73	20.50
ACD—anterior chamber depth; AL—axial length; SD—standard deviation.

present descriptive data of each group.

Detailed p values obtained by the statistical analysis comparing the formulas in each group are displayed in

Table 5. p values obtained by the statistical analysis comparing the unoptimized formulas in each group.

AL: <22 mm
	Friedman Test p Value	Wilcoxon Signed-Rank with Bonferroni Correction p Value
Group 1.1.	0.048	BU II–Hoffer Q	0.035
		BU II–Holladay 1	0.070
Group 2.1.	0.045	BU II–Hoffer Q	0.014
		BU II–Holladay 1	0.027
AL: 22–24.5 mm
Group 1.2.	<0.001	Holladay 1–Hoffer Q	<0.001
Group 2.2.	<0.001	BU II–Hoffer Q	<0.001
		BU II–Holladay 1	<0.001
		Hoffer Q–Holladay 1	0.002
		Hoffer Q–SRK/T	0.008
AL: >24.5 mm
Group 1.3	0.001	BU II–Hoffer Q	0.001
		BU II–Holladay 1	0.009
		BU II–SRK/T	0.001
Group 2.3.	0.5	-	-
Statistical significance: Friedman test p < 0.05; Wilcoxon signed-rank with Bonferroni correction p < 0.0125.

and

Table 6. p values obtained by the statistical analysis comparing the optimized formulas in each group.

AL: <22 mm opt
	Friedman Test p Value	Wilcoxon Signed-Rank with Bonferroni Correction p Value
Group 1.1.	0.271	-	-
Group 2.1.	0.163	-	-
AL: 22–24.5 mm
Group 1.2.	<0.001	BU II–Hoffer Q	0.007
		Holladay 1–Hoffer Q	<0.001
		Hoffer Q–SRK/T	0.001
Group 2.2.	<0.001	BU II–Hoffer Q	0.001
		BU II–Holladay 1	0.003
AL: >24.5 mm
Group 1.3	0.187	-	-
Group 2.3.	0.001	BU II–Hoffer Q	0.030
		Holladay 1–Hoffer Q	0.039
Statistical significance: Friedman test p < 0.05; Wilcoxon signed-rank with Bonferroni correction p < 0.0125.

.

Table 7. Prediction errors for groups with AL < 22 mm.

Group 1.1. (n:42 AL: <22 mm)
	BU II	Hoffer Q	Holladay 1	SRK/T
MAE(D) ± SD	0.240 ± 0.180	0.391 ± 0.215	0.334 ± 0.216	0.282 ± 0.182
MedAE	0.140	0.320	0.270	0.250
	BU II optimized	Hoffer Q optimized	Holladay 1 optimized	SRK/T optimized
MAE(D) ± SD	0.301 ± 0.176	0.422 ± 0.232	0.325 ± 0.127	0.342 ± 0.174
MedAE	0.270	0.400	0.340	0.400
Group 2.1. (n:96 AL: <22 mm)
	BU II	Hoffer Q	Holladay 1	SRK/T
MAE(D) ± SD	0.473 ± 0.369	0.576 ± 0.410	0.476 ± 0.356	0.449 ± 0.399
MedAE	0.415	0.510	0.365	0.285
	BU II optimized	Hoffer Q optimized	Holladay 1 optimized	SRK/T optimized
MAE(D) ± SD	0.453 ± 0.359	0.535 ± 0.353	0.488 ± 0.416	0.451 ± 0.427
MedAE	0.360	0.460	0.390	0.220
MAE(D) ± SD—mean absolute error ± standard deviation; MedAE—median absolute error.

,

Table 8. Prediction errors for groups with AL 22–24.5 mm.

Group 1.2. (n:354 AL: 22–24.5 mm)
	BU II	Hoffer Q	Holladay 1	SRK/T
MAE(D) ± SD	0.331 ± 0.223	0.337 ± 0.248	0.292 ± 0.221	0.305 ± 0.217
MedAE	0.280	0.310	0.270	0.260
	BU II optimized	Hoffer Q optimized	Holladay 1 optimized	SRK/T optimized
MAE(D) ± SD	0.288 ± 0.219	0.346 ± 0.231	0.293 ± 0.220	0.280 ± 0.223
MedAE	0.230	0.330	0.270	0.210
Group 2.2. (n:234 AL: 22–24.5 mm)
	BU II	Hoffer Q	Holladay 1	SRK/T
MAE(D) ± SD	0.246 ± 0.210	0.368 ± 0.251	0.319 ± 0.212	0.296 ± 0.230
MedAE	0.180	0.340	0.280	0.250
	BU II optimized	Hoffer Q optimized	Holladay 1 optimized	SRK/T optimized
MAE(D) ± SD	0.250 ± 0..186	0.326 ± 0.217	0.306 ± 0.209	0.296 ± 00.211
MedAE	0.180	0.280	0.260	0.240
MAE(D) ± SD—mean absolute error ± standard deviation; MedAE—median absolute error.

and

Table 9. Prediction errors for groups with AL > 24.5 mm.

Group 1.3. (n:318 AL: >24.5 mm)
	BU II	Hoffer Q	Holladay 1	SRK/T
MAE(D) ± SD	0.273 ± 0.196	0.334 ± 0.230	0.316 ± 0.217	0.344 ± 0.246
MedAE	0.250	0.300	0.300	0.290
	BU II optimized	Hoffer Q optimized	Holladay 1 optimized	SRK/T optimized
MAE(D) ± SD	0.276 ± 0.202	0.315 ± 0.232	0.311 ± 0.218	0.328 ± 0.248
MedAE	0.280	0.280	0.280	0.280
Group 2.3. (n:60 AL: >24.5 mm)
	BU II	Hoffer Q	Holladay 1	SRK/T
MAE(D) ± SD	0.131 ± 0.153	0.162 ± 0.177	0.113 ± 0.082	0.148 ± 0.079
MedAE	0.080	0.140	0.080	0.160
	BU II optimized	Hoffer Q optimized	Holladay 1 optimized	SRK/T optimized
MAE(D) ± SD	0.107 ± 0.086	0.178 ± 0.191	0.101 ± 0.0.82	0.181 ± 0.071
MedAE	0.100	0.110	0.075	0.170
MAE(D) ± SD—mean absolute error ± standard deviation; MedAE—median absolute error.

indicate the MAE and MedAE in each AL group for optimized and unoptimized constants.

For AL < 22 mm (Table 7), in the SN60WF group (Group 1.1.) Unoptimized, BU II had the smallest MAE (0.240 D) and MedAE (0.140) and Hoffer Q had the greatest values (MAE = 0.391 D, MedAE = 0.320). Friedman test showed significant statistical differences between the absolute prediction errors for the four formulas (p = 0.048), but Wilcoxon signed rank test with Bonferroni correction revealed no statistically significant superiority of the BU II formula compared to Hoffer Q (p = 0.035) and Holladay 1 (p = 0.070). Optimized, BU II also showed the smallest MAE (0.301 D) and MedAE (0.270) and Hoffer Q had the greatest values (MAE = 0.422 D, MedAE = 0.400). Friedman test showed no significant statistical differences between the absolute prediction errors for the four optimized formulas (p = 0.271).

In the ZCB00 group with AL < 22 mm (Group 2.1.) the SRK/T formula had the smallest values for the MAE (0.449 D) and MedAE (0.285) and Hoffer Q showed the worst results (MAE = 0.567 D, MedAE = 0.510). Friedman test showed significant statistical differences between the absolute prediction errors for the four formulas (p = 0.045), but Wilcoxon signed rank test with Bonferroni correction revealed no statistically significant superiority of the BU II formula compared to Hoffer Q (p = 0.014) and Holladay 1 (p = 0.027). The optimized formulas showed similar results, with the SRK/T formula having the smallest values for the MAE (0.451 D) and MedAE (0.220), and Hoffer Q showed the worst results (MAE = 0.535 D, MedAE = 0.460). There were, however, no significant statistical differences between the absolute prediction errors for the four optimized formulas (p = 0.163).

For AL between 22 and 24.5 mm (Table 8), in the SN60WF group (Group 1.2.), without optimization, Holladay 1 had the smallest MAE (0.292 D), and SRK/T had the smallest MedAE (0.260), Hoffer Q had the greatest MAE (0.337 D) and MedAE (0.310). Friedman test showed significant statistical differences between the absolute prediction errors for the four formulas (p < 0.001). Wilcoxon signed-rank test with Bonferroni correction revealed significant inferiority of the Hoffer Q formula but only when compared to Holladay 1 (p < 0.001). After optimization, SRK/T had the smallest MAE (0.280 D) and MedAE (0.210), Hoffer Q had the greatest MAE (0.346 D) and MedAE (0.330). Friedman test showed significant statistical differences between the absolute prediction errors for the four formulas (p < 0.001). Wilcoxon signed-rank test with Bonferroni correction revealed significant inferiority of the Hoffer Q formula compared to Holladay 1 (p < 0.001), SRK/T (p = 0.001), and BU II (p = 0.007).

In the ZCB00 group with AL between 22 and 24.5 mm (Group 2.2.), the unoptimized BU II formula had the smallest values for the MAE (0.246 D) and MedAE (0.180), and Hoffer Q the greatest MAE (0.368 D) and MedAE (0.340). Friedman test showed significant statistical differences between the absolute prediction errors for the unoptimized formulas (p < 0.001). Wilcoxon signed-rank test with Bonferroni correction revealed a significant superiority of BU II compared to Hoffer Q (p < 0.001) and Holladay 1 (p < 0.001). Hoffer Q showed significant inferiority also to Holladay 1 (p = 0.002) and SRK/T (p = 0.008). After optimization, the results were similar, with the BU II formula having the smallest values for the MAE (0.250 D) and MedAE (0.180), and Hoffer Q the greatest MAE (0.326 D) and MedAE (0.280). Friedman test showed significant statistical differences between the absolute prediction errors for the optimized formulas (p < 0.001). Wilcoxon signed-rank test with Bonferroni correction revealed a significant superiority of BU II compared to Hoffer Q (p = 0.001) and Holladay 1 (p = 0.003).

For AL > 24.5 mm (Table 9), in the SN60WF group (Group 1.3.) BU II had the smallest MAE (0.273 D) and MedAE (0.250), SRK/T had the greatest MAE (0.344 D), and Hoffer Q and Holladay 1 had the greatest MedAE (0.300). Friedman test showed significant statistical differences between the absolute prediction errors for the unoptimized formulas (p = 0.001). Wilcoxon signed-rank test with Bonferroni correction revealed a significant superiority of BU II compared to Hoffer Q (p = 0.001), Holladay 1 (p = 0.009) and SRK/T (p = 0.001). After optimization, BU II maintained the smallest MAE (0.276 D), SRK/T the greatest MAE (0.328 D), and all the formulae showed a MedAE of 0.280. Friedman test showed no significant statistical differences between the absolute prediction errors for the optimized formulas (p = 0.187).

In the ZCB00 group with AL > 24.5 mm (Group 2.3.), the Holladay 1 formula had the smallest MAE (0.113 D). The smallest MedAE (0.080) was for both Holladay 1 and BU II. Hoffer Q formula had the greatest MAE (0.162 D) and SRK//T the greatest MedAE (0.160). Friedman test showed no significant statistical differences between the absolute prediction errors for the unoptimized formulas (p = 0.5). After optimization, Holladay 1 formula had the smallest MAE (0.101 D) and MedAE (0.075), and SRK/T had the greatest MAE (0.181 D) and MedAE (0.070). Friedman test showed significant statistical differences between the absolute prediction errors for the optimized formulas (p = 0.001), but Wilcoxon signed rank test with Bonferroni correction revealed no statistically significant inferiority of the Hoffer Q formula compared to BU II (p = 0.030) and Holladay 1 (p = 0.039). Considering this group had fewer eyes (60) which have been selected to exclude myopic retinopathy and other ocular pathologies, the results are more uniform compared to the SN60WF group.

4. Discussion

This study showed a variety of results depending on the axial length and lens type.

For eyes with an AL under 22 mm, the Hoffer Q is the most popular formula, which was reported by several studies to be the most accurate [13,14,15,16]. Olsen et al. concluded that SRK/T and Holladay 1 formulas had lower MAEs than the Hoffer Q [17]. Melles et al. showed BU II to have the lowest mean absolute prediction error for short eyes and Hoffer Q-the greatest [4]. Kane et al. also showed Hoffer Q to perform the worst, and Holladay 1 showed the lowest MAE [2].

In our study, for Group 1.1., BU II had the lowest MAE and MedAE, and for Group 2.1. it was SRK/T. Contrary to what was expected, Hoffer Q performed the worst for eyes with axial length between 20.68 mm and 22 mm, resembling the findings of recent studies by Kane et al. [2], Cooke et al. [3] and Melles et al. [4]. Friedman test had a p value for both groups under 0.05, but Wilcoxon signed rank test with Bonferroni correction revealed no statistically significant differences between formulas. After optimization, the results were similar, with BU II (for Group 1.1.) and SRK/T (for Group 2.1.) performing the best and Hoffer Q having the lowest performance, but the statistical significance between these two formulas decreased.

For eyes with an AL between 22 and 24.5 mm, there were statistically significant differences between the absolute errors of the evaluated formulas. For Group 1.2., Holladay 1 showed superior results compared to Hoffer Q before optimization. After optimization, BU II and SRK/T performance increased and also became significantly better than Hoffer Q. For Group 2.2. BU II performed better than Holladay 1, and Hoffer Q performed worse than all the other three formulas. After optimization, BU II remained superior to Hoffer Q and Holladay 1, but p values increased, and Hoffer Q’s performance got better.

For eyes with an AL > 24.5 mm, there were also statistically significant differences between the absolute errors of the evaluated formulas in both lens groups. In Group 1.3. BU II showed superior results compared to Hoffer Q, Holladay 1, and SRK/T. However, the statistical significance disappeared after optimization (p = 0.187). In Group 2.3, Holladay 1 and BU II performed best but showed no significant differences to the other formulas (p = 0.5). After optimization, their performance increased (p = 0.001), but Wilcoxon signed rank test with Bonferroni correction revealed no statistically significant differences between them and Hoffer Q (p > 0.0125).

These results mirror the findings of other recent studies that proved the BU II formula to be the best suited for calculating intraocular lens (IOL) power for myopic eyes [18,19]. Additionally, Holladay 1′s superiority in Group 2.3. (AL: 24.52–25.73 mm) supports the recommendation of the Royal College of Ophthalmologists to be used for eyes measuring between 24.6–26.0 mm [20].

Barrett Universal II (BU II) formula showed the smallest mean absolute error in three groups with short (Group 1.1.), medium (Group 2.2.), and long (Group 1.3) axial length before and after optimization. Unoptimized, Holladay 1 had the best results in two groups of medium (Group 1.2) and long (Group 2.3) axial length, and SRK/T in one short axial length group (Group 2.1). After optimization, SRK/T performed best also in a medium axial length group (Group 1.2.), overtaking Holladay 1.

Studies evaluating the accuracy of new generation vergence formulas and formulas based on artificial intelligence showed that the performances of the Barrett Universal II and Hill-RBF formulas were comparable [21,22,23,24]. In a previous study on patients operated in our clinic, we proved the non-inferiority of the Barrett formula used to calculate the optimal diopter for trifocal IOL implanted in patients with a wide range of axial lengths [25].

The reason we chose to compare these formulas with the latest constants provided by the lens manufacturers and not use our constants optimization is that most surgeons do not spend time in real life optimizing lens constants each time a new formula or a specific lens becomes available, and they rely on what is accessible as a standard recommendation. For this reason, it is important to know which formula performs best with the given constants. Then, we also chose an accessible online optimization method that led to similar results but with decrease in the differences between formulas. For Barrett Universal II, after lens factor adjustment based on A-constant optimization, there were no significant changes in results. Khatib et al. compared Barrett Universal II with Hill-RBF and EVO formulas with and without optimization for the same reason and concluded that without optimizing these formulas, Barrett performed the best [24].

This study hints at the versatility of the Barrett Universal II formula, a fourth-generation formula that is now widely available for most optical biometers and provides a useful tool of calculation for eyes of all axial lengths.