To compare the accuracy of a new intraocular lens (IOL) power formula (Kane formula) with existing formulas using IOLMaster, predominantly model 3, biometry (measures variables axial length, keratometry and anterior chamber depth) and optimised lens constants. To compare the accuracy of three new or updated IOL power formulas (Kane, Hill-RBF V.2.0 and Holladay 2 with new axial length adjustment) compared with existing formulas (Olsen, Barrett Universal 2, Haigis, Holladay 1, Hoffer Q, SRK/T).

A single surgeon retrospective case review was performed from patients having uneventful cataract surgery with Acrysof IQ SN60WF IOL implantation over 11 years in a Melbourne private practice. Using optimised lens constants, the predicted refractive outcome for each formula was calculated for each patient. This was compared with the actual refractive outcome to give the prediction error. Eyes were separated into subgroups based on axial length as follows: short (≤22.0 mm), medium (>22.0 to <26.0 mm) and long (≥26.0 mm).

The study included 846 patients. Over the entire axial length range, the Kane formula had the lowest mean absolute prediction error (p<0.001, all formulas). The mean postoperative difference from intended outcome for the Kane formula was −0.14+0.27×1 (95% LCL −1.52+0.93×43; 95% UCL +0.54+1.03×149). The formula demonstrated the lowest absolute error in the medium axial length range (p<0.001). In the short and long axial length groups, no formula demonstrated a significantly lower absolute mean prediction error.

Using three variables (AL, K, ACD), the Kane formula was a more accurate predictor of actual postoperative refraction than the other formulae under investigation. There were not enough eyes of short or long axial length to adequately power statistical comparisons within axial length subgroups.

Modern intraocular lens (IOL) formulas have provided unprecedented accuracy.

There are no publications assessing the new Kane formula and the RBF/Holladay 2 formulas following recent modifications.

The Kane formula provided improved accuracy over widely used modern formulas.

There was no increase in relative accuracy of the RBF and Holladay 2 formulas following their modification.

Use of the Kane formula should be given strong consideration in IOL selection.

Refractive expectations following cataract surgery are increasing. Modern biometry, newer intraocular lens (IOL) formulas and surgical techniques have all contributed to an improvement in refractive outcome prediction accuracy. In 2011, a large series reported 71% and 95% of cases were within 0.5 and 1.0D of predicted refraction.

Older generation formulas: Haigis, Hoffer Q, Holladay 1 and SRK/T are used less frequently as more modern formulas exhibiting greater accuracy are now available. With incorporation into biometers, these formulas are more accessible and less prone to transcription errors when compared with those accessed via stand-alone software or the internet. Recent studies reporting large series

The Hill-RBF method uses adaptive learning from a large dataset to predict refractive outcomes. For a given eye, it relies on adequate numbers of eyes of a similar dimension to provide an accurate prediction. If the dataset has insufficient number of eyes of a similar dimension, an out of bounds message is provided. Kane

To our knowledge, no currently published study has assessed the Hill 2.0, Kane or Holladay 2 with new axial length adjustment.

This study was performed on patients in the Author’s (BC) private practice in Melbourne, Australia with ethics approval obtained from the local ethics committee.

Inclusion criteria were patients 18 years and over having uncomplicated conventional or femtosecond laser assisted cataract surgery performed by a single surgeon (BC) at a private operating facility. Capsulotomies were centred on the pupil with implantation of an Acrysof IQ SN60WF (Alcon Laboratories) inserted through a 2.4 mm clear corneal incision.

Exclusion criteria were factors that might impact the postoperative refractive outcome which included: (1) preoperative comorbidities (significant corneal scarring, keratoconus or other ectasia, keratoplasty, past laser vision correction, corneal relaxing incisions), (2) intraoperative complication (anterior or posterior capsule tear, vitreous prolapse or zonular dehiscence), (3) postoperative complications (persistent corneal oedema) or (4) postoperative corrected distance visual acuity worse than 6/12, refraction performed before day 21 postoperatively or incomplete documentation. If both eyes of one patient met the inclusion criteria, one eye was randomly chosen for inclusion.

Preoperative biometry was performed using the IOLMaster biometer models 3, 500 or 700 (software 3.2, 7.5 and 1.50, respectively). Postoperative refraction was performed by an orthoptist. For analysis, values were transcribed manually from the patient electronic medical record into an Excel spreadsheet (Microsoft, Redmond, Washington, USA). Lens thickness and central corneal thickness were only available where biometry was performed with IOLMaster 700 model as the earlier models did not measure these parameters.

The results for the Kane were provided by the author (Kane) prior to the calculation of the other formulas. Predictions for the Haigis,

The constant for each formula was optimised to produce a mean prediction error (ME) of zero (or as close as possible) by performing multiple iterations of the data using varying constants. For the Haigis formula, only the a0 constant was optimised.

For some formulas, a ME of zero could not be obtained due to limitations in how many decimal places could be entered for the constant into the calculator. In these cases, the small residual mean error was removed by adjusting the refractive prediction error for each eye by an amount equal to the ME in that group as described in the JCRS editorial by Wang

The predicted postoperative refraction for each patient was calculated using the optimised IOL constants. The prediction error was then calculated as the actual postoperative refraction minus the refractive result predicted by each formula.

The mean absolute error (MAE), median absolute prediction error (MedAE), ME and SD of the prediction error (STDEV) as well as the percentage of eyes that had a prediction error within ±0.25, 0.50 and 1.00 D were calculated for each formula. Eyes were separated into subgroups based on axial length as follows: short (≤22.0 mm), medium (>22.0 to <26.0 mm) and long (≥26.0 mm).

The differences in absolute error between formulas were assessed using the Friedman test. In the event of a significant result, posthoc analysis was undertaken using the Wilcoxon signed-ranks tests for pairwise comparisons with Bonferroni correction as suggested by Aristodemou

Of the 1402 patients having cataract surgery with implantation of the Alcon SN60WF IOL, 556 were excluded (see

Indications for subject exclusion from the analysis

Parameter | Eyes (n) |

Previous corneal surgery (PK, LVC, RK or PTK) | 14 |

Other corneal disease (KCN, ectasia, PMD, corneal scars) | 15 |

CDVA less than 6/12 | 23 |

No postoperative refraction | 58 |

Incomplete biometry or out of range of any formula | 27 |

Both eyes operated on (random exclusion) | 419 |

KCN, keratoconus;LVC, laser vision correction;PK, penetrating keratoplasty;PMD, pellucid marginal degeneration; PTK, phototherapeutic keratectomy;RK, radial keratotomy.

Characteristics of eyes included in the final analysis

Parameter | Value: mean±SD (range) |

Axial length | 23.70±1.28 (20.49–31.77) |

Anterior chamber depth | 3.12±0.39 (2.01–4.36) |

Mean keratometry | 43.78±1.48 (39.65–48.12) |

Flat keratometry | 43.45±1.49 (38.05–47.64) |

Steep keratometry | 44.11±1.53 (39.93–50.37) |

Lens thickness | 4.56±0.45 (3.52–5.75) |

IOL power | 21.2±3.4 (6.0–30.0) |

Age | 77.8±9.58 |

Gender distribution | 364 male; 500 female |

IOL, intraocular lens.

Constants used for the different formulas

Formula | Lens constant | Optimised constant |

Barrett Universal | Lens factor | 118.75 |

Haigis | a0, a1, a2 | −0.946, 0.234, 0.217 |

Hill 2.0 | A constant | 118.69 |

Hoffer Q | ACD | 5.457 |

Holladay 1 | Surgeon factor | 1.68 |

Holladay 2 | ACD | 5.345 |

Kane | A constant | 118.73 |

Olsen | ACD | 4.47 |

SRK/T | A constant | 119.05 |

Over the entire axial length range, a statistically significant difference existed (see

Prediction errors for each formula, sorted by SD

Formula | MAE | ME | STDEV | MedAE | ±0.25 D | ±0.50 D | ±1.00 D |

Kane | 0.329 | 0.00 | 0.445 | 0.231 | 52.4 | 77.9 | 96.6 |

Olsen | 0.342 | 0.00 | 0.460 | 0.264 | 47.9 | 77.2 | 96.1 |

Hill 2.0 | 0.346 | 0.00 | 0.463 | 0.264 | 48.3 | 75.3 | 96.4 |

Barrett | 0.350 | 0.00 | 0.469 | 0.268 | 47.9 | 75.2 | 96.4 |

Holladay 2 | 0.357 | 0.00 | 0.477 | 0.273 | 46.8 | 76.0 | 95.5 |

Haigis | 0.358 | 0.00 | 0.480 | 0.271 | 45.5 | 75.5 | 96.1 |

Holladay 1 | 0.358 | 0.00 | 0.475 | 0.276 | 45.1 | 73.4 | 96.1 |

SRK/T | 0.369 | 0.00 | 0.489 | 0.293 | 44.7 | 72.1 | 95.9 |

Hoffer Q | 0.381 | 0.00 | 0.499 | 0.311 | 40.3 | 73.6 | 95.5 |

MAE, mean absolute prediction error;ME, mean prediction error;MedAE, median absolute prediction error; ST DEV, SD deviation of the prediction error.

The Olsen formula had the next lowest MAE (0.342), significantly lower than the remaining formulas (p<0.05) except compared with the Hill 2.0 (0.346) and the Barrett Universal 2 (0.350). Of the earlier generation formulas, Holladay 1 (0.358) and Haigis (0.358) had the lowest absolute error, significantly lower than Hoffer Q (0.381).

The Hill 2.0 provides an out of bounds statement when the biometry parameters are outside of the range of defined accuracy. The Hill 2.0 provided an out of bounds warning in 11.5% of cases. Interestingly, the MAE for the Hill 2.0 was 0.347 for in bound cases compared with 0.341 for out of bounds cases.

Intended, postoperative and difference between the intended and postoperative refractive error

Formula | Intended refractive outcome | Postoperative refractive outcome | Difference between intended and postoperative refractive error | ||||

SE | SCxA | SE | SCxA | SE | SCxA | ||

Kane | Mean (SD) | −0.70 (+0.66) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.54) | −0.14+0.27×1 |

95% LCL | −1.99 | −1.47–1.02×140 | −2.10 | −2.54+0.87×39 | −1.05 | −1.52+0.93×43 | |

95% UCL | +0.60 | +0.11+0.97×137 | 0.71 | +0.29+0.84×143 | 1.05 | +0.54+1.03×149 | |

Barrett | Mean (SD) | −0.70 (+0.68) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.56) | −0.14+0.27×1 |

95% LCL | −2.03 | −1.52–1.02×140 | −2.10 | −2.54+0.87×39 | −1.09 | −1.55+0.93×43 | |

95% UCL | +0.64 | +0.15+0.97×136 | 0.71 | +0.29+0.84×143 | 1.09 | +0.58+1.03×149 | |

Hill | Mean (SD) | −0.69 (+0.67) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.55) | −0.14+0.27×1 |

95% LCL | −2.00 | −1.48–1.02×140 | −2.10 | −2.54+0.87×39 | −1.08 | −1.55+0.93×42 | |

95% UCL | +0.61 | +0.12+0.97×137 | 0.71 | +0.29+0.84×143 | 1.08 | +0.56+1.03×148 | |

Olsen | Mean (SD) | −0.69 (+0.68) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.55) | −0.14+0.27×1 |

95% LCL | −2.02 | −1.51–1.02×140 | −2.10 | −2.54+0.87×39 | −1.08 | −1.55+0.93×43 | |

95% UCL | +0.64 | +0.15+0.97×137 | 0.71 | +0.29+0.84×143 | 1.07 | +0.55+1.03×149 | |

Holladay 2 | Mean (SD) | −0.70 (+0.67) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.56) | −0.14+0.27×1 |

95% LCL | −2.00 | −1.49–1.02×140 | −2.10 | −2.54+0.87×39 | −1.10 | −1.57+0.93×43 | |

95% UCL | +0.61 | +0.12+0.97×137 | 0.71 | +0.29+0.84×143 | 1.10 | +0.59+1.03×149 | |

H1 | Mean (SD) | −0.70 (+0.69) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.56) | −0.14+0.27×1 |

95% LCL | −2.04 | −1.53–1.02×140 | −2.10 | −2.54+0.87×39 | −1.10 | −1.57+0.93×42 | |

95% UCL | +0.65 | +0.16+0.97×137 | 0.71 | +0.29+0.84×143 | 1.10 | +0.59+1.02×148 | |

Haigis | Mean (SD) | −0.70 (+0.71) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.57) | −0.14+0.27×1 |

95% LCL | −2.09 | −1.58–1.03×140 | −2.10 | −2.54+0.87×39 | −1.11 | −1.57+0.93×43 | |

95% UCL | +0.70 | +0.21+0.97×137 | 0.71 | +0.29+0.84×143 | 1.11 | +0.59+1.02×149 | |

SRK/T | Mean (SD) | −0.70 (+0.70) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.62) | −0.14+0.27×1 |

95% LCL | −2.06 | −1.54–1.05×143 | −2.10 | −2.54+0.87×39 | −1.22 | −1.69+0.93×43 | |

95% UCL | +0.67 | +0.17+0.99×139 | 0.71 | +0.29+0.84×143 | 1.22 | +0.70+1.04×149 | |

Hoffer Q | Mean (SD) | −0.70 (+0.73) | −0.73+0.07×82 | −0.70 (+0.72) | −0.80+0.21×3 | 0.00 (+0.58) | −0.14+0.27×1 |

95% LCL | −2.13 | −1.62–1.03×140 | −2.10 | −2.54+0.87×39 | −1.14 | −1.61+0.93×42 | |

95% UCL | +0.74 | +0.25+0.97×137 | 0.71 | +0.29+0.84×143 | 1.14 | +0.63+1.02×148 |

Spherical equivalent (SE), Compound refractive error (SCxA), SD, Lower confidence limit (LCL), Upper confidence limit.

LCL, lower confidence limit ; SCxA, compound refractive error; SE, spherical equivalent ; UCL, upper confidence limit.

Mean absolute error for each formula by axial length

Formula | Short | Medium | Long |

Kane | 0.441 | 0.322 | 0.326 |

Olsen | 0.442 | 0.336 | 0.352 |

Hill 2.0 | 0.440 | 0.340 | 0.358 |

Haigis | 0.472 | 0.353 | 0.322 |

H1 | 0.438 | 0.343 | 0.545 |

Barrett | 0.479 | 0.344 | 0.331 |

Holladay 2 | 0.483 | 0.350 | 0.348 |

SRK/T | 0.475 | 0.360 | 0.407 |

HofferQ | 0.476 | 0.368 | 0.511 |

In the Medium axial length eyes group (n=774), there was a statistically significant difference between groups (p<0.01). The Kane formula was more accurate than all others (p<0.01 in all cases). There was no difference between the Barrett, Hill 2.0, Olsen and Holladay 1 formulas.

In the long axial length eyes group (n=44), there was a statistically significant difference (p<0.01) between groups. The most accurate formulas were Haigis, Kane, Barrett, Holladay 2, Olsen and Hill 2.0; however, there were no significant differences within this group. All were significantly more accurate than the earlier generation formulas: SRK/T, Hoffer Q and Holladay 1 (p<0.05).

No statistically significant difference in accuracy between the different IOLMaster biometers was noted. For the Haigis formula, the median absolute error for subjects having their biometry with Model 3 was 0.275 (IQR: 0.128–0.492), Model 500: 0.374 (0.198–0.631) and Model 700: 0.236 (0.120–0.468). Mood’s median test demonstrated no significant difference χ²(2)=5.59, p=0.061.

The Kane formula had the most accurate outcomes with the lowest MAE, STDEV, MedAE and highest percentage of eyes within 0.25, 0.50 and 1.00 D prediction errors. No other published studies have assessed this formula meaning we are unable to compare our results to other papers.

The Olsen formula had the next lowest MAE which was significantly lower compared with all other formulas except the Hill 2.0. In a study by Cooke

The largest study to assess the Hill-RBF showed it to have a higher MAE than the Barrett Universal 2, Holladay 1 and SRK/T formulas.

The Barrett Universal 2 has been shown to be the most accurate formula in previous IOL power studies;

The Holladay 2 formula has been updated with a new AL adjustment (replacing the Wang and Koch adjustment used previously). In this study, it had the fifth lowest MAE and failed to show a statistically significant improvement in accuracy compared with the Holladay 1, SRK/T or the Haigis.

This study follows the recommended method for IOL power studies suggested by Hoffer

A potential limitation of the study is the three different IOLMaster models used, although this is unlikely to have affected the outcome as measurements taken between the IOLMaster 500 and 700 have been shown to have excellent agreement.

Another limitation is that not all cases had measurements of lens thickness and CCT. The Olsen and Kane formulas use both LT and CCT as variables and the Holladay 2 and Barrett use LT and WTW as a variable. When these variables were included, all four formulas performed more accurately than when they were not available.

Cases underwent surgery over an 11-year period and biometry performed using three different IOLMaster models (3, 500 and 700). This may have had small impact on our results since the more modern formulas, in general, are more accurate when LT and CCT are available, parameters not measured on the older model 3. This may have had the effect of underestimating the prediction accuracy advantage of the newer formulas.

The numbers in this study were inadequate to perform a meaningful, adequately powered subgroup analysis comparing formula accuracy for short, medium or long axial length eyes. Short eyes remain the group with the highest absolute error and the Kane formula demonstrated no benefit. Similar to the finding of Melles,

With respect to the Haigis formula, we found no additional benefit with optimisation of all three constants over a0 constant optimisation, a finding reported elsewhere.

These results were obtained using lens constants optimised by the surgeon within their own group of patients. For an individual surgeon wanting to achieve similar results, it is important they optimise their own lens constants.

BC and JK planned the study, analysed the data, drafted, read and approved the manuscript. BC collected the data and submitted the study. BC and JK supervised the study and are its guarantors.

The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

JK is the owner of the JXK formula.

Not required.

Approval was obtained from the Royal Victorian Eye and Ear Hospital Human Research and Ethics Committee.

Not commissioned; externally peer reviewed.