Intraocular lens power formula accuracy: Comparison of 7

ARTICLE

Q

Pub

1490

Intraocular lens power formula accuracy:Comparison of 7 formulas

Jack X. Kane, MB BS, Anton Van Heerden, MB ChB, FRANZCO, Alp Atik, MB BS,Constantinos Petsoglou, MB BS, MMed(Clin.Epi), FRANZCO

2016 A

lished

PURPOSE: To assess the accuracy of 7 intraocular lens (IOL) power formulas (Barrett Universal II,Haigis, Hoffer Q, Holladay 1, Holladay 2, SRK/T, and T2) using IOLMaster biometry and optimizedlens constants.

SETTING: Public hospital ophthalmology department.

DESIGN: Retrospective case series.

METHODS: Data from patients having uneventful cataract surgery with Acrysof IQ SN60WF IOLimplantation over 5 years were obtained from the biometry and patient charts. Optimized lens con-stants were calculated for each formula and used to determine the predicted refractive outcome foreach patient. This was compared with the actual refractive outcome to give the prediction error.Eyes were separated into subgroups based on axial length (AL) as follows: short (%22.0 mm), me-dium (>22.0 to <24.5 mm), medium long (R24.5 to <26.0 mm), and long (R26.0 mm).

RESULTS: The study included 3241 patients. The Barrett Universal II formula had the lowest meanabsolute prediction error over the entire AL range (P < .001, all formulas) as well as in the medium(P < .001, all formulas), medium-long (P < .001, except Holladay 1 and T2), and long AL (P < .001,except T2) subgroups. No statistically significant difference was seen between formulas in the shortAL subgroup. Overall, the Barrett Universal II formula resulted in the highest percentage of eyeswith prediction errors between G0.25 diopter D, G0.50 D, and G1.00 D.

CONCLUSION: In eyes with an AL longer than 22.0 mm, the Barrett Universal II formula was a moreaccurate predictor of actual postoperative refraction than the other formulas.

Financial Disclosure: None of the authors has a financial or proprietary interest in any material ormethod mentioned.

J Cataract Refract Surg 2016; 42:1490–1500 Q 2016 ASCRS and ESCRS

Ongoing advances mean that cataract surgery isnow a refractive operation and not simply an extrac-tion procedure. Changes in surgical technique haveresulted in a more predictable postoperative intraoc-ular lens (IOL) position,1 and partial coherence inter-ferometry (PCI) has increased the precision ofpreoperative measurements, leading to improvedpostoperative refractive results.2 New IOL power for-mulas have attempted to improve the accuracy oftheir refractive outcome predictions, predominantlyby increasing the number of variables they assess.The number of variables assessed ranges from 2 (Hol-laday 1,3 Hoffer Q,4,5 SRK/T,6 T27) up to 7 (Holladay2A). Theoretically, increasing the number of relevantvariables assessed should increase the accuracy inpredicting postoperative refraction, but many of

SCRS and ESCRS

by Elsevier Inc.

these newer formulas have not been adequatelyassessed.

Few studies have evaluated a substantial number ofeyes across the entire axial length (AL) range. Aristo-demou et al.8 tested the Hoffer Q, Holladay 1, andSRK/T formulas in 8108 eyes (the largest IOL powerformula study) and found that the Hoffer Q was themost accurate formula for ALs below 21.0 mm (in 1of the 2 IOLs studied), the Holladay 1 trended towardthe highest accuracy in eyes from 23.5 mm to 26.0 mm,and in long eyes (O26.0 mm) the SRK/T was the mostaccurate formula. Narv�aez et al.9 studied 643 eyes us-ing the Holladay 2, Hoffer Q, Holladay 1, and SRK/Tformulas and found no significant difference betweenany of them. In 2043 eyes, Olsen et al.10 found no dif-ference between the Haigis, Hoffer Q, Holladay 1,

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1491IOL POWER FORMULA ACCURACY

and SRK/T formulas, except in eyes with an ALgreater than 27.0 mm, for which the SRK/T was themost accurate formula. Despite its popularity withUnited States surgeons,B the Holladay 2 has not beenshown to be more accurate than a suitably selectedthird-generation formula.11 The T2 formula is a modi-fication of the SRK/T formula aimed at preventingnonphysiologic behavior of the SRK/T.12 The T2 andthe Barrett Universal II formulas have never been as-sessed in large studies across the AL range beyondtheir original publications.

The aim of this study was to determine which of thecurrently used formulas for IOL selection (Holladay1,3 Hoffer Q,4,5 SRK/T,6 T2,7 Haigis,13 Barrett Univer-sal II,14 and Holladay 2A) is the best predictor of theactual postoperative refractive outcome.

PATIENTS AND METHODS

A retrospective chart review comprised all cataract surgeriesperformed from February 2010 to November 2015 at a largetertiary center. Institutional ethics approval was obtainedbefore the initiation of the study.

Inclusion criteria were uneventful phacoemulsificationcataract surgery with in-the-bag insertion of an Acrysof IQSN60WF IOL (Alcon Laboratories, Inc.) and preoperativebiometry performed using the IOLMaster (version 5.4, CarlZeiss Meditec AG), a PCI-based biometer. The IOL im-planted is single piece hydrophobic acrylic with an asphericbiconvex optic. If patients had bilateral phacoemulsifica-tion cataract extraction with insertion of the study IOL, arandomly selected eye was chosen for inclusion in the study.

Exclusion criteria were incomplete PCI biometry, cornealastigmatismmore than 3.0 diopters (D), complicated cataractsurgery, additional procedures during cataract surgery,postoperative corrected distance visual acuity (CDVA)worse than 6/12, refraction performed before 14 days post-operatively, postoperative complications, and incompletedocumentation.

Preoperative biometry measurements were accesseddirectly from the database of the PCI-based biometer usedto assess all patients. The remaining variables were obtainedfrom the electronic medical record. Subjective refraction wasperformed after 14 days postoperatively on all included pa-tients by orthoptic staff or by optometrists in the community.Any eye without a formal refraction (even with a CDVA

Submitted: May 19, 2016.Final revision submitted: June 21, 2016.Accepted: July 4, 2016.

From the Department of Ophthalmology (Kane, Van Heerden, Atik),Alfred Health, Melbourne, and the Discipline of Clinical Ophthal-mology (Kane, Petsoglou), University of Sydney, Sydney, Australia.

Presented at the ASCRS Symposium on Cataract, IOL and Refrac-tive Surgery, New Orleans, Louisiana, USA, May 2016.

Corresponding author: Jack X. Kane, MB BS, Department ofOphthalmology, The Alfred Hospital, 55 Commercial Road, Mel-bourne, Victoria 3004, Australia. E-mail: [email protected].

J CATARACT REFRACT SURG -

better than 6/6) was excluded. No details of lens thicknesswere used in the study.

The Haigis, Hoffer Q, Holladay 1, and SRK/T formulaswere programmed into Excel spreadsheets (MicrosoftCorp.) according to their original publications and errata.The results obtainedwere validated against A-scan printoutsfrom the PCI biometer. Data were entered into the HolladayIOL Consultant softwareA to assess the Holladay 2 formula,the official T2 Excel spreadsheetC to assess the T2 formula,and the online calculatorD to assess the Barrett Universal IIformula. Separate computer programs were written by 1author (J.X.K.) to automatically enter patient data and/orextract the appropriate results from the respective calcula-tors for theHolladay 2, Barrett Universal II, and T2 formulas.

The constants for the Hoffer Q, Holladay 1, and SRK/Tformulas were optimized as follows: For each patient, theIOL constant for each formula was varied in 0.001 steps un-til the difference between the predicted spherical equivalent(SE) and the actual SE for that patient was zero. For eachformula, the optimized IOL constant was then calculatedas the mean of all the individual patients' IOL constants(excluding outliers further than 2 standard deviations[SDs] from the sample mean). The Haigis formula under-went triple optimization by calculating the anterior cham-ber depth (ACD) constant for the Haigis (dHaigis)formula that would have resulted in the actual postopera-tive refractive result. As with the other formulas, outliersfurther than 2 SDs from the sample mean were excluded.A double linear regression analysis was then performedto find the constants a0, a1, and a2 such that the equationdHaigis Z a0 C a1 � ACD C a2 � AL was best satisfied.

The optimized SRK/T constant was used to calculate theT2 formula result as recommended by the authors.7 The con-stant for the Holladay 2 formula was optimized in the IOLConsultant program.A The recommended lens constant forthe Barrett Universal II formula was used because at present,no method exists to optimize the lens constant using the on-line calculator.

The predicted postoperative SE refraction for each patientwas calculated using the optimized IOL constants. The pre-diction error was then calculated as the actual postoperativerefraction minus the refractive result predicted by each for-mula using the optimized lens constants.

Themean numerical prediction error (ME), mean absoluteprediction error (MAE), and median absolute predictionerror (MedAE) were calculated for each formula. The per-centages of eyes that had a prediction error of G0.25 D,G0.50 D, G1.00 D, and G2.00 D were calculated for eachformula. Subgroup analysis was performed based on thefollowing AL groups: short (%22.0 mm), medium (O22.0to !24.5 mm), medium-long (R24.5 to !26.0 mm), andlong (R26.0 mm)

A statistician was consulted about the appropriatemethods for analysis. The differences in absolute error be-tween formulas were assessed using the Friedman test. Inthe event of a significant result, post hoc analysis was per-formed using the Conover test.E After Bonferroni correctionfor multiple comparisons, a P value less than 0.0071 wasconsidered statistically significant. Statistical analysis wasperformed using R software (R Project, R Foundation).

RESULTS

Of the 6041 patients who had cataract surgery withIOL insertion, 3241 were eligible for inclusion in this

VOL 42, OCTOBER 2016

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Table 1. Study population characteristics.

Parameter Value

Sex (%)Female 54.4Male 45.6

Eye used (%)Right 51.4Left 48.6

Mean AL (mm) G SD 23.50 G 1.06Mean K (D) G SD 43.71 G 1.51Mean IOL power (D) G SD 21.48 G 2.91

AL Z axial length; IOL Z intraocular lens; K Z keratometry

Table 2. Number of eyes and reasons for exclusion from thestudy.*

Parameter Eyes (n)

Total surgeries in study period(before exclusions)

8488

Eyes with study IOL implanted (before exclusions) 6041Preop exclusion: inadequate biometry,corneal astigmatism, bilateral cataract surgery

1640

Intraop exclusion: complications, suturedwound, combined procedures,inadequate details

385

Postop exclusion: CDVA !6/12, no postop VA,no refraction O14 days, postop complication

2312

Included eyes 3241

CDVA Z corrected distance visual acuity; IOL Z intraocular lens;VA Z visual acuity*Each eye might have more than 1 reason for exclusion.

1492 IOL POWER FORMULA ACCURACY

study. Table 1 and Table 2 show the characteristics ofthe study population and the reasons for exclusion.

Constants Used

Optimizations of lens constants resulted in a Holla-day 1 surgeon factor of 1.686, an SRK/T A-constant of118.824, a Hoffer Q personalized ACD of 5.462, and aHolladay 2 constant of 5.630. The Haigis a0, a1, and a2constants were 0.996, 0.279, and 0.129, respectively,and the recommended constant of 118.99 was usedfor the Barrett Universal II formula.

Results Over the Entire Axial Length Range

There was a statistically significant difference inabsolute error between the 7 IOL power formulasover the entire AL range (c2[6] Z 62.76, P ! .001).Table 3 shows theMAE,MedAE, andME for the entirepatient sample. Figure 1 shows the MAEs for each for-mula plotted according to AL group.

The Barrett Universal II formula had a significantlylower absolute error than all other IOL power for-mulas (P ! .001 in all cases). The T2 formula had alower absolute error than the SRK/T,Haigis, Holladay2, and Hoffer Q formulas (all P! .001). The Holladay

Table 3. Prediction errors over the entire AL range for each formula.

Formula Haigis Hoffer Q Holladay I

MAE 0.420 0.427 0.408MedAE 0.337 0.347 0.326ME 0.01 �0.01 0.00Eyes within PE (%)

G0.25 D 38.8 37.9 39.4G0.50 D 68.3 67.2 69.4G1.00 D 92.9 92.7 93.7G2.00 D 99.6 99.6 99.6

MAE Z mean absolute prediction error; MedAE Z median absolute prediction er


2 formula had a higher absolute error than the Holla-day 1 formula, which was statistically significantover the entire AL range (P ! .001).

For the third-generation formulas, the Holladay 1had a lower absolute error than the Hoffer Q(P! .001) and SRK/T (P! .001). The SRK/T formulawas more accurate than the Hoffer Q formula(P ! .001). Figure 2 shows the overall percentage ofeyes with prediction errors between G0.25 D, G0.50 D,G1.00 D, and G2.00 D. The Barrett Universal II for-mula showed considerably higher percentages ofeyes within these prediction error targets than theother formulas.

Short Eyes

There was no statistically significant difference inthe absolute error between the 7 IOL power formulasin eyes with a short AL (c2[6] Z 8.40, P Z .210).Table 4 shows the MAE and MedAE for eyes withan AL less than 22.0 mm. No post hoc analysis was

SRK/T Barrett Universal II T2 Holladay 2

0.413 0.385 0.407 0.4200.335 0.305 0.330 0.341

�0.01 �0.19 �0.03 0.00

38.3 43.5 39.9 37.969.6 72.3 70.0 67.493.8 94.5 93.9 93.799.7 99.9 99.7 99.7

ror; ME Z mean prediction error; PE Z prediction error


Figure 1.Mean absolute error plotted against AL groups for the Barrett Universal II, Hoffer Q, Holladay 1, Holladay 2, Haigis, SRK/T, and T2formulas. The formulas are grouped to allow easier visualization.


performed because of the lack of a statistically signif-icant result.

Figure 3 shows the percentage of eyes within predic-tion errors ofG0.25D,G0.50D,G1.00D, andG2.00Din this subgroup. The Haigis formula showed thehighest percentage of eyes within G0.25 D, the Holla-day 1 formula showed the highest percentage withinG0.50 D (followed closely by the Haigis), and theT2 formula showed the highest percentage withinG1.00 D.

Medium Eyes

In eyes with a medium AL, there was a statisticallysignificant difference in absolute error between the7 IOL power formulas (c2[6] Z 46.92, P ! .001).Table 5 shows the MAE and MedAE in the mediumAL subgroup. The Barrett Universal II formula hada lower absolute error than the other 6 formulas inthe medium AL group (P ! .001 compared with

Figure 2. The percentage of eyes over the entire AL range with aprediction error between G0.25 D, G0.50 D, and G1.00 D for eachof the 7 formulas.


each formula). There was no significant difference be-tween the T2 formula and the SRK/T formula in themedium AL range. The Holladay 1 formula per-formed better than the Holladay 2 formula(P! .001). The Holladay 1 formula had a lower abso-lute error than the Haigis formula (P ! .001) and theHoffer Q formula (P ! .001); however, the differencewas not statistically significant compared with theSRK/T formula (P Z .875). The SRK/T formula wassignificantly more accurate than the Haigis andHoffer Q formulas (both P ! .001). Figure 3 showsthe percentage of eyes within the prediction errorsof G0.25 D, G0.50 D, G1.00 D, and G2.00 D in thissubgroup. The highest percentage of eyes withineach of these predictions errors was seen using theBarrett Universal II formula.

Medium-Long Eyes

There was a statistically significant difference inabsolute error between the 7 IOL power formulasin medium-long AL eyes (c2[6] Z 24.22, P ! .001).Table 6 shows the MAE and MedAE for themedium-long AL subgroup. The Barrett Universal IIformula had the lowest MAE, and this differencewas statistically significant compared with the Haigis,Holladay 1, SRK/T, and Holladay 2 formulas (allP ! .001) but not compared with the Holladay 1 orT2 formulas (P Z .082 and P Z .172, respectively).No difference existed between the T2 and theHolladay1 formulas; however, a statistically significant differ-ence existed between the T2 and all remainingformulas including the SRK/T (all P! .001). The Hol-laday 1 formula had a lower absolute error than the


Table 4. Prediction errors in the short axial length group for each formula.

Formula Haigis Hoffer Q Holladay I SRK/T Barrett Universal II T2 Holladay 2

MAE 0.473 0.499 0.453 0.458 0.469 0.459 0.466MedAE 0.334 0.441 0.377 0.397 0.395 0.415 0.383ME �0.09 �0.22 �0.07 �0.04 �0.26 �0.10 �0.07Eyes within PE (%)

G0.25 D 36.5 28.2 29.5 32.7 30.8 33.3 31.4G0.50 D 62.8 55.8 63.5 59.6 62.2 60.3 61.5G1.00 D 91.0 91.0 92.3 92.3 92.3 92.9 91.7G2.00 D 100.0 100.0 99.4 99.4 100.0 99.4 100.0

MAE Z mean absolute prediction error; MedAE Z median absolute prediction error; ME Z mean prediction error; PE Z prediction error


Holladay 2 formula in medium-long eyes (P ! .001)and was also better than the Hoffer Q (P! .001), Hai-gis (P! .001), and SRK/T (P! .001) formulas. Usingthe SRK/T formula, there was no statistically signifi-cant reduction in absolute error compared with theHaigis (P Z .720) or the Holladay 2 (P Z .013).Figure 3 shows the percentage of eyes within the pre-diction errors of G0.25 D, G0.50 D, G1.00 D, andG2.00 D in this subgroup. The Barrett Universal IIhad the highest percentage of eyes within each of theprediction error values.

Long Eyes

The absolute error between the 7 IOL powerformulas in long AL eyes showed a statistically

Figure 3. The percentage of eyes with a prediction error withinG0.25 D,GAL subgroups for each of the 7 formulas.


significant difference (c2[6] Z 18.52, P Z .005).Table 7 shows the MAE and MedAE in this subgroup.The Barrett Universal II had the lowest MAE of all for-mulas assessed, and the differencewas statistically sig-nificant comparedwith the Haigis, Hoffer Q, Holladay1, Holladay 2, and SRK/T formulas (all P ! .001).The SRK/T formula had lower absolute errors thanthe T2 formula (P ! .001) and all other formulas (allP ! .001), except the Barrett Universal II. The Holla-day 2 formula had a lower MAE than the Holladay 1formula; however, the difference between the for-mulas was not statistically significant (P Z .025).

Figure 3 shows the percentage of eyes within theprediction errors of G0.25 D, G0.50 D, G1.00 D,and G2.00 D in this subgroup. The SRK/T formula

0.50 D, andG1.00 D for the short, medium, medium-long, and long


Table 5. Prediction errors in the medium axial length group for each formula.


MAE 0.415 0.420 0.404 0.408 0.386 0.405 0.416MedAE 0.335 0.339 0.323 0.329 0.300 0.330 0.337ME �0.01 �0.02 �0.01 �0.02 �0.20 �0.03 �0.02Eyes within PE (%)

G0.25 D 39.0 39.0 40.1 38.6 42.7 39.0 37.9G0.50 D 69.0 68.1 69.8 70.8 71.3 69.5 68.1G1.00 D 93.0 92.9 93.8 93.9 94.2 93.5 94.0G2.00 D 99.6 99.6 99.7 99.8 99.9 99.7 99.7



had the highest percentage of eyes within a predic-tion error of G0.25 D, the T2 formula within a pre-diction error of G0.50 D, and the Barrett UniversalII and SRK/T formulas within a prediction error ofG1.00 D.

DISCUSSION

Our study of 3241 eyes of 3241 patients is, to ourknowledge, the second largest series of eyes reportedon 1 IOL type. Our study reports on 5 of the commonlyused formulas (Haigis, Hoffer Q,Holladay 1, Holladay2, and SRK/T) and 2 formulas (Barrett Universal II andT2) that have never been retested in a large seriesacross the entire AL range despite the promising re-sults in their initial publications.7,14 Overall, the per-centages of eyes with prediction errors betweenG0.25 D, G0.50 D, and G1.00 D for each formulawere similar to those in the study by Aristodemouet al.15 and easily above the benchmark standard sug-gested for the National Health Service.16

Over the entire AL range, the Barrett Universal IIwas themost accurate formula by a significant margin,having a lower MAE and a higher percentage of eyeswith prediction errors between G0.25 D, G0.50 D,and G1.00 D than the other 6 formulas assessed. No

Table 6. Prediction errors in the medium-long axial length group for ea

Formula Haigis Hoffer Q Holladay I

MAE 0.409 0.415 0.385MedAE 0.347 0.357 0.316ME 0.13 0.14 0.05Eyes within PE (%)

G0.25 D 38.4 34.9 40.6G0.50 D 68.5 68.8 71.2G1.00 D 93.8 94.1 95.4G2.00 D 99.5 99.5 99.7

MAE Z mean absolute prediction error; MedAE Z median absolute prediction er


previous large study has assessed the Barrett Univer-sal II formula over the entire AL range, thus preven-ting a comparison of our results. The largest IOLpower study over the entire AL range15 found the Hol-laday 1 formula was slightly more accurate than theother third-generation formulas (SRK/T and HofferQ), and this result was replicated in our study.

The discussion is broken down into various ALgroups followed by comparisons between selectedformulas.

The Hoffer Q is the most popular formula for use ineyes with an AL of 22.0 mm or lessB and has been re-ported as the most accurate formula for short eyes instudies by Hoffer17 (although the study included only10 eyes with a short AL), Gavin and Hammond18

(although it was tested only against the SRK/T),and Aristodemou et al.8 (although only in eyes withan AL !21.0 mm). The study by Aristodemouet al.8 found the Hoffer Q formula had a lower MAEin 1 of the 2 IOL groups studied (PZ .0003); however,in the other IOL group, the Hoffer Q formula had ahigher MAE than the Holladay 1 formula in the ALrange of less than 21.0 mm (P Z .04). In eyes withan AL of 21.0 to 21.99 mm, the Hoffer Q formulawas never more accurate than the other 2 formulasin either IOL group. Other studies have reported the

ch formula.

SRK/T Barrett Universal II T2 Holladay 2

0.414 0.338 0.385 0.4050.341 0.270 0.305 0.3340.12 �0.13 0.03 0.12

38.7 46.2 39.5 41.466.7 76.6 71.2 67.294.4 97.8 94.9 93.599.7 100.0 99.7 99.7

ror; ME Z mean prediction error; PE Z prediction error


Table 7. Prediction errors in the long axial length group for each formula.


MAE 0.526 0.589 0.586 0.484 0.435 0.498 0.544MedAE 0.392 0.467 0.441 0.419 0.370 0.440 0.404ME 0.21 0.34 0.38 0.06 �0.20 �0.05 0.22Eyes within PE (%)

G0.25 D 36.0 33.3 29.3 38.7 34.7 30.7 32.0G0.50 D 57.3 53.3 57.3 62.7 62.7 64.0 57.3G1.00 D 88.0 82.7 86.7 92.0 92.0 86.7 88.0G2.00 D 98.7 98.7 97.3 97.3 100.0 100.0 97.3



Haigis to be the most accurate formula in shorteyes,19,20 although the superiority of the Haigis for-mula over the Hoffer Q formula might occur onlywhen the ACD is less than 2.40 mm.21 In contrast, Ol-sen and Hoffmann10 noted a tendency for the SRK/Tand Holladay 1 formulas to have lower MAEs thanthe Hoffer Q and Haigis formulas.

In our study, 156 eyes had an AL of 22.0 mm or less,with the Holladay 1 formula having the lowest MAEfollowed by the SRK/T, T2, Holladay 2, and BarrettUniversal II formulas. Surprisingly, the Haigis andHoffer Q formulas had the 2 highest MAEs and theHoffer Q formula had the lowest percentage of eyeswithin the prediction errors of G0.25 D, G0.50 D,and G1.00 D. Regardless, the difference between for-mulas was not statistically significant, making itimpossible to make any inferences about IOL powerformula accuracy for eyes with short ALs based onthis study.

The inaccuracy of the commonly used IOL powerformulas to predict postoperative refractive error inshort eyes is well established8,17 and was also seen inour study. Nevertheless, all formulas performedwithin the guidelines recommended by Gale et al.16

Most eyes (2638) in our study had a medium AL(between 22.0 mm and 24.5 mm). The Barrett UniversalII was the most accurate formula in this AL range, withthe lowest MAE (statistically significant over all otherformulas) and highest percentage of eyes with G0.25 D,G0.50 D, G1.00 D, and G2.00 D prediction errors.Our results are consistent with those reported in Bar-rett's initial publication for medium length eyes.14

The only other study of the Barrett Universal II for-mula in this AL range did not find any formula to bemore accurate than the others used in 48 patients.22

In our study, the Holladay 1 was the next bestperforming formula behind the Barrett Universal IIformula. It did not show a statistically significant dif-ference over the T2 or SRK/T formulas; however, itwas significantly better than the Holladay 2, theHaigis, and the Hoffer Q formulas (all P ! .001).


Our results for the third-generation formulas (Holla-day 1, SRK/T, and Hoffer Q) agree with the findingsin the large study by Aristodemou et al.8 that theHolladay 1 formula resulted in the lowest MAE ineyes with a medium AL. Hoffer17 also found thatthe Holladay 1 formula had the lowest MAE for me-dium-length eyes compared with the Hoffer Q,SRK/T, and Holladay 2 formulas.

The most accurate IOL power formula in medium-long eyes was previously not clearly defined. Hoffer17

found the SRK/T formula to be the most accurate (fol-lowed by Holladay 1). Aristodemou et al.8 showed theHolladay 1 formula to be more accurate than both theSRK/T and Hoffer Q formulas. Narv�aez et al.9 foundno difference between formulas. Wang and Chang23

found that the Haigis formula was the most accurate.Our study contained 372 eyes with a medium-long

AL and found that eyes in this AL group had lowerMAEs than eyes in the short, medium, or long ALgroups. The Barrett Universal II formula had thelowest MAE followed by the T2 and Holladay 1 for-mulas. The difference between the Barrett UniversalII and other formulas was statistically significant(P ! .001) except compared with the T2 formula(PZ .172) andHolladay 1 formula (PZ .082). The Bar-rett Universal II formula also resulted in a significantlyhigher percentage of eyes with prediction errors be-tween G0.25 D, G0.50 D, G1.00 D, and G2.00 Dcompared with the other formulas. Our findingsmirror those in the original publication by Barrett.14

No other study has since been performed using theBarrett Universal II formula and looking specificallyat this AL for comparison. Our finding that the Holla-day 1 formula had a lower MAE than the SRK/T andHoffer Q formulas (both P ! .001) is congruous withthe findings by Aristodemou et al.8 in medium-longAL eyes.

In our study, 77 eyes had an AL of 26.00 mm orabove and we found that the most accurate formulawas the Barrett Universal II followed by the SRK/T,T2, Haigis, Holladay 2, Holladay 1, and Hoffer Q.



A similar conclusion was reported by the only recentstudy to report on the Barrett Universal II formula ineyes with a long AL.24

Our results agree with studies by Aristodemouet al.,8 Olsen and Hoffmann,10 and Hoffer17 thatshowed the SRK/T was the most accurate formulacompared with the Hoffer Q, Holladay 1, Holladay2, and Haigis formulas. In our study, the SRK/T for-mula performed significantly better than the Haigisformula. Previous studies25,26 that reported the Haigisformula to be more accurate failed to optimize lensconstants, which possibly explains the differentconclusions.

The difficulty in predicting the refractive outcome ineyes with a long AL was reconfirmed in our study.With long eyes, each formula had a much higherMAE and lower percentages of eyes within the predic-tion errors compared with results in eyes with a me-dium or medium-long AL.

The T2 formula, except for its original publication,has not been studied using standard methods ofcomparing IOL power formulas. Over the entire ALrange, we noted the T2 to be more accurate, albeit bya smaller difference than reported in the original paper(0.0165 D compared with 0.0054 D).7 We found no sig-nificant difference between the 2 formulas in the shortor the medium AL group. In the medium-long ALgroup, the T2 formula was significantly more accuratethan the SRK/T (MAE 0.385 versus 0.338; P ! .001),with a corresponding increase in the percentage ofeyes within prediction errors in the G0.25 D, G0.50D, and G1.00 D ranges. Interestingly, the T2 formulaperformed less accurately than the SRK/T formula ineyes with a long AL (MAE 0.498 versus 0.484;P ! .001). The original paper did not comment onthe accuracy of the SRK/T and T2 formulas in eachAL range.

The Holladay 1 and Holladay 2 formulas have beencompared in several studies with variable results.Hoffer's study17 of 317 eyes found that the Holladay2 formula had a higher MAE than the Holladay 1 for-mula across the full AL range and in the medium andmedium-long AL subgroups. In that study, the Holla-day 2 formula had a lower MAE in long eyes andshort eyes. No statistical analysis was performed onthese results. In 643 eyes, Narv�aez et al.9 failed toshow a statistically significant difference betweenthe Holladay 1 and Holladay 2 formulas in any ALgroup. Our study showed that the Holladay 2formuladwithout the use of the lens thicknessvariabledwas less accurate than the Holladay 1 acrossthe entire AL range (MAE 0.408 versus 0.420;P ! .001). The difference in the medium (0.404 versus0.416; P! .001) and medium-long (0.385 versus 0.405;P ! .001) AL groups also favored the Holladay 1


formula and was statistically significant. These find-ings are in agreement with the conclusions of Hoffer.17

The improved accuracy of the Holladay 2 formula inlong AL eyes (MAE 0.544 versus 0.586) was not statis-tically significant in our study.Nevertheless, this resultalso occurred in studies by Abulafia et al.24 and Banget al.,25 indicating that the additional variables in theHolladay 2 formula might reduce the error in eyeswith longer AL compared with the Holladay 1formula.

A recent editorial by Hoffer et al.27 proposed a pro-tocol for IOL power formula studies to prevent thevariations and errors commonly seen. Our approachusing only 1 eye from each patient, optical biometry,1 IOL model, eyes with postoperative CDVA betterthan 6/12, and optimized lens constants in third-generation and onward formulas complied with theirprotocol.

Our approach differs in 2 ways. First, we usedrefraction from 14 days onward (rather than waiting1 month) because this is when multiple studies haveshown the refraction stabilizes,28 in particular whenusing single-piece IOLs.29,30 Second, we performednonparametric statistics with post hoc testing and re-ported on MAEs, as suggested by Aristodemouet al.31 in response to the editorial rather than “simply[comparing] median absolute prediction errors27” be-tween formulas.

The reasoning for not comparing MAEs is that ab-solute errors do not follow a normal Gaussian distri-bution and in non-Gaussian functions, the medianmight be a better representation of the central loca-tion of the data. One of the worst outcomes thatcan occur after cataract surgery and a commonreason for litigation32 is significant deviation fromthe expected refractive outcome. The MedAE is lessaffected by outliers than the MAE. Hence, by usingthe MedAE as a marker of formula accuracy ratherthan the MAE we might inadvertently recommendformulas that could lead to this undesirableoutcome. (See worked example 1 in Figure 4.)Furthermore, the vast majority of IOL power studiesreport MAEs, and our current understanding aboutthe most accurate formulas is heavily based on theMAE. If the MAE is now an inappropriate measureto report, we must reassess our current understand-ing of IOL power formulas; if this is necessary, itshould be based on a considered discussion ratherthan an unreferenced point in an editorial.27

The absence of lens thickness measurements is themain deficiency in our study and precluded usfrom making conclusions on the accuracy of theHolladay 2 or Barrett Universal II formulas usingall available variables and from evaluating theOlsen formula. The lens thickness variable might


Figure 4. Worked example 1 (MAE Z mean absolute predictionerror; MedAE Z median absolute prediction error).


not significantly alter the MAE of the Holladay2 formula33; nonetheless, assessing these newer gen-eration formulas using all possible variables wouldbe preferable. This will become more feasible withthe introduction of biometers capable of measuringlens thickness.

Another potential limitation of the study is the in-clusion of data from patients operated on bydifferent surgeons and refracted by different optom-etrists (at our center and others in the community).This might have introduced bias resulting from dif-ferences in operating style and refracting technique.The variation between surgeons in modern cataractsurgery does not significantly affect refractive re-sults,15 and the variation in refraction between op-tometrists in a single center might be minimal34 butcould vary between centers.35 Still, only includingpatients operated on by a single surgeon and re-fracted by a single person would severely reducethe sample size and limit the ability of a study todetect small, but important differences betweenIOL power formulas.

Our study is significant for several reasons. First, toour knowledge, it is the only study to assess 7 of themost commonly used IOL power formulas across theentire AL range using a large enough patient cohortto detect differences between the formulas.

Second, the inclusion of the Barrett Universal IIformula and its accurate results are significant.


Only 2 papers (aside from the original publication)have studied the Barrett Universal II formula, 1that focused on long AL eyes24 and 1 that concen-trated on multifocal IOLs over the entire AL range,albeit with a cohort of only 48 patients.22 Over theentire patient sample in our study, the Barrett Uni-versal II formula had a significantly lower MAEand resulted in the highest percentage of eyes withinprediction errors ofG0.25 D,G0.50 D,G1.00 D, andG2.00 D compared with the other IOL power for-mulas. The lower MAE of the Barrett Universal II for-mula was also seen in the medium, medium-long,and long AL subgroups. This superiority occurredagainst IOL power formulas using fully optimizedlens constants.

The third significant finding is the nonsuperiority oftheHolladay 2 formula comparedwith other older for-mulas. Despite being promulgated since 1996 and en-joying widespread use (especially in the U.S.),B theHolladay 2 formula failed to establish itself as themost accurate formula in any of the AL groups stud-ied. It was significantly less accurate than the BarrettUniversal II and Holladay 1 formulas over the entireAL range. Our findings should prompt users of theHolladay 2 who currently do not measure lens thick-ness to measure this variable or change the formulathey use. We emphasize that we make no commenton the accuracy of the Holladay 2 formula when lensthickness is used.

Fourth, the inclusion of the T2 formula, which hasnever been included in conventional studies of IOLpower formula accuracy (excluding the original pub-lication), is noteworthy. Our study confirmed that thechanges implemented in the T2 formula were effec-tive in increasing the accuracy of the SRK/T formulaoverall, although in long AL eyes, the T2 formula wasless accurate than the SRK/T formula. The T2 failedto distinguish itself as the most accurate formula inany of the AL subgroups and is not currently inte-grated into the common biometers or computer soft-ware packages for IOL power calculation. Bothissues are significant barriers to the adoption of theT2 formula despite its improved accuracy over theSRK/T formula.

In conclusion, our study of 3241 patients providesstrong evidence that the Barrett Universal II formulais able to more accurately predict the postoperativerefraction for eyes with a medium, medium-long, orlong AL compared with the 6 other IOL powerformulas. Although none of the formulas performedpoorly, themarked difference between the Barrett Uni-versal II formula and the other IOL power formulas foreyes with an AL longer than 22.0 mm should promptserious consideration of its use in these eyes by cata-ract surgeons worldwide.



WHAT WAS KNOWN

� Using optimized lens constants, all currently used IOL po-wer formulas result in reasonably accurate predictions ofpostoperative refraction, although it is unclear whethernewer generation formulas are more accurate than theirpredecessors.

WHAT THIS PAPER ADDS

� It is the first evaluation of the Barrett Universal II, T2, andHolladay 2 formulas in a study large enough to detect thedifferences between formulas.

� The Barrett Universal II formula was a more accurate pre-dictor of actual postoperative refraction than the other 6formulas, even with lens constant optimization.

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VOL
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First author:Jack X. Kane, MB BS

Department of Ophthalmology, AlfredHealth, Melbourne, Australia

































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Documents

Intraocular lens power formula accuracy: Comparison of 7