A Comparison of the Accuracy of 6 Modern Toric Intraocular Lens Formulas


      To compare the accuracy of the Abulafia-Koch, the Barrett, the EVO 2.0, the new Holladay 2 with total surgical-induced astigmatism, the Kane, and the Næser-Savini toric intraocular lens (IOL) power formulas using a large database of toric IOL refractive outcomes.


      Retrospective consecutive case series.


      Eight hundred twenty-three eyes of 823 patients who had a toric IOL inserted during surgery.


      One eligible eye from patients having uncomplicated cataract surgery with insertion of an Alcon SN6AT(2-9) IOL (Alcon Laboratories, Inc, Fort Worth, TX) from 1 surgeon were included in the study. Both preoperative and postoperative biometry were measured using either the IOLMaster 500 or 700 (Carl Zeiss Meditec AG, Jena, Germany). Using vector calculation, the predicted postoperative refractive astigmatism was calculated for each formula. This was compared with the actual postoperative refractive astigmatism to give the prediction error.

      Main Outcome Measures

      Mean absolute prediction error, standard deviation of the prediction error, and percentage of eyes with a prediction error within ±0.50 diopter (D).


      The Kane formula showed the highest proportion of eyes with a prediction error within ±0.50 D with 65.6%, followed by the Barrett formula (59.9%), Abulafia-Koch formula (59.5%), EVO 2.0 formula (58.9%), Næser-Savini formula (56.7%), and Holladay 2 formula (53.9%). The Kane formula showed a statistically significantly lower mean absolute prediction error (P < 0.001) and a significantly lower variance of the prediction error (P < 0.01) compared with all other formulas. No statistically significant difference existed among the mean absolute prediction errors for the Abulafia-Koch, Barrett, and EVO 2.0 toric formulas.


      Use of the Kane toric formula significantly improved the prediction of postoperative astigmatic outcome compared with the other formulas studied.

      Abbreviations and Acronyms:

      ATR (against-the-rule), D (diopter), ELP (effective lens position), IOL (intraocular lens), SIA (surgical-induced astigmatism), WTR (with-the-rule)
      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic and Personal
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


      Subscribe to Ophthalmology
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • Wolffsohn J.S.
        • Bhogal G.
        • Shah S.
        Effect of uncorrected astigmatism on vision.
        J Cataract Refract Surg. 2011; 37: 454-460
        • Holland E.
        • Lane S.
        • Horn J.D.
        • et al.
        The AcrySof toric intraocular lens in subjects with cataracts and corneal astigmatism: a randomized, subject-masked, parallel-group, 1-year study.
        Ophthalmology. 2010; 117: 2104-2111
        • Sun X.Y.
        • Vicary D.
        • Montgomery P.
        • Griffiths M.
        Toric intraocular lenses for correcting astigmatism in 130 eyes.
        Ophthalmology. 2000; 107 (discussion 1781–1782): 1776-1781
        • Visser N.
        • Berendschot T.T.J.M.
        • Verbakel F.
        • et al.
        Comparability and repeatability of corneal astigmatism measurements using different measurement technologies.
        J Cataract Refract Surg. 2012; 38: 1764-1770
        • Koch D.D.
        The posterior cornea: hiding in plain sight.
        Ophthalmology. 2015; 122: 1070-1071
        • Simsek S.
        • Yasar T.
        • Demirok A.
        • et al.
        Effect of superior and temporal clear corneal incisions on astigmatism after sutureless phacoemulsification.
        J Cataract Refract Surg. 1998; 24: 515-518
        • Jin H.
        • Limberger I.J.
        • Ehmer A.
        • et al.
        Impact of axis misalignment of toric intraocular lenses on refractive outcomes after cataract surgery.
        J Cataract Refract Surg. 2010; 36: 2061-2072
        • International Organization for Standardization
        ISO 11979-1:2018(en), ophthalmic implants—intraocular lenses.
        (Accessed 15.11.19)
        • Barrett G.
        Barrett toric formula.
        (Accessed 14.09.19)
        • Abulafia A.
        • Koch D.D.
        • Wang L.
        • et al.
        New regression formula for toric intraocular lens calculations.
        J Cataract Refract Surg. 2016; 42: 663-671
        • Savini G.
        • Næser K.
        • Schiano-Lomoriello D.
        • Ducoli P.
        Optimized keratometry and total corneal astigmatism for toric intraocular lens calculation.
        J Cataract Refract Surg. 2017; 43: 1140-1148
        • Yeo T.K.
        EVO 2.0 toric formula.
        (Accessed 18.09.19)
        • Holladay J.T.
        • Pettit G.
        Improving toric intraocular lens calculations using total surgically induced astigmatism for a 2.5 mm temporal incision.
        J Cataract Refract Surg. 2019; 45: 272-283
        • Connell B.J.
        • Kane J.X.
        Comparison of the Kane formula with existing formulas for intraocular lens power selection.
        BMJ Open Ophthalmol. 2019; 4: e000251
        • Melles R.B.
        • Kane J.X.
        • Olsen T.
        • Chang W.J.
        Update on intraocular lens calculation formulas.
        Ophthalmology. 2019; 126: 1334-1335
        • Abulafia A.
        • Koch D.D.
        • Holladay J.T.
        • et al.
        Pursuing perfection in intraocular lens calculations: IV. Rethinking astigmatism analysis for intraocular lens-based surgery: suggested terminology, analysis, and standards for outcome reports.
        J Cataract Refract Surg. 2018; 44: 1169-1174
        • Holladay J.T.
        Holladay IOL Consultant Software & Surgical Outcomes Assessment. 1105.
        Holladay Consulting, 2019, Bellaire, TX2019
        • Kane J.X.
        Kane formula.
        (Accessed 12.07.19)
        • Holladay J.T.
        • Moran J.R.
        • Kezirian G.M.
        Analysis of aggregate surgically induced refractive change, prediction error, and intraocular astigmatism.
        J Cataract Refract Surg. 2001; 27: 61-79
        • Naeser K.
        Assessment and statistics of surgically induced astigmatism.
        Acta Ophthalmol. 2008; 86: 1-28
        • Næser K.
        Astigmatism terminology for corneal and intraocular lens–based surgery.
        J Cataract Refract Surg. 2019; 45: 254-255
        • Anderson M.J.
        Distance-based tests for homogeneity of multivariate dispersions.
        Biometrics. 2006; 62: 245-253
        • Canovas C.
        • Alarcon A.
        • Rosén R.
        • et al.
        New algorithm for toric intraocular lens power calculation considering the posterior corneal astigmatism.
        J Cataract Refract Surg. 2018; 44: 168-174
        • Naeser K.
        • Hjortdal J.
        Multivariate analysis of refractive data: mathematics and statistics of spherocylinders.
        J Cataract Refract Surg. 2001; 27: 129-142
        • Holladay J.T.
        • Koch D.D.
        • Abulafia A.
        • et al.
        J Cataract Refract Surg. 2019; 45: 255-256
        • Aristodemou P.
        • Knox Cartwright N.E.
        • Sparrow J.M.
        • Johnston R.L.
        Statistical analysis for studies of intraocular lens formula accuracy.
        Am J Ophthalmol. 2015; 160: 1085-1086
        • Akman A.
        • Asena L.
        • Güngör S.G.
        Evaluation and comparison of the new swept source OCT-based IOLMaster 700 with the IOLMaster 500.
        Br J Ophthalmol. 2016; 100: 1201-1205
        • Hoffer K.J.
        • Aramberri J.
        • Haigis W.
        • et al.
        Protocols for studies of intraocular lens formula accuracy.
        Am J Ophthalmol. 2015; 160: 403-405.e1
        • Wang L.
        • Koch D.D.
        • Hill W.
        • Abulafia A.
        Pursuing perfection in intraocular lens calculations: III. Criteria for analyzing outcomes.
        J Cataract Refract Surg. 2017; 43: 999-1002
        • Cade B.S.
        • Richards J.D.
        Permutation tests for least absolute deviation regression.
        Biometrics. 1996; 52: 886

      Linked Article