Accuracy of intraocular lens power calculation formulas after laser refractive surgery in myopic eyes: A meta-analysis

Background: 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 studies published between Jan 1, 2009 and Aug 11, 2019. Primary outcomes were the percentages of refractive prediction error within ±0.5D and ±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 signicantly higher 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 signicantly 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 signicantly 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 eyes after myopic refractive surgery.


Background
Patients who have had corneal excimer laser surgery are now facing cataract surgery with aging. It is a challenge for all ophthalmologists to calculate the intraocular lens (IOL) power in eyes after refractive surgery. As we all know, corneal refractive surgery changes the corneal morphology, resulting in incorrectly estimating corneal curvature with traditional biometric instruments and formulas. Calculating the IOL power using the three generation formulas result in signi cant hyperopic error in eyes with previous myopic corneal refractive surgery [1]. For most myopic patients, the need for spectacles and hyperopia shift after cataract surgery were particularly 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 with patients after corneal refractive surgery. It could be classi ed into 2 main groups that the refractive historical data are known or not know. 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 history method was proved to be not as accurate as it was proposed. Several formulas that exclude the dependence of the historical data are available, 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 traditional formulas and the historical data method, the predictability among above formulas is quite different in studies. Early studies displayed that 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 new method (OCT formula) was used by cataract surgeon recent years. Huang [18] reported that OCT formula had a signi cantly lower mean absolute error than Haigis-L and Shammas-PL. Wang [17] indicated that OCT formula had a signi cantly higher precise than Barrett true K no history and ASCRS average methods. Therefore, the debate about the best formula for IOL power calculation in eyes after corneal refractive surgery still exists. The purpose of this meta-analysis was to compare the accuracy of IOL degree calculation formulas without historical data in eyes after myopic refractive surgery.

Literature search
There were two independent investigators (H. L. and J. L.) searched the databases of PubMed, EMBASE, Web of science and Cochrane library. We searched and selected relevant studies published between Jan 1, 2009 and Aug 11, 2019, with using the following terms for

Inclusion and exclusion criteria
Inclusion 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 of the 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 partial coherence interferometry (PCI, IOL Master); (4) IOL constants were optimized. Exclusion criteria for studies were: (1) patients who had hyperopic 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 refractive biometry [15], Shammas-PHL [19] and Olsen formulas [20] were excluded because of the limited use in clinical work.

Data extraction and quality assessment
We compared the Haigis-L, Shammas-PL, Barrett true K no history, Double-K SRK/T, W-K-M, ASCRS average and OCT formulas which were 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 calculation formula. The two authors (H. L. and J. L.) independently extracted the data and compared the results. The discrepancy was resolved by agreeing with another author (H. S.). We used a modi ed check-list adapted from the QUADAS-2 tool to assess the quality of the evidence [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 used and its percentages of refractive prediction error within ±0.5D and ±1.0D, and the postoperative refraction time and refraction method.

Statistical analysis
The target outcome was the percentages of refractive prediction error within ±0.5D and ±1.0D of each formula. The refractive prediction error was calculated by subtracting the postoperative spherical equivalent from the predictive spherical equivalent produced by each formula. For categorical outcomes, we calculated pooled estimate of the odds ratio (OR) with a xed-effects model. The I 2 statistic was used to determine heterogeneity across studies, such that heterogeneity was quanti ed irrespective of the number of studies. An I 2 value greater than 50% was considered as substantial heterogeneity. We also conducted sensitivity analysis and subgroup analysis to evaluate the change in overall effect when the I 2 value was greater than 50%. Funnel plots was performed to evaluate the publication bias and small-study effect. Data pooling was done by using Review Manager (version 5.3, Cochrane Collaboration, Oxford, UK). Pvalue less than 0.05 was considered to be statistically signi cant.

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

Study characteristics and quality assessment
In total, there were 1167 eyes enrolled in the 16 included studies ( Table 1). Most of the studies (n = 15) included patients implanting a monofocal 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 information on the comprehensive assessment. For patient selection, three studies had inappropriate exclusions, resulting in a high risk of 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 of the studies were of high quality.

Heterogeneity and subgroup analysis
The I 2 values and 95% con dence interval (CI) are shown in Figure 4 and 5. In pairwise comparison, substantial heterogeneity was detected in two pairs and the random-effect model was applied. The sensitivity analysis showed that by omitting Cho 2018, I 2 signi cantly decreased to 0% in the comparison of the percentage of refractive prediction error within ±1.0D between Haigis-L and Shammas-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 IOL constant 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 I 2 value decreased. There was no signi cantly statistical nding of the funnel plot (Appendix 5).

Discussion
Calculating the IOL power in eyes after refractive surgery is still a challenging task for all ophthalmologists. The various methods make it di cult to evaluate the precise between studies. To our knowledge, this is the rst meta-analysis to assess the accuracy of the different IOL power calculation formulas with on idea of the historical data in eyes after myopic refractive surgery. 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, 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); mean absolute 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 the authentic MAE due to the wrong methodology. On the other hand, a few studies did not compare the MedAE of different formulas which was not a normal distribution. For the virgin eyes after phacoemulsi cation, the benchmark standard is that 55% should be within ±0.5D and 85% within ±1.0D of predictive error [24]. Based on these reasons, we assessed the predictive e ciency of different IOL power calculation formulas in eyes after refractive surgery by measuring the percentage of refractive prediction error within ±0.50D and ±1.0D.
Our meta-analysis suggested that, only the overall percentages of refractive prediction error within ±0.5D (±1.0D) of Barrett true K no history, ASCRS average and OCT formula have reached the benchmark standard that 55% should be within ±0.5D and 85% within ±1.0D of 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 is more predictably accurate than Shammas-PL and W-K-M methods; the popular Haigis-L formula produced results associated with less accuracy in predictions than ASCRS average; the latest calculation method, OCT formula accuracy is better than Haigis-L and Shammas-PL. In the percentage of refractive prediction error within ±1.0D analysis, only the Haigis-L performed better than W-K-M formula.
In the early studies, the IOL calculation method based on clinical historical data was favored by cataract surgeons and even as a gold standard 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 other methods [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 the IOL power calculation. Double K methods could combine with different formulas, such as SRK/T, Hoffer Q, Holladay II formulas, which was used for several years. Then, a number of regression formulas-Shammas-PL [5] which uses data available at the time of cataract surgery to predict the post refractive surgery keratometry and W-K-M [13] method which convert anterior corneal power from Atlas topography -are described in different articles. Haigis-L uses linear regression to optimize the estimate of corneal power from standard keratometry [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 the other three formulas [12]. After that, a large number of studies have shown that the accuracy of the Haigis-L is comparable to that of the Shammas-PL formula, while the W-K-M and Double K formulas are less accurate [17,27]. But in our analysis, there is no statistically signi cant difference in the percentage of refractive error percentage of the above four formulas, only the Haigis-L has better percentage of 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 the mathematical formula has never been published. However, some studies have found it leads to accurate refractive results and is now considered as one of the most reliable options both after myopic and hyperopic LASIK/PRK [15,28]. Another reliable option was the ASCRS calculator which produced an average IOL power, the combined method became a good choice for surgeons, especially those who cannot choose the proper calculation method or judge which method is best [16,17]. The ASCRS average and Barrett true K no history formulas also had a good prediction and reliability in our analysis. Another OCT formula [10] was the latest formula which was used since 2013, and only a few studies have reported and compared the accuracy of it. The faster speed of corneal mapping and higher axial resolution of the OCT gave cataract surgeries new choice to measure both the anterior and posterior corneal power [10]. In our 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 there was also a bias caused by the variability of the patient characteristics, IOL types and the single-center analysis. But it was accepted by most of the authors when comparing the accuracy of IOL power calculation formulas. Next, optical biometric data of all eligibility studies were measured using PCI. As the popularity of the Scheimp ug imaging using in eyes after refractive surgery, the precise of various formulas with optical biometry measured by it needs to be further con rmed. Third, only 150 eyes calculated IOL power by OCT formula, the statistical power may be insu cient when we compared with other formulas. Finally, we did not include the intraoperative refractive biometry, Shammas-PHL and Olsen formulas because of the limited trials.

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

Consent for publication
Not applicable.

Availability of data and materials
The datasets supporting the conclusions of this article are included within the article and its additional le.  The overall percentage of refractive prediction error within ±0.5D and ±1.0D of the included formulas. (Barrett true K means Barrett true K no history; Double-K means Double-K SRK/T; W-K-M means Wang-Koch-Maloney; ASCRS average means average degree from ASCRS calculator; OCT means optical coherence tomography formula; D means diopter)