Assessing the Accuracy of Refractive Prediction of Different IOL Formulas in Medium Long Eyes

Abbreviations

ACD: Anterior Chamber Depth; AD: Aqueous Depth; AXL: Axial Length; IOL: Intraocular Lens; WTW: White-To-White.

Introduction

Modern-day cataract surgery has gradually transformed into a refractive procedure with a high demand for spectacle independence. To improve the post-operative refractive outcomes, there has been an ongoing attempt to increase the accuracy of the intraocular lens (IOL) power calculation formulas [1, 2, 3]. Over time, there has been a remarkable change in the IOL power calculations from simple first and second generations formulas like SRK-I and SRK-II, in which the effective lens position was constant for each patient, to third (SRK/T, Holladay 1, Hoffer Q), fourth (Haigis, Holladay 2, Hill-RBF) and fifth generation formulas (Barrett Universal II, Olsen) [4]. In these newer formulas, the effective lens position is determined for each individual eye by using multiple biometry variables including keratometry, axial length (AXL), pre-operative anterior chamber depth (ACD), white- to-white diameter (WTW) and lens thickness (LT) which predict the IOL power with better precision and accuracy [5]. Ray tracing is a promising approach to calculating IOL power which is the basis of the Olsen and Okulix formula [6]. Formulas derived using artificial intelligence (Pearl DGS, Kane) are also growing in popularity [4].

Despite these advances, accurate prediction of IOL power in myopic eyes still poses a challenge with higher probability of attaining a postoperative hyperopic surprise. Precise AXL measurement preoperatively is of particular significance as they account for 54% of prediction errors in IOL power calculations [7]. Several studies have been designed to measure and compare the accuracy of different formulas in long eyes [8, 9, 10, 11, 12, 13]. In our study, we aim to evaluate and compare the absolute prediction errors between seventeen different IOL power calculation formulas for medium long eyes (>25mm) and to analyse the correlation between the median absolute error (MAE) provided by different formulas and multiple biometric variables like AXL, keratometry, and ACD.

Patients and Methods

Our study is retrospective data collection for cataract surgery performed at a tertiary Ophthalmology centre.

Local ethics approval was sought from the hospital ethics committee for data collection and the tenets of the declaration of Helsinki were followed. Medical records of patients from January 2008 to July 2019 with AXL >25mm that underwent uncomplicated cataract surgery at our centre were reviewed. In patients with both AXL >25mm, one eye was randomly selected in the study due to the correlation between eyes [14].

The inclusion criteria were as follows: (1) Biometric measurements (AXL, K1K2, ACD) assessed by LenStar 2 (Haag-Streit International, Switzerland, LS 900). (2) Had undergone pre-operative and post-operative assessment and subjective refraction at least 3 weeks post- surgery. (3) Cataract surgery performed by phacoemulsification and in-the-bag monofocal lens implantation with 2.4mm clear corneal incision. (4) All eyes implanted with Alcon AcrySof IQ SN60WF intraocular lens. (5) Postoperative BCVA of 6/12 or better at 3+ weeks follow-up.

The exclusion criteria were as follows: (1) Patients with history of any previous intraocular surgery or any intraoperative or postoperative complication (2) Patients with cognitive impairment or pre-existing ocular disease that may impact the post-operative refraction including keratoconus, corneal scarring, amblyopia, glaucoma or any other retinal pathology. (3) Post-operative follow-up of less than one month.

For the study we noted the patients’ demographics, laterality, pre-operative and post-operative subjective refraction, keratometry readings, AXL, ACD, and IOL power from the biometry device.

The pre-operative and post-operative spherical equivalent were determined for each patient [spherical power + ½ cylindrical power].

Statistical Analysis

In this analysis, the power is the probability the Friedman test can correctly reject the null hypothesis that the absolute zero re-centred prediction errors between different IOL formulas are all the same.

To estimate the power, simulations were conducted based on the natural error distributions of the IOL formulas. Following are the steps:

Simulate the prediction errors of 17 IOL formulas for 100/200/300/……/1,300 sample points based on the associated empirical distributions.

Re-centre the prediction errors to 0 and convert them to absolute prediction errors (APE) Conduct Friedman test to see whether the effects between the IOL formulas are significant (p <= 0.05) for each simulation Repeat step 1-3 5,000 times. Assuming the absolute re- centred prediction errors from seventeen IOL formulas are indeed different, the proportion of simulations that were significant will be the power that the Friedman test can correctly reject the null hypothesis.

Based on this simulation, the estimated power for the analysis with 101 samples (5 outliers excluded) is ~100% to reject the null hypothesis that the absolute zero re-centred prediction errors between different IOL formulas are all the same.

Through the deviation testing, out of 106 samples (1802 data points in 17 IOL formula), 23 outliers were spotted in 5 samples. They were excluded from the analysis data.

The Shapiro-Wilk test and Q-Q plot were used to determine the normality of distribution of data.

Estimated Power vs. Simulation

The estimated powers for all sample sizes are 100%.

Estimated Power vs. Sample Size

The estimated power for the analysis for 101 samples is ~100% to reject the null hypothesis that the absolute zero re- centred prediction errors between different 17 IOL formulas are all the same. The Friedman test was used to determine the statistically significant difference between APE of the different IOL formulas.

Results

A total of 106 patients were included in the study with a mean age of 77.96 ± 9.08 years (range = 46 to 93 years). 57.5% were male patients. The mean ± SD, median and the percentiles of all the variables in this study are tabulated below (Table 1).

Discussion

The increase in incidence of myopia day by day is a constant stress on the health resources worldwide. It is estimated that by 2050, 50% of the world population will be affected by myopia [16]. Even though the prevalence is more in east and southeast-Asian countries [17, 18], due to the current migration and resettling of population, and the change in lifestyle factors, this condition has affected all the countries world-wide [19]. Infact, the Sydney Myopia study conducted in 2006 reported an incidence of myopia of 31% [20]. In a few years’ time, there will be a rise in the myopic patients requiring cataract surgeries with spectacle independence. Our study focuses on mild to moderate myopic eyes as the majority of myopes fall in this category [21].

Despite the continued aim to improve outcomes in myopic eyes, there are errors in axial length calculation, effective lens position prediction, and lens constant optimisation. Hyperopic surprise is a common complication post cataract surgery in myopic patients and thus choosing the correct formula becomes a crucial part in the surgery preparation. With so many different formulas currently available, we aimed to compare them to find the formulas with least prediction errors and least hyperopic surprise.

In our study, we found that the Okulix and Olsen PO formulas have the least variation even though they tend to have slightly higher MPE and trend towards more myopic outcomes. However, on reducing the mean to zero, these two formulas have their MedPE closer to zero than the rest of the formulas which is statistically significant. They also had least number of patients with postoperative refractive error >± 1.0D. They also tend to have lower MedPE when comparing across different K1, K2, ACD, AD, and AXL values and quantile groups. Interestingly, the rest of the formulas had similar SD.

In a study by Abulafia, et al. [22] that compared the SRK/T, Hoffer Q, Haigis, Barrett Universal II, Holladay 2, and Olsen formulas, found that all these formulas met the benchmark criteria of having PE of ± 0.5D in at least 71% of eyes and they performed similar in patients with AXL >26mm and requiring IOL power ≥ 6.0D. Similarly, in our cohort, we found the Barrett U2, Kane, Okulix, Olsen PO, and Pearl DGS formulas meeting these benchmark criteria.

Doshi, et al. [9] found that all 3 of the formulas (Holladay 1, Hoffer Q, and SRK-T) performed well in AXL >24.5mm with the Haigis formula showing more hyperopic results.

Though this study did not measure AXL with an IOL Master/ Lenstar. In our study, the Haigis formula, however, showed a more myopic tendency and the HofferQ formula resulted in a significant hyperopic result.

There are several studies in literature comparing the different third and fourth generation formulas and most of the studies have found them to be comparable in predicting refractive errors in myopic eyes [11, 23, 24, 25, 26]. However, there are not many studies reporting accuracy of newer formulas.

Okulix is one of the newer formulas which works on ray-tracing software and uses multiple biometric values (including AXL, IOL curvature radii, IOL central thickness, asphericity, refractive index, corneal topography, and CCT) to determine the IOL power. In a study comparing Okulix with the pre-existing formulas like SRK-T and Hoffer Q, they noted that MPE by Okulix was not significantly different from that of the other two formulas (P=0.25) and 63.5% of eyes had their prediction errors within ± 0.50D [27]. In our study, the MPE of Okulix was determined to be -0.20D but had a small standard of deviation. Due to the skewed data points, the MedPE after reducing the mean to zero, the Okulix formula performed well (-0.002). It also had the highest number of patients with postoperative refractive error within ± 0.5D (88%).

The only other formula to perform similarly in our study was the Olsen PO. Olsen formula uses a specialised C-constant, which is basically a ratio by which the empty capsular bag will capture and fix the new IOL after implantation. This increases the accuracy of predicting the effective lens position by using the preoperative ACD and LT measurements [23]. This is now included in the Lenstar LS 900 machine. PhacoOptics is a unique IOL power calculation tool and data management approach which incorporates exact and paraxial ray tracing to effectively determine the correct IOL power to implant. We found that Olsen PO has a MPE of -0.315 with a smaller standard of deviation similar to Okulix. Given the skewed data sets, the MedPE after reducing the mean to zero was -0.005 with 77% of patients having a postoperative refractive outcome of within ± 0.5D.

EVO (Emmetropia verifying Optical) formula is based on the theory of emmetropisation and in a study comparing the EVO with Barrett U2, Haigis, Kane, and SRK-T, the EVO performed better in long AXL than the others [28].

Pearl DGS (Postoperative spherical Equivalent prediction using Artificial intelligence and Linear algorithms) was developed by Debellemanière, Gatinel and Saad and is based on the prediction of the theoretical internal lens position. This formula was determined to have lower SD (± 0.269D) than the Olsen, K6, EVO, and Barrett U2 formula [29].

This study, despite being retrospective in nature, had the following strengths: First, we compared between seventeen different formulas in long to medium long eyes, which is majority of the cohort of the booming myopic population. Second, a single IOL type was used to overcome bias between different IOL designs. Third, we incorporated the newer generation formulae for the comparison with the traditional ones. However, short follow-up period, sample size and multiple surgeons were some limitations of the study. Conclusions Okulix and Olsen PO formulas have the MedPE closest to zero with smaller standard of deviation then the rest of the formulas. The Barrett U2, EVO, Haigis, Hill RBF 3.0, Holladay 2 NLR, Kane, K6, Okulix, Olsen Lenstar, Olsen PO, Pearl DGS, T2 formulas tend to have more myopic MPE whereas the Hoffer Q, Holladay 1, Holladay 2 2014, SRK T, VRF formulas have more hyperopic MPE.