Refractive accuracy is 1 of the key tenets of successful cataract surgery, with improvements in surgical technique1 and in preoperative measurements2 contributing to increasing accuracy.
Modern intraocular lens (IOL) power formulas have also contributed to the increase in accuracy. The differences in the derivation method and metrics used are summarized in Table 1. Although the Holladay 2 formula (the first “newer generation” formula) was not the most accurate in large cohort studies,3–5 there has been progress. The Barrett Universal 2 (Barrett) and the Olsen6 formulas are more accurate than both older generation formulas and the Holladay 2 formula.3,4 The recently developed Hill-RBF formula (version 1.0) was found to be less accurate than the Barrett and the best-performing third-generation formulas in the only large-scale study to date.7
Further attempts to improve the accuracy of some of these modern IOL formulas have been implemented with version 2.0 of the Hill-RBF formula (hereafter “Hill 2.0”) based on a size-increased database. Similarly, a new axial length (AL) adjustment has been incorporated into the Holladay 2 formula8 (Holladay 2-AL adjusted). The Kane formulaA is based on theoretical optics and incorporates both regression and artificial intelligence components to further refine its predictions. The formula was developed using approximately 30 000 cases from selected refractive cataract practices and then using high-performance cloud-based computing to create its algorithm. The Kane formula requires the AL, keratometry, anterior chamber depth, and sex to make its predictions. The addition of IOL thickness and central corneal thickness significantly improves the accuracy of the formula; however, it is optional.
The aim of the current study was to assess the accuracy of these new/updated IOL formulas in a large population to determine which is the best overall predictor of the actual postoperative refractive outcome. A subgroup analysis will also examine each AL subgroup and differing IOL types.
A retrospective chart review was conducted on all cataract surgeries performed from May 2008 until November 2017 at 2 National Health Service trusts in the United Kingdom. Institutional review board approval was granted. Inclusion criteria were uneventful phacoemulsification cataract surgery with the insertion of 1 of the following 4 different IOL types: SA60AT (Alcon Laboratories, Inc.), Superflex Aspheric 920H, C-Flex Aspheric 970C (Rayner Intraocular Lenses Limited Akreos Adapt AO (Bausch & Lomb, Inc.), and preoperative biometry performed using partial coherence interferometry (IOLMaster; Carl Zeiss Meditec AG). Exclusion criteria were incomplete biometry using the IOLMaster, corneal astigmatism greater than 4.0 D, other corneal disease, previous vitrectomy, complicated cataract surgery, postoperative corrected distance visual acuity worse than 20/40, or postoperative complications.
All data including preoperative biometry data were collected from the electronic medical record (Medisoft; Medisoft Limited). If patients underwent bilateral phacoemulsification cataract extraction, then a randomly selected eye was chosen for inclusion in the study.
Subjective manifest refraction was performed preoperatively and postoperatively by hospital or community optometrists. Only eyes with formal refractions were included in the study. No details of crystalline lens thickness, central corneal thickness, or white-to-white measurements were used.
The Hoffer Q,9 Holladay 1,9 Haigis,11 and SRK/T12 formulas were calculated using already validated4 Excel spreadsheets (Microsoft Corporation) according to their original publications and errata. The Kane formula was calculated by author J.X.K. The Holladay 2-AL adjusted formula was calculated using the Holladay IOL consultant software,B and the Olsen formula was calculated with the PhacoOptics software. The Hill 2.0C and the BarrettD formulas were calculated through their respective websites.
The constant for each of the formulas was optimized either within the spreadsheets or through trialing different constants for the black box formulas until the mean prediction error was zero. The Haigis formula underwent single optimization using ULIB-optimized (User Group for Laser Interference Biometry) constants for a1 and a2, as suggested by Melles et al.5
Some calculators limit the entry of IOL constants to only 2 decimal places, which makes it impossible to achieve a mean error of exactly zero. In these cases, the mean error was reduced to as small a value as possible by constant optimization. The mean error was then fully “zeroed” by adjusting the refractive prediction error for each eye by an amount equal to the overall mean prediction error for that formula as described by Wang et al.13 The prediction error was calculated as the actual postoperative refraction minus the formula-predicted refractive result.
The mean numerical prediction error, mean absolute prediction error (MAE), median absolute prediction error (MedAE), and standard deviation of prediction error (STDEV) were calculated for each formula. The percentages of eyes that had a prediction error of ±0.25 diopter (D), ±0.50 D, and ±1.00 D were calculated for each formula. The subgroup analysis was performed based on the AL for short (AL ≤ 22.0 mm), medium (22.0 mm < AL < 26.0 mm), and long (AL ≥ 26.0 mm) eyes and based on the IOL type. The mean rank score was calculated for each subgroup analysis as recommended by Cooke et al.3
The differences in the absolute error between formulas were assessed using the Friedman test, and in the event of a significant result, post hoc analysis was undertaken using the Wilcoxon test with Bonferroni correction, as suggested by Aristodemou et al.14 A P value less than .05 was considered statistically significant. Statistical analysis was performed in R (R Project; R Foundation).
A total of 13 351 eyes having uneventful cataract surgery, with the insertion of 1 of 4 IOL types and a postoperative corrected distance visual acuity of at least 20/40, were included in the study. Excluded from the initial database were 219 eyes with corneal pathology, 44 eyes with previous vitrectomy, 6 eyes with previous laser corrective surgery, and 89 eyes with anterior corneal astigmatism of greater than 4.0 D; 12 993 eyes remained. After randomly excluding 1 eye of patients who had both eyes eligible for inclusion, 10 930 eyes remained. The demographics are shown in Table 2. The optimized IOL constants used are shown in Table 3. The Friedman test on the absolute prediction error of each formula revealed a significant difference between formulas (P < .001), with post hoc analysis showing a significant difference between the Kane formula and all other formulas (P < .001 for all). Newer generation formulas (Hill 2.0, Olsen, Holladay 2-AL adjusted, and Barrett) had lower MAE compared with third-generation formulas (all P < .05). The Kane formula also had the lowest MedAE, STDEV, and highest percentage of eyes within 0.25 D, 0.50 D, and 1.00 D (Table 4).
Significant Results by Axial Length
The MAE for each AL subgroup is shown in Table 5. For short eyes, the Kane formula had the lowest MAE compared with all other formulas (P < .01). The Holladay 2-AL adjusted, Olsen, Holladay 1, and Hill 2.0 formulas were more accurate than the Barrett, SRK/T, and Haigis formulas (all P < .05). No significant difference existed between the Holladay 2-AL adjusted, Olsen, Holladay 1, Hill 2.0, and Hoffer Q formula. In medium eyes, the Kane formula had the lowest MAE compared with all other formulas (P < .001). The Hill 2.0 and Olsen formulas were more accurate than the third-generation formulas and the Haigis formula (all P < .05). There was no significant difference between the Barrett and Olsen formulas (P = .28) nor between the Barrett, Holladay 2-AL adjusted, and Holladay 1 formulas. In long AL eyes, the Kane formula had the lowest MAE compared with all other formulas (P < .05 compared with Barrett and P < .001 compared with all others). The Barrett formula had a lower MAE compared with the remainder of the formulas (P < .05). The Hill, Olsen, and Holladay 2-AL adjusted formulas were more accurate than the Holladay 1 and Hoffer Q formulas (P< .01).
Significant Results by Intraocular Lens Type
Figure 1 shows the MAE of each formula for each IOL type. The Kane formula was more accurate compared with all other formulas for the SA60AT IOL (P < .001), CFlex IOL (P < .001), and Akreos Adapt IOL (P < .05) and more accurate than all formulas (P < .01) except the Barrett (P = .4) and Hill 2.0 (P = .06) formulas for the SuperFlex IOL. For the SA60AT IOL, the Hill 2.0, Olsen, Barrett, and Holladay 2-AL adjusted formulas performed better than the third-generation formulas (all P < .01). For the CFlex IOL, the Olsen, Hill 2.0, and Holladay 1 formulas performed better than the Haigis, Barrett, and SRK/T formulas (all P < .05). For the SuperFlex IOL, the Kane and Barrett formulas were more accurate than all formulas (P < .01), except for the Hill 2.0 formula. The Hill 2.0 formula was not more accurate compared with the Holladay 2-AL adjusted (P = .31) or the Olsen (P = .11) formula but was more accurate than the remainder of formulas (P < .01). For the Akreos Adapt IOL, the Hill, Olsen, Holladay 2-AL adjusted, and Barrett formulas were more accurate than the SRK/T formula (P < .05) but not more accurate than the Hoffer Q, Holladay 1, or Haigis formula.
To our knowledge, this is the first study to assess the Kane, Hill 2.0, and Holladay 2-AL adjusted formulas. In our cohort, the Kane formula was found to be the most accurate. It also had the lowest MAE, standard deviation of error, median absolute error, and highest percentage of eyes within 0.25 D, 0.50 D, and 1.00 D. In the short, medium, and long AL subgroups, the Kane formula had the lowest MAE, which was statistically significant compared with all other formulas (P < .01). For each IOL subgroup studied, the Kane formula had the lowest MAE, which was statistically significant compared with all other formulas, except in the SuperFlex IOL group, in which the Kane formula had the lowest MAE, which was statistically significant compared with all formulas except the Barrett and the Hill 2.0 formulas. No published study on the Kane formula exists to compare our results.
Multiple studies3–5 have shown the Barrett Universal 2 formula is more accurate than the third-generation and Haigis formulas, which was confirmed in this study. The Holladay 2 formula has recently updated its AL adjustment method.5 Before its adjustment, the Holladay 2 formula was found to be less accurate than the Barrett formula before its new adjustment.3,4,7 In our cohort, the Holladay 2-AL adjusted formula had a similar MAE, a lower STDEV, and higher percentages of eyes within 0.50 D and 1.00 D than the Barrett formula, indicating improvement of the formula.
The Hill 2.0 formula uses a larger database for its artificial intelligence algorithm, which has improved its accuracy compared with other formulas. In the first study to assess the Hill-RBF formula (version 1.0), it was less accurate than the Barrett, Holladay 1, SRK/T, T2, and Ladas Super Formula.7 A study by Roberts et al.15 found the Hill-RBF formula (v1.05) to have the third lowest mean absolute numerical error of the 5 formulas studied. In our study, the Hill 2.0 formula had the second lowest MAE and STDEV, third lowest MedAE, and second highest percentage of eyes within 0.50 D, indicating improvement.
For each of the AL groups, the Kane formula had the lowest MAE, which was statistically significant in all cases (P < .01). In the short AL eyes, the Holladay 2-AL adjusted formula had the second lowest MAE, although there was no statistically significant difference found between it and the Olsen, Holladay 1, or Hill 2.0 formula, which is a similar finding to the study by Gökce et al.16 In the medium AL group, the Hill 2.0 formula had the second lowest MAE. Both the Hill 2.0 and the Olsen formulas were more accurate than the third-generation and Haigis formulas. In the long AL group, the Barrett formula had the second lowest MAE, which was statistically significant compared with the other formulas (P < .05) and is consistent with other findings.7
The overall predictability of the data (approximately 72.0% within 0.50 D) is lower than that of Melles et al.,5 which had 80.0% of eyes for the SA60AT IOL. Melles et al.5 used predictions made by the Lenstar 900 optical biometer (Haag-Streit) that, which would be expected to improve outcomes and may explain the differences between the 2 studies. The results in our study are similar to the results seen in the EUREQUO data, which reported 72.7% of eyes (of 282, 811 cases) as achieving a prediction error within 0.50 D.17
The different IOL models have different results with a variation in the mean absolute error between models from 0.340 for the Superflex and 0.405 for the C-Flex. This is likely explained by the ranges that these IOLs are available in. The Superflex is available from −10.0 to +22.0 D, and the C-Flex is available from +8.00 to +34.0. The worst performance of the C-Flex is explained by the C-Flex being implanted in more short AL eyes (which have a higher MAE compared with longer AL eyes).
The order of accuracy for the formulas changes in some cases depending on which IOL model is used. All IOL formulas are based on data derived from clinical practice and the IOL type that the formula is based on may lead to changes in the performance of that particular formula for that particular IOL. For example, the Hoffer Q formula performed better for the Akreos Adapt AO IOL than it did for the other IOL models. This may be because the Akreos Adapt AO IOL has a similar configuration as the JFCLRU (Alcon Laboratories, Inc,) IOL, which the Hoffer Q formula is based on. IOL manufacturers do not provide exact configurations, which makes it difficult to make further comparisons.
The absence of crystalline lens thickness, central corneal thickness, and white-to-white measurements limits our ability to draw further conclusions about formula accuracy. The Olsen formula and Kane formula both use crystalline lens thickness and central corneal thickness to make their predictions, whereas the Barrett Universal 2 and Holladay 2-AL adjusted formulas use crystalline lens thickness and white-to-white measurements. The inclusion of these extra variables may improve the accuracy of these formulas nevertheless, these additional variables are optional extras in the formulas mentioned previously, with none of them being an absolute requirement. Given many surgeons use older biometers that do not have the ability to measure the crystalline lens thickness or central corneal thickness, this study will assist in decision-making about IOL formulas.
Another potential limitation is the inclusion of data from multiple surgeons and refractions performed by different practitioners might introduce bias due to differences in operating style and technique. However, in modern surgery and optometry, this has been shown to only minimally impact results.18,19 Furthermore, studies with only a single surgeon and a single person performing refraction are unlikely to reach the number of cases required for significance and in themselves may be biased. The multicenter, multisurgeon approach described here might have greater generalizability and is advantageous.
This study includes a large number of short and long AL eyes and enough numbers for each IOL type to be adequately powered to detect relevant effects in all categories. The strict criteria for IOL formula studies that have been suggested by Hoffer et al.,20 with statistical analysis as suggested by Aristodemou et al.,14 have been carefully followed, although we prefer to compare formulas by the MAE rather than MedAE, as per Kane et al.4 and Wang et al.13 Few studies have been able to assess the Hill-RBF formulas because of the daily entry limits and pop-up blockers; we used computer programs that assisted us gathering data.
This study shows the ongoing improvement in IOL formulas and, hence, the potential for ongoing improvement in patient refractive results. The 2 updated formulas (Hill 2.0 and Holladay 2-AL adjusted) performed better than previously, and the Hill 2.0 formula outperforming the Barrett formula, which previously was shown to be the most accurate. The new Kane IOL formula demonstrated a significant improvement over current IOL formulas overall in short and in long AL eyes and for each IOL type.
WHAT WAS KNOWN
- The Barrett Universal II formula was the most accurate predictor of postoperative refraction compared with third-generation and newer generation formulas, including the Hill-RBF formula (version 1.0).
WHAT THIS PAPER ADDS
- The Kane formula was a more accurate predictor of postoperative refraction compared with all other formulas.
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