Evaluation of 9 IOL power calculation formulas using a heteroscedastic statistical method and a new method of IOL constant optimization

Abstract

Purpose

To evaluate the prediction accuracy of 9 IOL power calculation formulas using a heteroscedastic statistical analysis and a novel method for IOL constant optimization.

Design

Retrospective case series.

Methods

The LenStar LS900 (Haag-Streit, Koeniz, Switzerland) was used for the preoperative biometry. The predicted SE refraction of the implanted IOL were calculated for: Barrett Universal II, EVO-2.0, Hill RBF-3.0, Hill-RBF 2.0, Kane, PEARL-DGS, SRK-T, Hoffer-Q and Holladay-1. IOL constants were optimized prior to the analysis. A heteroscedastic statistical method was used to compare the standard deviation (SD) of prediction errors (PE).

Results

Two hundred seventy-eight eyes of 278 patients were included. The SD of the Kane was 0.4214D and was the lowest in this database. The SD of the PE of the Kane and EVO 2.0 were significantly lower than the SRK-T, Holladay 1, and Hoffer-Q. The SD of the PE of the PEARL formula was significantly lower than the SRK-T and Hoffer-Q. The SD of the PE of the Hill-RBF 3.0 was not significantly different to the Hill-RBF 2.0, Kane, EVO 2.0, Barrett Universal II and PEARL. No significant difference was found between the SD of the PE of the new generation formulas analysed.

Conclusions

the lowest SD of the prediction error was provided by Kane, followed by EVO 2.0 and PERL-DGS formulas. However, no statistically significant differences were found between the SD of the PE of new generation formulas. Further studies are necessary to evaluate the accuracy of these formulas in extreme eyes.

Keywords

IOL power calculation Evaluation of IOL power calculation formulas

Introduction

Intraocular lens (IOL) power calculation is a field in constant evolution. The predictability of IOL power calculation have improved with the use of new optical biometers and modern IOL power calculation formulas.^1–3

Within the ever-changing landscape of IOL power calculation, continual assessment of calculation methods is essential to gauge the accuracy of new proposals against established ones. Recently, the standard deviation (SD) of the prediction error (PE) has been proposed as the primary method for formula comparison.⁴ However, the SD of the PE tends to distribute in an asymmetric fashion. For that reason, the use of heteroscedastic statistical method is needed to perform comparisons between SD of the PE of different formulas.⁴

One limitation for most of new generation IOL power calculation formulas is that they are unpublished. Optimizing IOL constant by an iteration method without knowing the code of the formula can be impracticable for large databases. Univariate analysis the SD of the PE overcomes this limitation for formula comparison as this parameter is not affected by IOL constant optimization.⁴ However, IOL constant optimization is still relevant for the analysis of the percentage of eyes within a given PE and is crucial for clinical practice to reduce systematic errors in IOL power calculation.^5,6 Recently, a new method for IOL optimization has been proposed.⁷ The aim of this study was to evaluate the prediction accuracy of 9 different IOL power calculation formulas using a heteroscedastic statistical analysis and a recently described methodology for IOL constant optimization.

Methods

Consecutive medical records of patients who had undergone uneventful cataract surgery with IOL implant at capsular bag at our institution from May 2020 to January 2021 were retrospectively reviewed in search for patients who met the following inclusion criteria: patients older than 18 years old, optical biometry performed with the LenStar LS900 (Haag-Streit, Koeniz, Switzerland), implantation of Medicontour 877-PAY (Medicontur Medical Engineering Ltd., Zsambek, Hungary) or Eyecee One Croma (Bausch and Lomb, USA) and a subjective refraction at least 1 month postoperatively with visual acuity >= 0.6 decimal. Patient with corneal disease, history of strabismus, significant retinal disease or history of prior ophthalmic surgery were excluded from the analysis.

Cataract surgery was performed by 9 different surgeons, by phacoemulsification under topical anaesthesia by 2.20 mm corneal incision. All routine postoperative refractions were performed by a trained optometrist, under standard protocols, with a refraction line of 5.50m. The refraction distance was converted to 6.0 m by adjusting for the vergence distance by adding 1/6 - 1/[test distance in meters] to the spherical equivalent refraction.^8,9 The study conformed to the tenets of the Declaration of Helsinki and was approved by the ethics committee of our institution.

Optical biometry and Formulas

The LenStar LS900 (Haag-Streit, Koeniz, Switzerland) was used for the preoperative biometry in all the patients included in the study. The predicted postoperative SE refraction of the implanted IOL were calculated for 9 different formulas: SRK-T, Hoffer-Q, Holladay-1, Barrett Universal II, Emmetropia Verifying Optical (EVO) 2.0, Hill RBF-2.0, Hill RBF-3.0, Kane and PEARL-DGS.^10–16 The online version of the new generation formulas was accessed by a custom-made web scrapping code programmed in Python 3.6.

Statistical analysis

Statistical analysis was applied according to the heteroscedastic statistical method and considering the standard deviation (SD) of the prediction error (PE) as the primary parameter to evaluate formula performance.⁴ P values were adjusted for multiple comparisons. An adjusted P value less than 0.05 was considered statistically significant. Prior to the analysis, for each IOL model separately, the systematic errors of the formulas were minimized by constant optimization applying the method proposed by Gatinel et al.⁷

Results

Two hundred seventy-eight eyes of 278 patients were included. Table 1 shows the baseline characteristics of the sample included in the study. Mean age was 72.52 ± 7.33 years. From the eyes included, 103 (37.38%) were from male patients and 144 (51.79%) were right eyes. The refractive prediction outcomes are presented in Table 2. No out of bound cases were noted for the Hill-RBF 2.0 and Hill-RBF 3.0 formulas.

Table 1.

Baseline characteristics of the sample included in the study. K = mean keratometry; ACD = Anterior Chamber Depth; LT = Lens Thickness; WTW = White To White; CCT = Central Corneal Thickness; SD = Standard Deviation.

Parameter	Total sample (n = 278)		877 – PAY (n = 120)		Eyee-Cee One (n = 158)
	Mean ± SD	Range	Mean ± SD	Range	Mean ± SD	Range
K (D)	44.06 ± 1.55	39.59–47.80	44.17 ± 1.55	40.32–47.80	44.03 ± 1.52	39.59–47.78
Axial Length (mm)	23.37 ± 1.16	20.90–30.20	23.34 ± 1.22	20.90–30.20	23.36 ± 1.09	20.91–28.73
ACD (mm)	3.09 ± 0.35	2.17–3.85	3.05 ± 0.34	2.17–3.85	3.11 ± 0.35	2.26–3.85
LT (mm)	4.57 ± 0.36	3.56–5.48	4.58 ± 0.36	3.76–5.48	4.56 ± 0.36	3.56–5.42
WTW (mm)	11.93 ± 0.42	10.73–13.12	11.92 ± 0.39	11.01–12.87	11.92 ± 0.44	10.73–13.12
CCT (μm)	542.33 ± 34.13	450–639	537.85 ± 36.26	450.00–611.00	544.96 ± 31.88	471.00–639.00
IOL power (D)	22.05 ± 3.24	1–30	21.45 ± 3.34	1.00–29.00	22.57 ± 3.10	8.00–30.00

Table 2.

Refraction prediction errors of the formulas and percentage of eyes within certain range of prediction error.

Formula	IOL model	Initial Const	Mean PE	Optimized constant	Mean PE (optimized)	SD	Mean AE	Median AE	±0.25	±0.5	±1
Barrett UII	877-PAY	118.9	−0.077	118.818	0.006	0.436	0.324	0.268	47.58	77.42	95.16
	EyeeCee	119.7	−0.115	119.577	−0.004	0.454	0.349	0.287	43.04	79.11	96.20
	All	-		-		0.446	0.337	0.270	45.68	78.78	96.76
Kane	877-PAY	118.9	−0.1219	118.757	−0.001	0.388	0.289	0.225	55.65	83.87	95.97
	EyeeCee	119.7	−0.347	119.331	−0.013	0.446	0.331	0.290	46.84	77.85	95.56
	All	-				0.421	0.312	0.240	50.71	81.29	96.76
RBF-3.0	877-PAY	118.9	−0.079	118.861	−0.008	0.413	0.306	0.238	49.19	81.45	95.16
	EyeeCee	119.7	−0.085	119.610	0.005	0.464	0.353	0.298	44.01	81.01	95.56
	All	-				0.442	0.332	0.261	48.20	81.29	96.04
RBF-2.0	877-PAY	118.9	−0.093	118.800	−0.004	0.417	0.306	0.238	50.00	77.42	95.97
	EyeeCee	119.7	−0.012	119.577	0.007	0.477	0.366	0.299	41.14	74.05	95.57
	All	-				0.451	0.341	0.283	45.32	76.61	96.76
PEARL-DGS	877-PAY	118.9	0.047	118.850	0.003	0.381	0.281	0.225	55.65	83.06	95.97
	EyeeCee	119.7	−0.202	119.506	−0.003	0.454	0.341	0.281	44.94	77.85	95.57
	All	-				0.423	0.314	0.248	51.07	81.29	96.76
EVO 2.0	877-PAY	118.9	−0.037	118.861	−0.006	0.393	0.300	0.218	55.65	83.06	95.16
	EyeeCee	119.7	−0.258	119.425	0.004	0.452	0.335	0.270	47.47	78.47	96.84
	All	-				0.424	0.313	0.238	51.79	81.29	97.12
SRK-T	877-PAY	118.9	−0.059	118.838	0.001	0.454	0.336	0.277	44.35	79.03	94.35
	EyeeCee	119.7	−0.235	119.450	0.002	0.485	0.364	0.269	44.94	70.89	93.67
	All	-				0.471	0.352	0.266	45.68	74.82	94.60
Hoffer Q	877-PAY	5.50	0.007	5.492	−0.004	0.464	0.357	0.300	41.94	70.16	95.16
	EyeeCee	5.96	−0.142	5.871	−0.003	0.501	0.384	0.325	41.77	70.25	96.20
	All	-				0.485	0.373	0.305	42.44	71.58	96.76
Holladay-1	877-PAY	1.84	−0.021	1.825	0.005	0.442	0.330	0.257	47.58	75.81	94.35
	EyeeCee	2.34	−0.143	2.102	−0.006	0.476	0.362	0.297	42.41	72.78	96.20
	All	-				0.461	0.347	0.285	45.68	74.82	96.40

SD of the PEs

The results of the heteroscedastic statistical analysis of the SD of PE are represented in Table 3. The SD of the Kane was 0.4214D and was the lowest in this database (Figure 1). The SD of the PE of the Kane and EVO 2.0 were significantly lower than the SRK-T, Holladay 1, and Hoffer-Q. The SD of the PE of the PEARL formula was significantly lower than the SRK-T and Hoffer-Q. The SD of the PE of the Hill-RBF 3.0 was not significantly different to the Hill-RBF 2.0, Kane, EVO 2.0, Barrett Universal II and PEARL. No significant difference was found between the SD of the PE of the new generation formulas analysed.

Table 3.

Heteroscedastic statistical analysis by the SD of prediction errors. Adjusted P values are shown for the comparation between formulas. BUII = Barrett Universal II.

Fórmula	SD
BUII	0,4456	1,0000
Kane	0,4214	0,2472	1,0000
EVO 2.0	0,4267	0,7094	0,7094	1,0000
Hill RBF 3.0	0,4419	0,7094	0,3564	0,7094	1,0000
Hill RBF 2.0	0,4514	0,7094	0,1434	0,5417	0,7094	1,0000
PEARL 2.0	0,4236	0,7083	0,7094	0,7094	0,6938	0,4183	1,0000
SRK-T	0,4710	0,2123	0,0038	0,0253	0,1795	0,5715	0,0448	1,0000
Hoffer-Q	0,4847	0,0505	0,0006	0,0627	0,0828	0,3899	0,0261	0,7094	1,0000
Holladay	0,4607	0,4912	0,0099	0,3035	0,6736	0,7094	0,1858	0,7094	0,1858	1,0000
		BUII	Kane	EVO 2.0	Hill RBF 3.0	Hill RBF 2.0	PEARL 2.0	SRK-T	Hoffer-Q	Holladay

Percentage of cases within a given PE

The percentage of cases within a given PE for each IOL model included is decomposed at Table 2. Overall, the percentage of eyes with PEs within 0.25 D, ± 0.50 D and ±1.0 D ranged from 38.84% to 51.79%, 69.78% to 81.29%, 94.60% to 97.12%, respectively (Figure 2).

Disccussion

IOL power calculation is an area in constant evolution, making it essential to constantly evaluate the results provided by the new releases on the field. This study was designed to evaluate the accuracy of 9 different IOL power calculation formulas employing a heteroscedastic statistical analysis and a new method for IOL constant optimization.^4,7

In an article recently published by Holladay et al. it is suggested to use SD of PE as the primary method for formula comparison.⁴ However, performing a contrast of hypothesis comparing based on the SD cannot be done directly as the SD tends to distribute in an asymmetric fashion. For that reason, the use of heteroscedastic statistical method is suggested.

Different approaches have been proposed to increase the predictability of IOL power calculation formulas.¹⁷ In this study, we included and compared different new generation IOL power calculation formulas with different calculation methods.^17,18 Click or tap here to enter text. One promising strategy is the use of big data and artificial intelligence. Recently, the Hill-RBF 3.0 has been released and it is available online.¹³ This formula is based on significantly greater database than its predecessor the Hill-RBF 2.0 and has increased the number of parameters used for IOL power calculation by adding the central corneal thickness (CCT), white-to-white distance (WTW) and patient's sex. The Hill-RBF 3.0 formula has been evaluated previously and showed promising results in terms of predictability of IOL power calculation.^18–20

In consonance with previous studies, new generation formulas obtained a higher percentage of eyes between within 0.5D of PE compared to SRK-T, Hoffer-Q, Holladay 1 and Haigis.^1–3 In this study the Hill-RBF 3.0 showed an improvement compared to the Hill-RBF 2.0 in terms of percentage of eyes in 0.5D PE (81.295% and 76.619% respectively). Compared to other new generation formulas, the Hill-RBF 3.0 showed identical results in percentage of eyes in 0.5D PE as the Kane, EVO 2.0 and PEARL and a higher percentage than the Barrett UII (81.295% and 78.777% respectively).

In a previous study performed by Tsessler et al. the Hill-RBF 3.0 formula was compared with other 10 formulas including the Hill RBF-2.0 by means of a heteroscedastic statistical method.¹⁹ In that study, the Hill RBF-3.0 formula was ranked as the best formula and was statistically significantly better than its predecessor the Hill RBF-2.0 (SD 0.285D and 0.309D respectively, p = 0.036). Their results differ slightly to the findings of our study. Although in our study the Hill-RBF 3.0 obtained better results than the Hill RBF-2.0 this difference was not statistically significant (SD 0.441D and 0.451D respectively, p = 0.709). In addition, the accuracy of the Hill RBF 3.0 was inferior to that of the Kane, PEARL and EVO 2.0. However, this difference was not statistically significant.

The results reported at this paper reflect the advancement in the accuracy of IOL power calculation during the lasts decades. The heteroscedastic statistical analysis performed found that the SD of the PE of Kane and EVO 2.0 were significantly lower than those of the Holladay 1, and the SD of the PE of Kane, EVO 2.0 and PEARL were significantly lower than the SD of PE of SRK-T and Hoffer-Q. We did not find significant differences between the SD of the PE of new IOL power calculation formulas.

Although IOL constant optimization would not affect the results of the heteroscedastic statistical analysis performed in this study, optimizing constants is still relevant for the comparison of the percentage of eyes within a given PE. In this study, we performed a IOL constant optimization by a new method proposed by Gatinel et al.⁷ This method requires the calculation of the expected refraction for the IOL implanted and to compare it to the measured spherical equivalent to obtain the mean error. The mean error, the average mean keratometric power and the mean IOL power are entered in a second equation and the optimized IOL constant is returned. Then, a second calculation using the optimized IOL constant is required to test the accuracy of the optimization. For all the formulas analysed, the mean error after optimization was less than 0.015D after a single optimization. Although, a mean error of this magnitude is not clinically relevant, if for research purposes a lower mean error is aimed, this method may be limited to zeroing out the first two decimal places, as the lens power output of most of the unpublished formulas are rounded to 2 decimal places.⁷

The main limitation of our study is that it had a relatively small sample size of 272 eyes, with few eyes with extreme of unusual biometry features (8 eyes with AL >26 mm and 28 eyes with AL <22 mm). For that reason, segmented analysis by biometrical parameters could not be performed. Another limitation of the study is the inclusion of two different IOL models. To overcome this limitation, IOL constant optimization was performed individually and results of IOL power calculation accuracy were reported separately for each IOL model.

In conclusion, the highest prediction accuracy between the formulas analysed was found with Kane, followed by EVO 2.0 and PERL-DGS. However, no statistically significant difference was found between the SD of the PE of new generation formulas. Further studies are necessary to evaluate the accuracy of these formulas in extreme eyes.

Footnotes

Acknowledgement

The authors want to acknowledge the Department of Ophthalmology of the General University Hospital of Elche.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Daniel Romero-Valero

Alicia Cárceles

Carlos E. Monera Lucas

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