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Accuracy of intraocular lens power calculation formulas after laserrefractive surgery in myopic eyes: A meta-analysisHongyu Li 

Tianjin Eye Hospital https://orcid.org/0000-0002-3362-1773Jun Li 

Tianjin Eye HospitalHui Song  ( songhui221@sina.com )

https://orcid.org/0000-0001-6804-3232

Research article

Keywords: IOL power calculation, refractive surgery, meta-analysis

Posted Date: October 1st, 2019

DOI: https://doi.org/10.21203/rs.2.15435/v1

License: This work is licensed under a Creative Commons Attribution 4.0 International License.   Read Full License

Version of Record: A version of this preprint was published on May 1st, 2020. See the published version athttps://doi.org/10.1186/s40662-020-00188-1.

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AbstractBackground: To compare the accuracy of intraocular lens power calculation formulas after refractive surgery in myopic eyes. 

Methods: We searched the databases on the PubMed, EMBASE, Web of science and Cochrane library to select relevant studiespublished between Jan 1, 2009 and Aug 11, 2019. Primary outcomes were the percentages of refractive prediction error within ±0.5Dand ±1.0D. 

Results: The results of this meta-analysis were investigated from 16 studies, including 7 common methods (Haigis-L, Shammas-PL,Double-K SRK/T, Barrett true K no history, Wang-Koch-Maloney, ASCRS average and OCT formula). ASCRS average yielded signi�cantlyhigher percentage of refractive prediction error within ±0.5D than Haigis-L, Shammas-PL and W-K-M (P=0.009, 0.01, 0.008, respectively).Barrett true K no history also yielded signi�cantly higher percentage of refractive prediction error within ±0.5D than Shammas-PL and W-K-M (P=0.01, <0.0001, respectively), and the same result was found by comparing OCT formula with Hiaigi-L and Shammas-PL (P=0.03,0.01, respectively). Only the Haigis-L had signi�cantly higher percentages than W-K-M method in the ±1.0D group (P = 0.04). 

Conclusion: We suggest that the ASCRS average and Barrett true K no history formula should be used to calculate the IOL power in eyesafter myopic refractive surgery.

BackgroundPatients who have had corneal excimer laser surgery are now facing cataract surgery with aging. It is a challenge for allophthalmologists to calculate the intraocular lens (IOL) power in eyes after refractive surgery. As we all know, corneal refractive surgerychanges the corneal morphology, resulting in incorrectly estimating corneal curvature with traditional biometric instruments andformulas. Calculating the IOL power using the three generation formulas result in signi�cant hyperopic error in eyes with previousmyopic corneal refractive surgery [1]. For most myopic patients, the need for spectacles and hyperopia shift after cataract surgery wereparticularly disturbing. Three main sources of error in IOL calculation after corneal refractive surgery exist: radius measurement error [2],keratometer index error [3] and IOL formula error [4].

Over the past few decades, various methods have been proposed to address the accuracy of predictability in IOL degree calculation withpatients after corneal refractive surgery. It could be classi�ed into 2 main groups that the refractive historical data are known or notknow. The clinical history method was once considered the gold standard for the IOL calculation in patients with refractive surgery.However, cataract surgeons still experience situations where historical data are not available or not credible. Thus, the clinical historymethod was proved to be not as accurate as it was proposed. Several formulas that exclude the dependence of the historical data areavailable, including the Shammas-PL [5], Haigis-L [6], Barrett true K no history [7], Wang-Koch-Maloney (W-K-M) [8], Double-K method [9],OCT formula [10], various IOL calculators [11] and others. Although the accuracy of these formulas is higher than the traditionalformulas and the historical data method, the predictability among above formulas is quite different in studies. Early studies displayedthat Haigis-L and Shammas-PL had a good precise in IOL power calculation in eyes after corneal refractive surgery [12, 13]. Abula�a [7]and Vrijman [14] showed Barrett true K no history was signi�cantly more accurate than Haigis-L and Shammas-PL. Ianchulev [15]suggested Barrett true K no history produced smaller percentage of refractive prediction error within ±0.5D and ±1.0D than Haigis-L.After Wang et.al provided the ASCRS calculator, the combined method became a good choice for surgeons [16, 17]. Another newmethod (OCT formula) was used by cataract surgeon recent years. Huang [18] reported that OCT formula had a signi�cantly lowermean absolute error than Haigis-L and Shammas-PL. Wang [17] indicated that OCT formula had a signi�cantly higher precise thanBarrett true K no history and ASCRS average methods. Therefore, the debate about the best formula for IOL power calculation in eyesafter corneal refractive surgery still exists. The purpose of this meta-analysis was to compare the accuracy of IOL degree calculationformulas without historical data in eyes after myopic refractive surgery.

Methods

Literature searchThere were two independent investigators (H. L. and J. L.) searched the databases of PubMed, EMBASE, Web of science and Cochranelibrary. We searched and selected relevant studies published between Jan 1, 2009 and Aug 11, 2019, with using the following terms forPubMed: (Lenses Intraocular [Mesh] OR Intraocular Lens [Title/Abstract] OR Implantable Contact Lens [Title/Abstract] OR IOL[Title/Abstract]) AND (Refractive Surgical Procedures [Mesh] OR Laser Corneal Surgeries [Title/Abstract] OR Laser Keratectomy

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[Title/Abstract] OR Laser Corneal Surgeries [Title/Abstract] OR Keratomileusis, Laser In Situ [Mesh] OR LASIK [Title/Abstract] OR Laser-Assisted Stromal In Situ Keratomileusis [Title/Abstract] OR Photorefractive Keratectomy [Mesh] OR PRK [Title/Abstract]) AND (calculat*OR formula*) AND (last 10 years [PDat]). Regardless of the primary outcome or language, we have considered all possible studies forreview. The two authors respectively evaluated the titles and abstracts of all searched studies and performed a manual search bysearching the reference list of all the eligibility articles.

Inclusion and exclusion criteriaInclusion criteria for studies were: (1) patients who had laser-assisted in situ keratomileusis (LASIK), photorefractive keratectomy (PRK)or laser-assisted subepithelial keratomileusis (LASEK) for myopia and subsequent uneventful cataract surgery; (2) at least two types ofthe following IOL power calculation formulas must be involved: Haigis-L, Double-K SRK/T, Shammas-PL, Barrett true K no history, W-K-M, OCT formula and ASCRS average (Available at: http://www. http://www.ascrs.org); (3) Optical biometry measured by partialcoherence interferometry (PCI, IOL Master); (4) IOL constants were optimized. Exclusion criteria for studies were: (1) patients who hadhyperopic refractive surgery or radial keratotomy surgery; (2) the percentage of refractive prediction error within ±0.5 diopter (D) and±1.0D are unavailable; (3) eyes that have not in-the-bag �xed IOL implantation or another ocular surgery. Intraoperative refractivebiometry [15], Shammas-PHL [19] and Olsen formulas [20] were excluded because of the limited use in clinical work.

Data extraction and quality assessmentWe compared the Haigis-L, Shammas-PL, Barrett true K no history, Double-K SRK/T, W-K-M, ASCRS average and OCT formulas whichwere used to calculate the IOL power in eyes after myopic corneal refractive surgery. The primary outcome assessed were as follows:the percentages of refractive prediction error within ±0.5D and ±1.0D. The higher proportion, the higher precision of the calculationformula. The two authors (H. L. and J. L.) independently extracted the data and compared the results. The discrepancy was resolved byagreeing with another author (H. S.). We used a modi�ed check-list adapted from the QUADAS–2 tool to assess the quality of theevidence [21, 22]. Study characteristics extracted from the retrieved studies were the �rst author, year of publication, sample size,demographic data (age, axial lengths, anterior chamber depth, corneal power, IOL power and mean refraction error), the formula usedand its percentages of refractive prediction error within ±0.5D and ±1.0D, and the postoperative refraction time and refraction method.

Statistical analysisThe target outcome was the percentages of refractive prediction error within ±0.5D and ±1.0D of each formula. The refractive predictionerror was calculated by subtracting the postoperative spherical equivalent from the predictive spherical equivalent produced by eachformula. For categorical outcomes, we calculated pooled estimate of the odds ratio (OR) with a �xed-effects model. The I2 statistic wasused to determine heterogeneity across studies, such that heterogeneity was quanti�ed irrespective of the number of studies. An I2 valuegreater than 50% was considered as substantial heterogeneity. We also conducted sensitivity analysis and subgroup analysis toevaluate the change in overall effect when the I2 value was greater than 50%. Funnel plots was performed to evaluate the publicationbias and small-study effect. Data pooling was done by using Review Manager (version 5.3, Cochrane Collaboration, Oxford, UK). Pvalueless than 0.05 was considered to be statistically signi�cant.

ResultsA total of 1144 articles were initially identi�ed by literature search (Figure 1). Among them, 1104 records were left after duplicatesremoval, of which 793 records were removed due to irrelevance. The remaining 40 trials were chosen for full-text evaluation. Amongthem, 3 studies did not have percentage data, 16 studies included only one of the selected IOL calculation formulas, 15 studies wereunder hyperopic laser refractive surgery or radial keratotomy surgery.

Study characteristics and quality assessmentIn total, there were 1167 eyes enrolled in the 16 included studies (Table 1). Most of the studies (n = 15) included patients implanting amonofocal IOL in the capsular bag, only one trial had multifocal IOL implantation, and one trial included patients with unclear exclusion.The quality assessment included in the study was performed using the modi�ed QUADAS–2 (Figure 2). Appendix 1 provides detailed

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information on the comprehensive assessment. For patient selection, three studies had inappropriate exclusions, resulting in a high riskof bias. Seven studies did not clarify the patient enrollment methods, resulting in an unclear risk of bias. For reference standard and�ow assessment, one study performed the subjective refraction and its follow-up time was less than 3 weeks. For index test, sixteen ofthe studies were of high quality.

OutcomesAmong the 1167 eyes enrolled, 1019 eyes were calculated with Haigis-L, 1055 with Shammas-PL, 279 with Barrett true K no history, 291with Double-K SRK/T, 433 with W-K-M, 332 with ASCRS average and 150 with OCT formula. The overall percentages of refractiveprediction error within ±0.5D (±1.0D) of the above formulas are 46.22% (78.61%), 47.68% (80.47%), 59.14% (86.74%), 26.46% (51.89%),45.50% (77.14%), 62.35% (87.95%) and 65.33% (91.33%), respectively (Figure 3).

Percentage of refractive prediction error within ±0.5DFigure 4 showed the comparisons of the percentage of refractive prediction error within ±0.5D between Haigis-L and the other formulas.The percentage of refractive prediction error within ±0.5D calculated by the Haigis-L was signi�cantly lower than ASCRS average (Figure4e, P = 0.009) and OCT formula (Figure 4f, P = 0.03). Shammas-PL also produced signi�cantly lower percentage of refractive predictionerror within ±0.5D than Barrett true K no history, ASCRS average and OCT formula (Appendix 2, P = 0.01, 0.01, 0.01, respectively). Thepercentage of refractive prediction error within ±0.5D obtained by Barrett true K no history and ASCRS average was signi�cantly higherthan W-K-M (Appendix 2, P < 0.0001 and P = 0.008, respectively).

Percentage of refractive prediction error within ±1.0DFigure 5 showed the comparisons of the percentage of refractive prediction error within ±1.0D between Haigis-L and the other formulas.There are no statistical signi�cances of the other formula pairwise comparison. Only the percentage of refractive prediction error within±1.0D calculated by Haigis-L was signi�cantly higher than W-K-M (Figure 5d, P = 0.04).

Heterogeneity and subgroup analysis

The I2 values and 95% con�dence interval (CI) are shown in Figure 4 and 5. In pairwise comparison, substantial heterogeneity wasdetected in two pairs and the random-effect model was applied. The sensitivity analysis showed that by omitting Cho 2018, I2

signi�cantly decreased to 0% in the comparison of the percentage of refractive prediction error within ±1.0D between Haigis-L andShammas-PL and between Haigis-L and W-K-M (Appendix 4. P = 0.0004, 0.004, respectively). Cho et.al did not show the detail of the IOLconstant optimization procedure and not report whether the keratometry used to calculate IOL power was from IOL Master or not. Thus,after omitting this study, the I2 value decreased. There was no signi�cantly statistical �nding of the funnel plot (Appendix 5).

DiscussionCalculating the IOL power in eyes after refractive surgery is still a challenging task for all ophthalmologists. The various methods makeit di�cult to evaluate the precise between studies. To our knowledge, this is the �rst meta-analysis to assess the accuracy of thedifferent IOL power calculation formulas with on idea of the historical data in eyes after myopic refractive surgery. The results of thismeta-analysis were investigated from 16 studies, including 7 common methods (Haigis-L, Shammas-PL, Double-K SRK/T, Barrett true Kno history, W-K-M, ASCRS average and OCT formula).

There are many indicators for evaluating the accuracy of IOL power calculation formulas, such as mean arithmetic error (MAE); meanabsolute error (MedAE); a variance of the prediction error; and the percentage of the refractive prediction error within ±0.5D, ±1.0D and±2.0D. However, many studies did not optimize the IOL constant to make the MedAE to equal zero [23], so it is di�cult to get theauthentic MAE due to the wrong methodology. On the other hand, a few studies did not compare the MedAE of different formulas whichwas not a normal distribution. For the virgin eyes after phacoemulsi�cation, the benchmark standard is that 55% should be within ±0.5Dand 85% within ±1.0D of predictive error [24]. Based on these reasons, we assessed the predictive e�ciency of different IOL powercalculation formulas in eyes after refractive surgery by measuring the percentage of refractive prediction error within ±0.50D and ±1.0D.

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Our meta-analysis suggested that, only the overall percentages of refractive prediction error within ±0.5D (±1.0D) of Barrett true K nohistory, ASCRS average and OCT formula have reached the benchmark standard that 55% should be within ±0.5D and 85% within ±1.0Dof refractive prediction error. OCT formula has the highest value of overall percentages which were 65.33% within ±0.5D and 91.33%within ±1.0D. In the percentage of refractive prediction error within ±0.5D analysis: the Barrett true K no history and ASCRS average ismore predictably accurate than Shammas-PL and W-K-M methods; the popular Haigis-L formula produced results associated with lessaccuracy in predictions than ASCRS average; the latest calculation method, OCT formula accuracy is better than Haigis-L andShammas-PL. In the percentage of refractive prediction error within ±1.0D analysis, only the Haigis-L performed better than W-K-Mformula.

In the early studies, the IOL calculation method based on clinical historical data was favored by cataract surgeons and even as a goldstandard for several years. However, the clinical historical data from the time of the refractive surgery are often missing or incomplete.Many studies indicated that the accuracy of IOL power prediction of the clinical history method was signi�cantly lower than othermethods [4]. Thus, we did not analysis the methods using clinical historical data. In 2003, Aramberri[9] showed the double K methods:using keratometry of pre-refractive surgery to estimate the effective lens position (ELP) and keratometry post-refractive surgery for theIOL power calculation. Double K methods could combine with different formulas, such as SRK/T, Hoffer Q, Holladay II formulas, whichwas used for several years. Then, a number of regression formulas—Shammas-PL [5] which uses data available at the time of cataractsurgery to predict the post refractive surgery keratometry and W-K-M [13] method which convert anterior corneal power from Atlastopography – are described in different articles. Haigis-L uses linear regression to optimize the estimate of corneal power from standardkeratometry [6], which is the most popular method for IOL power calculation after refractive surgery, especially for Asian and German[25, 26]. Unlike double-K method, the Shammas-PL and Haigis-L determine the ELP without the central corneal power data. Before 2014,the accuracy of the Haigis-L, Shammas-PL, and W-K-M formulas was comparable, and the Double K method was slightly lower than theother three formulas [12]. After that, a large number of studies have shown that the accuracy of the Haigis-L is comparable to that of theShammas-PL formula, while the W-K-M and Double K formulas are less accurate [17, 27]. But in our analysis, there is no statisticallysigni�cant difference in the percentage of refractive error percentage of the above four formulas, only the Haigis-L has better percentageof refractive predicted error within ±1.0D than the W-K-M method. Barrett true K no history [7] formula was �rst proposed in 2009, but themathematical formula has never been published. However, some studies have found it leads to accurate refractive results and is nowconsidered as one of the most reliable options both after myopic and hyperopic LASIK/PRK [15, 28]. Another reliable option was theASCRS calculator which produced an average IOL power, the combined method became a good choice for surgeons, especially thosewho cannot choose the proper calculation method or judge which method is best [16, 17]. The ASCRS average and Barrett true K nohistory formulas also had a good prediction and reliability in our analysis. Another OCT formula [10] was the latest formula which wasused since 2013, and only a few studies have reported and compared the accuracy of it. The faster speed of corneal mapping andhigher axial resolution of the OCT gave cataract surgeries new choice to measure both the anterior and posterior corneal power [10]. Inour meta-analysis, OCT formula which included 150 eyes, has a better accuracy than the Shammas-PL and Haigis-L formulas. However,due to the limited eyes of the eligibility articles, further efforts should be made to con�rm our �ndings.

This meta-analysis has several limitations. Firstly, several studies were retrospective case series with a limited sample size, and therewas also a bias caused by the variability of the patient characteristics, IOL types and the single-center analysis. But it was accepted bymost of the authors when comparing the accuracy of IOL power calculation formulas. Next, optical biometric data of all eligibilitystudies were measured using PCI. As the popularity of the Scheimp�ug imaging using in eyes after refractive surgery, the precise ofvarious formulas with optical biometry measured by it needs to be further con�rmed. Third, only 150 eyes calculated IOL power by OCTformula, the statistical power may be insu�cient when we compared with other formulas. Finally, we did not include the intraoperativerefractive biometry, Shammas-PHL and Olsen formulas because of the limited trials.

ConclusionsPresent study indicated that the application of Barrett true K no history and ASCRS average formula in the eyes after refractive surgeryare promising with the higher percentage of eyes within ±0.5D of prediction error when compared to Shammas-PL and W-K-M. ASCRSaverage also had higher percentage than Haigis-L formula. We suggest that the ASCRS average and Barrett true K no history formulashould be used to calculate the IOL power in eyes after myopic refractive surgery. OCT formula should emphasize the assessmentcriteria regarding IOL power calculation approaches for further larger controlled studies.

Abbreviations

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IOL: intraocular lens

W-K-M: Wang-Koch-Maloney

OCT: optical coherence tomography

ASCRS: American Society of Cataract and Refractive Surgery

D: diopter

LASIK: laser-assisted in situ keratomileusis

PRK: photorefractive keratectomy

LASEK: laser-assisted subepithelial keratomileusis

PCI: partial coherence interferometry

OR: odds ratio

CI: con�dence interval

MAE: mean arithmetic error

MedAE: mean absolute error

ELP: effective lens position

Declarations

Ethics approval and consent to participateThe study was performed in accordance with the ethical standards stated in the 1964 Declaration of Helsinki and was approved by therespective local clinical research ethics committees.

Consent for publicationNot applicable.

Availability of data and materialsThe datasets supporting the conclusions of this article are included within the article and its additional �le.

Competing interestsThe authors declare that they have no competing interests.

FundingThis study was supported by the Technology Foundation of Tianjin Health Bureau (grant no. 2014KY37, Jun Li)

Authors’ contributionsHongyu Li carried out the meta-analysis, and drafted the manuscript. Hui Song conceived of the study, and participated in itscoordination. Hongyu Li and Jun Li participated in the collections of data. Hui Song participated in the design of the study and helpedto revise the manuscript. All authors read and approved the �nal manuscript.

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AcknowledgementsWe would like to give special thanks to Yang Li for the language editing.

Authors’ informationA�liations

Clinical College of Ophthalmology, Tianjin Medical University, Tianjin, China

Hongyu Li

Clinical College of Ophthalmology, Tianjin Medical University, Tianjin Eye Institute, Tianjin Key Lab of Ophthalmology and VisualScience, Tianjin Eye Hospital, Tianjin, China

Jun Li & Hui Song

Corresponding Author

Correspondence to Hui Song

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TablesTable 1. Characteristics of study participants

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Author Year Eyes Age(year) AL(mm) Follow(days) Refraction HL SHL BTK DK WKM ASCRS OCT

Wang 2010 72 58±8 26.19±1.55 >21 objective √ √     √ √  

McCarthy 2011 173 57±0 26.9±1.86 203 objective √ √   √      

Huang 2013 46 61.5±8 NA >30 objective √ √         √

Saiki1 2013 25 54±9.9 26.39±0.99 >30 objective √ √   √      

Saiki2 2013 28 54±9.8 26.19±1.06 >30 objective √ √   √      

Yang 2013 62 61±6.79 25.98±1.55 90-180 objective √ √     √ √  

Ianchulev 2014 246 NA 25.43±1.43 30-90 NA √ √          

Saiki 2014 24 54±10.6 NA >30 objective √ √   √      

Wang 2015 104 63±7 25.46±1.3 21-90 objective √ √ √   √   √

Potvin 2015 101 NA 25.83±1.36 NA NA √ √     √    

Abulafia 2016 58 NA 25.85±1.35 >21 objective √ √ √   √ √  

Helaly 2016 45 51.27±7.31 28.66±2.78 30-120 objective √ √   √      

Wu 2017 10 50.3±9 30.06±2.87 >90 subjective √ √          

Cho 2018 56 54.6±9.37 27.04±2.36 90 objective √ √ √   √    

Vrijman 2019 64 NA 25.28±1.4 NA NA √ √ √     √  

Wang 2019 53 64.5±7.1 25.72±1.64 >21 objective √   √        

*AL: axial length; HL: Haigis-L; SHL: Shammas-PL; BTK: Barrett true K no history; DK: Double-K SRK/T; WKM:Wang-Koch-Maloney; ASCRS: ASCRS average; OCT: optical coherence tomography formula; NA: not available

Figures

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Figure 1

Flowchart of articles selection (RK= radial keratotomy)

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Figure 2

Quality assessment of the eligibility studies according to the modi�ed QUADAS-2

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Figure 3

The overall percentage of refractive prediction error within ±0.5D and ±1.0D of the included formulas. (Barrett true K means Barrett trueK no history; Double-K means Double-K SRK/T; W-K-M means Wang-Koch-Maloney; ASCRS average means average degree from ASCRScalculator; OCT means optical coherence tomography formula; D means diopter)

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Figure 4

Forest plots comparing the percentage of refractive prediction error within ±0.5D between Haigis-L and Shammas-PL(a), Barrett true Kno history(b), Double-K SRK/T(c), W-K-M(d), ASCRS average(e) and OCT formula(f) (Note: Barrett true K means Barrett true K no history)

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Figure 5

Forest plots comparing the percentage of refractive prediction error within ±1.0D between Haigis-L and Shammas-PL(a), Barrett true Kno history(b), Double-K SRK/T(c), W-K-M(d), ASCRS average(e) and OCT formula(f) (Note: Barrett true K means Barrett true K no history)

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