## Discussion

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 *et al,*17 the PhacoOptics version of the Olsen formula (Olsen PO) showed the least accurate result of the formulas assessed when using the IOLMaster biometer but strangely the most accurate when using the Lenstar biometer. Our study showed the Olsen PO formula to have the second lowest MAE out of the formulas assessed indicating the Olsen PO formula may perform well using the IOLMaster biometer.

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.4 The updated version of the Hill-RBF performed better in our study outperforming each of these formulas although the increased accuracy compared with the Barrett was not statistically significant. Although the Hill-RBF website reports an out of bounds ‘will be less common’, in our study 11.5% of calculations returned an ‘Out of Bounds’ prediction which is significantly higher than the 1.4% found in the study by Kane *et al* and the 4.3% found in the Melles *et al* study. Interestingly, the MAE found for the Hill 2.0 in the ‘Out of Bounds’ group was lower than ‘In bounds’ group indicating that the boundary model may be imprecise in identifying cases where the calculation is likely to be inaccurate.

The Barrett Universal 2 has been shown to be the most accurate formula in previous IOL power studies;2 4 however, it has never been assessed against the Kane, the Hill 2.0 and only once against the Olsen PO formula.2 In our study, the Barrett Universal 2 had a lower MAE than the SRK/T and Hoffer Q which is similar to the findings in other studies.2 3 17

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 *et al*18 except we used the MAE of formulas to rank their accuracy as suggested by Kane *et al*3 and Wang *et al*.14 The potential for bias from variation in operative style or refractive technique has been reduced as all patients included were operated on by a single surgeon, using a single IOL model and with relative consistency of staff performing the biometry and postoperative refraction. The high rate of follow-up (only 4.3% of patients without a postoperative refraction compared with 18.3% in Melles *et al*) is another strength of the study.

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.19 The IOLmaster models differ in their technique for measurement of anterior chamber depth, Model 500 measures with a slit beam and Model 700 uses swept source optical coherence tomography. Akman identified the Model 700 measured the ACD slightly shorter than the 500.19

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,2 the Hoffer Q formula demonstrated no advantage over other earlier generation formulas for short eyes.

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.2

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.