#### Abstract

To systematically compare and rank the predictability of no-history intraocular lens (IOL) power calculation methods after myopic laser refractive surgery.

PubMed, Embase, the Cochrane Library, and the U.S. trial registry (

Nineteen studies involving 1,098 eyes and 19 formulas were identified. A network meta-analysis for the percentage of eyes with a PE within ±0.50 D found that ray-tracing (Okulix), intraoperative aberrometry (Optiwave Refractive Analysis [ORA]), BESSt, and Seitz/Speicher/Savini (Triple-S) (D-K SRK/T), and Fourier-Domain OCT-Based formulas were more predictive than the Wang/Koch/Maloney, Shammas-PL, modified Rosa, Ferrara, and Equivalent K reading at 4.5 mm using the Double-K Holladay 1 formulas. With regard to ranking, the top four formulas as per the surface under the cumulative ranking curve (SUCRA) values for the percentage of eyes with a PE within ±0.50 D were the Okulix, ORA, BESSt, and Triple-S (D-K SRK/T). With regard to MAE, the ORA showed lower errors when compared to the Shammas-PL formula. In this regard, the top four formulas based on the SUCRA values were the Triple-S, BESSt, ORA, and Fourier-Domain OCT-Based formulas. The SToP (SRK/T), ORA, Fourier-Domain OCT-Based, and BESSt formulas had the lowest MedAE.

Considering all three outcome measures of highest percentages of eyes with a PE within ±0.50 and ±1.00 D, lowest MAE, and lowest MedAE, the top three no-history formulas for IOL power calculation in eyes with previous myopic corneal laser refractive surgery were: ORA, BESSt, and Triple-S (D-K SRK/T).

**[ J Refract Surg. 2020;36(7):481–490.]**

Laser in situ keratomileusis (LASIK), photorefractive keratectomy (PRK), and laser subepithelial keratomileusis (LASEK) are commonly performed surgical procedures for the correction of myopia. It is well recognized that previous corneal laser refractive surgery can cause difficulties in accurate biometry at the time of cataract surgery, for at least three reasons.^{1} First, the corneal power is inaccurately calculated because the ratio between the anterior and posterior corneal radii is changed, so that the standard keratometric index of 1.3375 is no longer valid. Second, corneal radii may be inaccurately measured in eyes with small or decentered optical zones. Third, the intraocular lens (IOL) position is inaccurately estimated by formulas using the corneal radius as a predictor. Taken together, these problems usually lead to IOL power underestimation and residual hyperopia in eyes that had been treated for myopia.^{2} During the past 20 years, many methods have been developed to improve the accuracy of IOL power calculation in these eyes.

Due to the difficulty in obtaining historical data (eg, the original corneal power and the laser-induced refractive change), no-history methods to calculate the IOL power are ideally the best options. Previous studies have also found that they can offer better outcomes with respect to historical methods.^{3,4} Only a few articles comprehensively compared and analyzed the many available no-history methods.^{5,6} Because it is time-consuming to calculate the IOL power with all of these methods and formulas, we aimed to assess which are the most accurate. In view of the different calculations used in previously published trials, traditional meta-analysis methods do not allow adequate comparison of all calculations. Therefore, we did a network meta-analysis of all relevant evidence to comprehensively compare and rank the no-history methods in patients who have had previous corneal laser refractive surgery and to establish a recommendation for formula selection.

### Methods

This systematic review complies with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) network meta-analysis extension statement (**Table A**, available in the online version of this article).^{7}

Table A: PRISMA 2009 Checklist |

#### Outcome Measurements

The percentage of eyes with a refractive prediction error (PE) within ±0.50 and ±1.00 diopters (D), mean absolute error (MAE), and median absolute error (MedAE) in refractive prediction were set as the outcome measurements.

#### Eligibility Criteria

Trials were included if they met the following criteria: (1) design: case series study; (2) population: patients having cataract surgery after prior corneal myopia laser refractive surgery, such as PRK, LASIK, epipolis laser in situ keratomileusis, LASEK, transepithelial PRK, sub-Bowman femtosecond laser–assisted laser in situ keratomileusis, or femtosecond laser–assisted LASIK; (3) interventions: no-history formulas were used to calculate the IOL power. With regard to the methods that modify the keratometric readings (eg, Maloney formula), when they were combined with different IOL power formulas in the same article (eg, Maloney with Double-K SRK/T and Maloney with Double-K Hoffer Q formulas), we selected only the most accurate combination (Maloney with Double-K-SRK/T formula); (4) comparisons: two or more formulas; and (5) outcomes: reported at least one of the above-mentioned outcome measurements. We excluded studies that (a) contained only one of the no-history methods or contained patients who had undergone hyperopic corneal laser refractive surgery or radial keratotomy, (b) had methods using Single-K formulas when Double-K formulas should have been applied,^{8} (c) were classified as no-history methods although they actually used some historical data, or (d) analyzed methods or formulas that were judged inappropriate because they did not address all three problems listed in the introduction. The language of studies was not restricted.

#### Search Methods

A systematic literature review was conducted using PubMed, Embase, The Cochrane Library, and the U.S. trial registry ( www.ClinicalTrial.gov) for trials published up to August 2019. The full search strategies are shown in **Table B** (available in the online version of this article). We also manually examined the reference lists of clinical trials, related meta-analyses, and systematic reviews to identify relevant studies.

Table B: Search Strategy |

#### Study Selection

Screening was performed by two independent investigators (JY, YW). They retrieved the full-text articles that appeared relevant after reviewing the titles and abstracts. They independently assessed full-text articles for final eligibility. Any discrepancy was resolved by focused discussion or consultation with an additional investigator (BS).

#### Data Extraction

Two investigators independently extracted information into an electronic database, including the participant and intervention characteristics, outcomes, and quantitative results for formula effects. For data that were missing or could not be directly obtained, we contacted the authors of trial reports or used GetData GraphDigitizer 2.24 ( http://getdata-graph-digitizer.com) to read data from figures.

#### Risk of Bias Assessment

To evaluate the study quality, the Quality Appraisal Tool for case series studies using a modified Delphi technique developed by the Institute of Health Economics was used.^{9} In this method, we judged “Yes,” “No,” or “Unclear/Partly stated” for each of the following sections: study objective (1 item), study population (5 items), intervention and co-intervention (2 items), outcome measure (3 items), statistical analysis (1 item), results and conclusions (5 items), competing interests and sources of support (1 item), and new item (2 items), with a total of 20 items. Those studies gaining at least 14 “Yes” responses out of 20 items were regarded as high quality.

#### Statistical Analysis

We first conducted traditional pairwise meta-analyses for direct comparisons using random-effects models. For binary outcomes (eg, percentage of eyes with a PE within ±0.50 D), relative effect sizes were calculated as odds ratios with 95% CIs. For continuous outcomes (eg, MAE), the relative effect sizes were calculated as weighted mean differences with 95% CIs. Because MedAE is not suitable for meta-analysis, only descriptive analyses were performed. For positive outcomes (ie, the percentage of eyes with a PE within ±0.50 or ±1.00 D, where higher values indicate better results, odds ratios greater than 1 correspond to beneficial treatment effects of the first formula compared to the second formula. For negative outcomes (ie, MAE, where higher values indicate worse results), weighted mean differences less than 0 correspond to beneficial treatment effects of the first formula compared to the second formula. We used visual inspection of the I^{2} statistic (values of 50% or more indicated substantial heterogeneity) to investigate the possibility of statistical heterogeneity. We used STATA software version 13.1 (StataCorp LP) for statistical analyses.^{10}

To incorporate indirect comparisons, we performed a network meta-analysis to compare different formulas and methods. These were conducted in STATA software version 13.1 using the mvmeta command. We estimated the relative rankings of each formula using ranking probabilities and surface under the cumulative ranking curve (SUCRA).^{11} SUCRA is a numeric presentation of the overall ranking and presents a single number associated with each formula for the given outcome measure (in this case, PE). SUCRA values range from 0% to 100%, with a value closer to 100% indicating a higher likelihood that a formula is in the top rank or one of the top ranks; for SUCRA values closer 0%, the more likely it is that the formula is in the bottom rank or one of the bottom ranks.

Inconsistency between direct and indirect evidence was assessed by a “node-splitting” approach, which separates direct from indirect evidence on a particular comparison (node) and the design-by-treatment interaction model assuming consistency throughout the entire network.^{12} Funnel plots were used to evaluate publication bias in the results between small and large studies.^{13} Once the plots are generated, the criterion of symmetry was used to visually inspect the publication bias. Because small sample size studies may lead to spuriously inflated effects and publication bias,^{13} we also undertook subgroup analyses investigating only methods that have been evaluated in at least three different studies and 100 eyes.

### Results

#### Literature Selection Results

**Figure A** (available in the online version of this article) shows the detailed steps of the study selection process. The literature search yielded 502 potentially relevant studies (detailed search strategy is shown in **Table B**). After duplicates were excluded, 365 studies remained. Of these, 41 potentially eligible studies were retrieved from the electronic databases and 4 additional studies were identified from the references of selected studies, yielding a total of 45. After excluding 26 studies on the basis of the pre-defined inclusion criteria, 19 studies^{3,6,14–30} were included in the network meta-analysis.

Figure A. Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) flow diagram. |

#### Study Characteristics and Network Geometry

A summary of all eligible studies is shown in **Table C** (available in the online version of this article). Included trials were published from 2009 to 2019. A total of 1,089 eyes whose IOL power was calculated by one of 19 no-history methods were evaluated. The included formulas were the Barrett True-K (unpublished), BESSt,^{31} Equivalent K reading (EKR) at 4.5 mm using the Double-K Holladay 1,^{19,32} Ferrara,^{33} Fourier-domain OCT-Based,^{34} Haigis-L,^{2} Hill-Potvin-Shammas,^{26} Koch-Maloney using the Haigis,^{30,35} Maloney with the Double-K SRK/T,^{25} modified Rosa,^{36} ray-tracing (Okulix),^{37} intraoperative aberrometry (Optiwave Refractive Analysis [ORA]),^{24} Seitz/Speicher/Savini (Triple-S),^{38} Shammas-PL,^{39} SToP (Holladay 1),^{40,41} SToP (SRK/T),^{42} Total Corneal Power 1 (TCP 1)^{17} using the Double-K Holladay 1,^{19,32} Total Corneal Refractive Power (TCRP) at 4 mm with the Haigis,^{27} and Wang/Koch/Maloney as calculated by the American Society of Cataract and Refractive Surgery website.^{3,35}**Table 1** and **Table D** (available in the online version of this article) show the brief description and abbreviations for the formulas and the number of trials and eyes involved in each formula.

Table C: Summary of studies included in the network meta-analysis |

Table 1: Brief Description and Abbreviations for the Formulas Included in the Network Meta-analysis |

Table D: The number of trials and eyes involved in each formula |

Almost all trials involved three or more formulas, with the exception of the articles by Saiki et al,^{14,15} Tang et al,^{20} and Wang et al,^{29} which had only two formulas. Of the included 19 trials, 4 (21.1%) recruited participants from Europe, 6 (31.6%) from Asia, and 9 (47.4%) from North America.

#### Risk of Bias Assessment Results

The risk of bias from the trials included in our study is shown in **Figure B** (available in the online version of this article). All trials gained the full “Yes” in terms of study objective, outcome measure, statistical analysis, competing interests, and sources of support. In sections of study population and results and conclusions, there were 18 trials obtaining at least 3 “Yes” responses. In addition, all trials gained half “Yes” responses in the intervention and co-intervention section; most trials were designed as retrospective rather than prospective. In total, 18 trials (94.7%) gained at least 14 “Yes” responses among 20 items and were regarded as high quality.

Figure B. The risk of bias of the trials included in the current study. |

#### Results of Meta-Analysis

*Direct Comparisons.***Figure C** (available in the online version of this article) shows the network of direct comparisons among the different formulas. **Figure D** (upper right) (available in the online version of this article) and **Tables E–G** (available in the online version of this article) show the direct comparisons between each pair of formulas with respect to the percentage of eyes with a PE within ±0.50 or ±1.00 D and MAE. In total, 17 trials involving 18 formulas were available for the comparison of the percentage of eyes with a PE within ±0.50 D. Direct comparisons found that Okulix, ORA, Fourier-Domain OCT-Based, and Barrett True-K formulas all showed superiority when compared to the Shammas-PL formula. The Shammas-PL formula was found to be better than the modified Rosa and Ferrara formulas. ORA and Fourier-Domain OCT-Based formulas were superior to the Haigis-L formula. The Hill-Potvin-Shammas, Barrett True-K, and Fourier-Domain OCT-Based formulas were better than the Wang/Koch/Maloney formula. The Triple-S and BESSt formulas were superior to the EKR 4.5 mm (D-K Holladay 1) formula. Considering the percentage of eyes with a PE within ±1.00 D, a total of 17 trials with 16 formulas were available. We found that the Triple-S formula showed superiority when compared to the Shammas-PL, EKR 4.5 mm (D-K Holladay 1), and SToP (Holladay 1) formulas. Okulix and ORA were superior to the TCRP 4 mm (Haigis) formula. The BESSt, ORA, and Barrett True-K formulas were better than the Shammas-PL formula. The Barrett True-K formula was superior to the Wang/Koch/Maloney formula. The above comparisons all showed statistically significant differences (*P* < .05).

Table E: Results of direct-comparison meta-analysis in percentage of eyes within ±0.50 D of prediction |

Table F: Results of direct-comparison meta-analysis in percentage of eyes within ±1.00 D of prediction |

Table G: Results of direct-comparison meta-analysis in respect of mean absolute error |

We found that 11 trials investigating 12 formulas reported sufficient data for MAE assessment. ORA showed a significantly lower error (*P* < .05) when compared to the Shammas-PL and Haigis-L formulas. The Haigis-L formula was better than the TCRP 4 mm (Haigis) formula. The Barrett True-K formula was superior to the Wang/Koch/Maloney and Shammas-PL formulas.

**Table H** (available in the online version of this article) and **Figure 1** show the descriptive analysis and formula ranking results for MedAE (there were 13 trials in which 17 formulas were involved). We found that the SToP (SRK/T), Fourier-Domain OCT-Based, ORA, and BESSt formulas had lower MedAE (0.31, 0.35, 0.35, and 0.37, respectively). However, 12 (70.6%) of the formulas were mentioned in only one trial.

Table H: A descriptive analysis for median absolute error |

*Combination of Direct and Indirect Comparisons.***Figure D** (bottom left) showed the results of the network meta-analysis for the IOL power formulas. The following comparisons all showed statistically significant differences (*P* < .05). With regard the percentage of eyes with a PE within ±0.50 D, Okulix, ORA, BESSt, Triple-S, and Fourier-Domain OCT-Based formulas were better than the Wang/Koch/Maloney, Shammas-PL, modified Rosa, Ferrara, and EKR 4.5 mm (D-K Holladay 1) formulas. Okulix, ORA, and Fourier-Domain OCT-Based formulas showed superiority when compared with the Haigis-L and TCRP 4 mm (Haigis) formulas. The Barrett True-K formula was superior to the Shammas-PL, Wang/Koch/Maloney, and Haigis-L formulas. The Hill-Potvin-Shammas formula was superior to the Wang/Koch/Maloney formula. With regard to the percentage of eyes with a PE within ±1.00 D, the Triple-S formula was superior to the Wang/Koch/Maloney, SToP (Holladay 1), Shammas-PL, Haigis-L, EKR 4.5 mm (D-K Holladay 1), TCRP 4 mm (Haigis), and Hill-Potvin-Shammas formulas. Okulix and ORA were both superior to the Shammas-PL, Haigis-L, and Wang/Koch/Maloney formulas. In addition, the BESSt, Barrett True-K, and Fourier-Domain OCT-Based formulas also showed a larger percentage of eyes within ±1.00 D when compared to the Wang/Koch/Maloney formula. The results of the network comparisons in MAE discovered that ORA formula showed lower errors when compared to the Shammas-PL formula.

**Figure 2** and **Tables I–K** (available in the online version of this article) showed the ranking probability results in the outcome measurements. With regard to ranking for PE within ±0.50 D, according to SUCRA, the best four formulas were: Okulix (85.1%), ORA (82.7%), BESSt (80%), and Triple-S (78.8%). The probability of Okulix being the best is approximately 32.7%, followed by BESSt (16.1%), Triple-S (14%), and ORA (9.5%). Similarly, the PE within ±1.00 D, according to SUCRA, the best four formulas were: Triple-S (92%), ORA (80%), BESSt (79.6%), and Okulix (74.8%). The probability of the Triple-S formula being the best is approximately 57.1%, which is higher than other formulas. The best top four as per SUCRA values on MAE were the Triple-S (21.9%), BESSt (23.7%), ORA (28.3%), and Fourier-Domain OCT-Based (35.3%) formulas. The probability of the above four being the best are approximately 26.4%, 23.9%, 10.1%, and 8.7%, respectively.

Table I: Results of network rank test in percentage of eyes within ±0.50 D of the prediction error |

Table J: Results of network rank test in percentage of eyes within ±1.00 D of the prediction error |

Table K: Results of network rank test in mean absolute error |

#### Inconsistency and Publication Bias

Node-splitting analysis in terms of PE within ±0.50 or ± 1.00 D and MAE showed significant consistency (*P* > .05) (**Tables L–N**, available in the online version of this article). We used the design-by-treatment interactions model and found that the global inconsistency existed in the MAE (*P* = .0046). The funnel plots showed that the included studies lie symmetrically around the 0 line (vertical line) with respect to the PE within ±0.50 or ±1.00 D and MAE (**Figures E–G**).

Table L: Node-splitting analysis of inconsistency in percentage of eyes within ±0.50 D of the prediction error |

Table M: Node-splitting analysis of inconsistency in percentage of eyes within ±1.00 D of the prediction error |

Table N: Node-splitting analysis of inconsistency in mean absolute error |

Figure E. The funnel plot in prediction refractive error within ±0.50 diopters. |

Figure F. The funnel plot in prediction refractive error within ±1.00 diopters. |

Figure G. The funnel plot in mean absolute error. |

#### Subgroup Analysis

There were 18 trials involving five formulas in total included in the analysis. The results of the subgroup analysis are shown in **Tables O–S** and **Figures H–J** (available in the online version of this article). There were 17, 17, and 11 trials in the subgroups for the PE within ±0.50 or ±1.00 D and MAE, respectively. With regard to the percentage of eyes with a PE within ±0.50 D, the Barrett True-K formula was statistically better than the Wang/Koch/Maloney, Shammas-PL, and Haigis-L formulas (*P* < .05). With respect to the percentage of eyes with a PE within ±1.00 D, the Fourier-Domain OCT-Based formula was significantly superior to the Wang/Koch/Maloney formula, and the Barrett True-K formula was significantly superior when compared to the Wang/Koch/Maloney and Haigis-L formulas (*P* < .05).

Table O: Meta-analysis results in subgroup analysis |

Table P: Results of network rank test in percentage of eyes within ±0.50 D of the prediction error in subgroup analysis |

Table Q: Results of network rank test in percentage of eyes within ±1.00 D of the prediction error in subgroup analysis |

Table R: Results of network rank test in mean absolute error in subgroup analysis |

Table S: Node-splitting analysis of inconsistency in subgroup analysis |

Figure H. The funnel plot of the prediction refractive error within ±0.50 D in subgroup analysis. |

Figure I. The funnel plot of the prediction refractive error within ±1.00 D in subgroup analysis. |

Figure J. The funnel plot of the mean absolute error in subgroup analysis. |

### Discussion

This is the first network meta-analysis to evaluate the accuracy of no-history formulas for IOL power calculation in eyes with previous corneal laser refractive surgery. The network meta-analysis demonstrated that Okulix, ORA, BESSt, and Triple-S (D-K SRK/T) formulas can be considered the most accurate options based on the percentage of eyes with a PE within ±0.50 or ±1.00 D. When looking at the MAE, the BESSt, Triple-S (with Double-K SRK/T), ORA, and Fourier-Domain OCT-Based formulas were the most accurate solutions. With regard to the MedAE, the lowest values were provided by the SToP (SRK/T), ORA, Fourier-Domain OCT-Based, and BESSt formulas. Considering all outcome measurement results, the ORA, BESSt, and Triple-S formulas were the most optimal choices to calculate IOL power in eyes having had previous corneal laser refractive surgery.

The current network meta-analysis found that Okulix software (Okulix, version 9.04; Tedics Peric & Joher GbR) developed to calculate the IOL power using ray-tracing based on corneal topography performs well when considering the percentage of eyes with a PE within ±0.50 or ±1.00 D. The good outcome may be related to the fact that, if the curvature measurements of both corneal surfaces are available, ray-tracing is not affected with the keratometric index error. Moreover, it accounts for spherical aberration. Also, when looking at the MedAE, ray-tracing is still considered an alternative option with acceptable results. However, Rabsilber et al^{43} evaluated IOL power calculations using ray-tracing in 10 eyes presenting with cataract after corneal laser refractive surgery and found slightly higher PE in those eyes with corneal radii exceeding 10 mm. Surgeons should be alert and carefully consider it when choosing the appropriate IOL power in individual cases.

The Fourier-Domain OCT-Based formula, which is also based on corneal topography to calculate the IOL power, provided a low MAE and MedAE. Good results are likely to be related to the use of the net corneal power. Good repeatability for the corneal power using the RTVue (Optovue Inc) has been reported in previous studies.^{21,44} The Fourier-Domain OCT-Based formula uses a Gaussian optical vergence model of the eye, not ray-tracing, which is the main difference compared to Okulix. Although the percentage of eyes with a PE within ±0.50 or ±1.00 D is not as high as with Okulix, it is still high and comparable to the benchmark standards for refractive outcomes after cataract surgery in the general population (National Health Service in the United Kingdom^{45} and Swedish National Cataract Register Study^{46}). The benchmark standards are: 55% of eyes with a PE within ±0.50 D and 85% with a PE within ±1.00 D. Further subgroup analyses with regard to the percentage of eyes with a PE within ±1.00 D also showed that the IOL power was more accurate using the Fourier-Domain OCT-Based formula.

ORA and the BESSt (with Double-K SRK/T) formulas provided the highest percentages of eyes with a PE within ±0.50 D, as well as the lowest MAE and MedAE. Unlike the two formulas mentioned above, the ORA and BESSt use different principles. The ORA system is specifically designed and calibrated to calculate the IOL power based on the aphakic formula to estimate the effective lens position.^{24} The BESSt formula modifies the keratometry readings according to the posterior/anterior corneal radius ratio and central corneal thickness,^{31} and these values are then entered into the Double-K SRK/T formula. As we all know, the keratometric value before refractive surgery is more valuable than the keratometric value after refractive surgery for estimating the effective lens position with the Double-K formula, which has high IOL power prediction accuracy.^{8,47} This makes it difficult when the preoperative data are not available. The estimation method of the keratometric value after refractive surgery from the BESSt formula has been combined with a modified effective lens position estimation method to augment IOL prediction accuracy.^{48} The Triple-S (D-K SRK/T) formula also performed well except in the MedAE.

It is worth mentioning that there are many other no-history methods that show good results in many studies, such as the anterior-posterior method and the central-peripheral method described by Saiki et al.^{14,15} Yet the above two methods did not adjust the keratometric values after LASIK, but used the value directly provided by the Pentacam (Oculus Optikgeräte GmbH), which is affected by the keratometric index error. For this reason, we decided to exclude these two formulas.

This network meta-analysis has several limitations inherent to the methodology applied. First, the included trials were conducted in Europe, Asia, and North America. Therefore, it is unclear whether the conclusions of our study apply to other populations. Second, both eyes of some patients were included and between-eye correlation is a potential limitation of the current analysis. Third, inconsistency was found in the network meta-analysis, which may be related to the above characteristic differences between the studies and the lack of research numbers and sample sizes. In addition, the methods such as SToP (SRK/T) and SToP (Holladay 1) only had one relevant study. The range of the CI in meta-analyses depends on the precision of the individual study estimates, which is influenced by the sample size and number of studies combined.^{13} Hence, insufficient studies and small sample size may affect the reliability of our results. To account for this, we did subgroup analyses looking at methods that have been used in at least 3 studies and 100 eyes. Although only six formulas were included, the results of the subgroup analysis were approximately consistent with parts of our network meta-analysis and support our conclusions. Other formulas not involved need to be further studied to confirm the accuracy of those methods.

On the basis of evidence from this network meta-analysis, the following evidence-based guidelines might be proposed: ORA, BESSt, and Triple-S (D-K SRK/T) formulas provided the highest percentages of eyes with a PE within ±0.50 and ±1.00 D, as well as the lowest MAE and MedAE.

### References

- Hoffer KJ. Intraocular lens power calculation after previous laser refractive surgery.
*J Cataract Refract Surg*. 2009;35(4):759–765. doi:10.1016/j.jcrs.2009.01.005 [CrossRef] - Haigis W. Intraocular lens calculation after refractive surgery for myopia: Haigis-L formula.
*J Cataract Refract Surg*. 2008;34(10):1658–1663. doi:10.1016/j.jcrs.2008.06.029 [CrossRef] - Wang L, Hill WE, Koch DD. Evaluation of intraocular lens power prediction methods using the American Society of Cataract and Refractive Surgeons Post-Keratorefractive Intraocular Lens Power Calculator.
*J Cataract Refract Surg*. 2010;36(9):1466–1473. doi:10.1016/j.jcrs.2010.03.044 [CrossRef] - Chen X, Yuan F, Wu L. Metaanalysis of intraocular lens power calculation after laser refractive surgery in myopic eyes.
*J Cataract Refract Surg*. 2016;42(1):163–170. doi:10.1016/j.jcrs.2015.12.005 [CrossRef] - Liu Xiaomin HY. Comparison of methods to calculate IOL power after corneal refractive surgery without history data.
*Zhonghua Yanshi Guangxue Yu Shijue Kexue Zazhi*. 2017;19(1):53–57. - Yang R, Yeh A, George MR, Rahman M, Boerman H, Wang M. Comparison of intraocular lens power calculation methods after myopic laser refractive surgery without previous refractive surgery data.
*J Cataract Refract Surg*. 2013;39(9):1327–1335. doi:10.1016/j.jcrs.2013.03.032 [CrossRef] - Hutton B, Salanti G, Caldwell DM, et al. The PRISMA extension statement for reporting of systematic reviews incorporating network meta-analyses of health care interventions: checklist and explanations.
*Ann Intern Med*. 2015;162(11):777–784. doi:10.7326/M14-2385 [CrossRef] - Aramberri J. Intraocular lens power calculation after corneal refractive surgery: double-K method.
*J Cataract Refract Surg*. 2003;29(11):2063–2068. doi:10.1016/S0886-3350(03)00957-X [CrossRef] - Moga C, Guo B, Schopflocher D, Harstall C.
*Development of a quality appraisal tool for case series studies using a modified delphi technique*. 2013. - Higgins JP, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in meta-analyses.
*BMJ*. 2003;327(7414):557–560. doi:10.1136/bmj.327.7414.557 [CrossRef] - Siontis GCM, Stefanini GG, Mavridis D, et al. Percutaneous coronary interventional strategies for treatment of in-stent restenosis: a network meta-analysis.
*Lancet*. 2015;386(9994):655–664. doi:10.1016/S0140-6736(15)60657-2 [CrossRef] - Dias S, Welton NJ, Caldwell DM, Ades AE. Checking consistency in mixed treatment comparison meta-analysis.
*Stat Med*. 2010;29(7–8):932–944. doi:10.1002/sim.3767 [CrossRef] - Egger M, Davey Smith G, Schneider M, Minder C. Bias in meta-analysis detected by a simple, graphical test.
*BMJ*. 1997;315(7109):629–634. doi:10.1136/bmj.315.7109.629 [CrossRef] - Saiki M, Negishi K, Kato N, et al. A new central-peripheral corneal curvature method for intraocular lens power calculation after excimer laser refractive surgery.
*Acta Ophthalmol*. 2013;91(2):e133–e139. doi:10.1111/aos.12007 [CrossRef] - Saiki M, Negishi K, Kato N, et al. Modified double-K method for intraocular lens power calculation after excimer laser corneal refractive surgery.
*J Cataract Refract Surg*. 2013;39(4):556–562. doi:10.1016/j.jcrs.2012.10.044 [CrossRef] - Saiki M, Negishi K, Kato N, Torii H, Dogru M, Tsubota K. Ray tracing software for intraocular lens power calculation after corneal excimer laser surgery.
*Jpn J Ophthalmol*. 2014;58(3):276–281. doi:10.1007/s10384-014-0304-x [CrossRef] - Savini G, Hoffer KJ, Schiano-Lomoriello D, Barboni P. Intraocular lens power calculation using a Placido disk-Scheimpflug tomographer in eyes that had previous myopic corneal excimer laser surgery.
*J Cataract Refract Surg*. 2018;44(8):935–941. doi:10.1016/j.jcrs.2018.05.018 [CrossRef] - Savini G, Barboni P, Carbonelli M, Ducoli P, Hoffer KJ. Intraocular lens power calculation after myopic excimer laser surgery: selecting the best method using available clinical data.
*J Cataract Refract Surg*. 2015;41(9):1880–1888. doi:10.1016/j.jcrs.2015.10.026 [CrossRef] - Savini G, Hoffer K, Barboni P, Balducci N, Schiano-Lomoriello D. Validation of the SToP formula for calculating intraocular lens power in eyes with previous myopic excimer laser surgery.
*J Cataract Refract Surg*. 2019;45(11):1562–1567. doi:10.1016/j.jcrs.2019.06.011 [CrossRef] - Tang M, Wang L, Koch DD, Li Y, Huang D. Intraocular lens power calculation after myopic and hyperopic laser vision correction using optical coherence tomography.
*Saudi J Ophthalmol*. 2012;26(1):19–24. doi:10.1016/j.sjopt.2011.10.004 [CrossRef] - Wang L, Tang M, Huang D, Weikert MP, Koch DD. Comparison of newer intraocular lens power calculation methods for eyes after corneal refractive surgery.
*Ophthalmology*. 2015;122(12):2443–2449. doi:10.1016/j.ophtha.2015.08.037 [CrossRef] - Abulafia A, Hill WE, Koch DD, Wang L, Barrett GD. Accuracy of the Barrett True-K formula for intraocular lens power prediction after laser in situ keratomileusis or photorefractive keratectomy for myopia.
*J Cataract Refract Surg*. 2016;42(3):363–369. doi:10.1016/j.jcrs.2015.11.039 [CrossRef] - Huang D, Tang M, Wang L, et al. Optical coherence tomography-based corneal power measurement and intraocular lens power calculation following laser vision correction (An American Ophthalmological Society thesis).
*Trans Am Ophthalmol Soc*. 2013;111:34–45. - Ianchulev T, Hoffer KJ, Yoo SH, et al. Intraoperative refractive biometry for predicting intraocular lens power calculation after prior myopic refractive surgery.
*Ophthalmology*. 2014;121(1):56–60. doi:10.1016/j.ophtha.2013.08.041 [CrossRef] - Kang BS, Han JM, Oh JY, Kim MK, Wee WR. Intraocular lens power calculation after refractive surgery: a comparative analysis of accuracy and predictability.
*Korean J Ophthalmol*. 2017;31(6):479–488. doi:10.3341/kjo.2016.0078 [CrossRef] - Potvin R, Hill W. New algorithm for intraocular lens power calculations after myopic laser in situ keratomileusis based on rotating Scheimpflug camera data.
*J Cataract Refract Surg*. 2015;41(2):339–347. doi:10.1016/j.jcrs.2014.05.040 [CrossRef] - Cho K, Lim DH, Yang CM, Chung ES, Chung TY. Comparison of intraocular lens power calculation methods following myopic laser refractive surgery: new options using a rotating Scheimpflug camera.
*Korean J Ophthalmol*. 2018;32(6):497–505. doi:10.3341/kjo.2018.0008 [CrossRef] - Vrijman V, Abulafia A, van der Linden JW, van der Meulen IJE, Mourits MP, Lapid-Gortzak R. Evaluation of different IOL calculation formulas of the ASCRS calculator in eyes after corneal refractive laser surgery for myopia with multifocal IOL implantation.
*J Refract Surg*. 2019;35(1):54–59. doi:10.3928/1081597X-20181119-01 [CrossRef] - Wang L, Spektor T, de Souza RG, Koch DD. Evaluation of total keratometry and its accuracy for intraocular lens power calculation in eyes after corneal refractive surgery.
*J Cataract Refract Surg*. 2019;45(10):1416–1421. doi:10.1016/j.jcrs.2019.05.020 [CrossRef] - Wu Y, Liu S, Liao R. Prediction accuracy of intraocular lens power calculation methods after laser refractive surgery.
*BMC Ophthalmol*. 2017;17(1):44. doi:10.1186/s12886-017-0439-x [CrossRef] - Borasio E, Stevens J, Smith GT. Estimation of true corneal power after keratorefractive surgery in eyes requiring cataract surgery: BESSt formula.
*J Cataract Refract Surg*. 2006;32(12):2004–2014. doi:10.1016/j.jcrs.2006.08.037 [CrossRef] - Holladay JT, Hill WE, Steinmueller A. Corneal power measurements using scheimpflug imaging in eyes with prior corneal refractive surgery.
*J Refract Surg*. 2009;25(10):862–868. doi:10.3928/1081597X-20090917-07 [CrossRef] - Ferrara G, Cennamo G, Marotta G, Loffredo E. New formula to calculate corneal power after refractive surgery.
*J Refract Surg*. 2004;20(5):465–471. doi:10.3928/1081-597X-20040901-09 [CrossRef] - Tang M, Li Y, Huang D. An intraocular lens power calculation formula based on optical coherence tomography: a pilot study.
*J Refract Surg*. 2010;26(6):430–437. doi:10.3928/1081597X-20090710-02 [CrossRef] - Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone laser-assisted in-situ keratomileusis.
*Trans Am Ophthalmol Soc*. 2004;102:189–196. - Rosa N, De Bernardo M, Borrelli M, Lanza M. New factor to improve reliability of the clinical history method for intraocular lens power calculation after refractive surgery.
*J Cataract Refract Surg*. 2010;36(12):2123–2128. doi:10.1016/j.jcrs.2010.07.017 [CrossRef] - Preussner PR, Wahl J, Lahdo H, Dick B, Findl O. Ray tracing for intraocular lens calculation.
*J Cataract Refract Surg*. 2002;28(8):1412–1419. doi:10.1016/S0886-3350(01)01346-3 [CrossRef] - Savini G, Barboni P, Zanini M. Intraocular lens power calculation after myopic refractive surgery: theoretical comparison of different methods.
*Ophthalmology*. 2006;113(8):1271–1282. doi:10.1016/j.ophtha.2006.03.024 [CrossRef] - Shammas HJ, Shammas MC, Garabet A, Kim JH, Shammas A, LaBree L. Correcting the corneal power measurements for intraocular lens power calculations after myopic laser in situ keratomileusis.
*Am J Ophthalmol*. 2003;136(3):426–432. doi:10.1016/S0002-9394(03)00275-7 [CrossRef] - Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW, Ruiz RS. A three-part system for refining intraocular lens power calculations.
*J Cataract Refract Surg*. 1988;14(1):17–24. doi:10.1016/S0886-3350(88)80059-2 [CrossRef] - Schuster AK, Schanzlin DJ, Thomas KE, Heichel CW, Purcell TL, Barker PD. Intraocular lens calculation adjustment after laser refractive surgery using Scheimpflug imaging.
*J Cataract Refract Surg*. 2016;42(2):226–231. doi:10.1016/j.jcrs.2015.09.024 [CrossRef] - Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula.
*J Cataract Refract Surg*. 1990;16(3):333–340. doi:10.1016/S0886-3350(13)80705-5 [CrossRef] - Rabsilber TM, Reuland AJ, Holzer MP, Auffarth GU. Intraocular lens power calculation using ray tracing following excimer laser surgery.
*Eye (Lond)*. 2007;21(6):697–701. doi:10.1038/sj.eye.6702300 [CrossRef] - Tang M, Chen A, Li Y, Huang D. Corneal power measurement with Fourier-domain optical coherence tomography.
*J Cataract Refract Surg*. 2010;36(12):2115–2122. doi:10.1016/j.jcrs.2010.07.018 [CrossRef] - Gale RP, Saldana M, Johnston RL, Zuberbuhler B, McKibbin M. Benchmark standards for refractive outcomes after NHS cataract surgery.
*Eye (Lond)*. 2009;23(1):149–152. doi:10.1038/sj.eye.6702954 [CrossRef] - Behndig A, Montan P, Stenevi U, Kugelberg M, Zetterström C, Lundström M. Aiming for emmetropia after cataract surgery: Swedish National Cataract Register study.
*J Cataract Refract Surg*. 2012;38(7):1181–1186. doi:10.1016/j.jcrs.2012.02.035 [CrossRef] - Walter KA, Gagnon MR, Hoopes PC Jr, Dickinson PJ. Accurate intraocular lens power calculation after myopic laser in situ keratomileusis, bypassing corneal power.
*J Cataract Refract Surg*. 2006;32(3):425–429. doi:10.1016/j.jcrs.2005.12.140 [CrossRef] - Ho JD, Liou SW, Tsai RJ, Tsai CY. Estimation of the effective lens position using a rotating Scheimpflug camera.
*J Cataract Refract Surg*. 2008;34(12):2119–2127. doi:10.1016/j.jcrs.2008.08.030 [CrossRef] - Savini G, Hoffer KJ, Schiano-Lomoriello D, Ducoli P. Estimating the preoperative corneal power with scheimpflug imaging in eyes that have undergone myopic LASIK.
*J Refract Surg*. 2016;32(5):332–336. doi:10.3928/1081597X-20160225-03 [CrossRef] - Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK.
*Ophthalmology*. 2004;111(10):1825–1831. doi:10.1016/j.ophtha.2004.04.022 [CrossRef]

Brief Description and Abbreviations for the Formulas Included in the Network Meta-analysis

^{a} | ||
---|---|---|

Barrett Universal II | ||

Barrett True-K | – | Based on an unpublished modification of Barrett Universal II formula. |

Double-K | ||

BESSt | – | Modifies corneal power measurements obtained by a rotating Scheimpflug camera. The calculated value can then be entered into a Double-K formula. |

Total Corneal Power 1 | TCP 1 | The value provided by the option Total Corneal Power 1 uses the Double-K Holladay 1 formula. |

Equivalent K Reading at 4.5 mm using the Double-K Holladay 1 | EKR 4.5 mm (D-K Holladay 1) | Calculated by the Scheimpflug camera and then entered into the Double-K Holladay 1 formula. |

Wang/Koch/Maloney | – | Modified Maloney method and uses the Double-K Holladay 1 formula. |

Maloney with Double-K SRK/T | Maloney (D-K SRK/T) | The adjusted corneal power is entered into the Double-K SRK/T formula. |

Seitz/Speicher/Savini (with Double-K SRK/T) | Triple-S | Modifies the measured post-laser refractive surgery keratometryand uses the Double-K SRK/T formula. |

SRK/T | ||

Ferrara | – | Uses a variable index, correlated to the axial length, to calculate corneal power, and is entered into the SRK/T formula. |

OCT system | ||

Fourier-Domain OCT-Based | OCT | Based on a Gaussian optical vergence model of the eye. |

Haigis | ||

Haigis-L | – | Modifies the measured anterior corneal radius. |

Total Corneal Refractive Power at 4 mm with the Haigis | TCRP 4 mm (Haigis) | The corneal power at 4 mm is calculated by ray-tracing through both anterior corneal surfaces, based on a Scheimpflug camera. |

Koch-Maloney with Haigis | K-M (Haigis) | Modified version of the original Maloney method. |

Shammas | ||

Hill-Potvin-Shammas | – | Based on the “true net power” in the 4-mm zone. |

Shammas-PL | – | Adjusted corneal power and then entered into the Shammas-PL formula. |

Rosa | ||

Modified Rosa | Rosa (R) | Modifies the original Rosa formula and uses a regression formula based on axial length and keratometry. |

Ray-tracing | ||

Ray-tracing (Okulix) | Okulix | Using ray-tracing based on corneal topography. |

Aberrometry | ||

Intraoperative aberrometry (Optiwave Refractive Analysis) | ORA | Based on the measurements of the intraoperative aphakic refraction. |

SToP | ||

SToP (Holladay 1)/SToP (SRK/T) | – | Adjust the lens power according to the posterior/anterior cornealradius ratio and (for the Holladay 1 only) the axial length. |

PRISMA 2009 Checklist

Title | 1 | Identify the report as a systematic review, meta-analysis, or both. | 1 |

Structured summary | 2 | Provide a structured summary including, as applicable: background; objectives; data sources; study eligibility criteria, participants, and interventions; study appraisal and synthesis methods; results; limitations; conclusions and implications of key findings; systematic review registration number. | 1 |

Rationale | 3 | Describe the rationale for the review in the context of what is already known. | 2 |

Objectives | 4 | Provide an explicit statement of questions being addressed with reference to participants, interventions, comparisons, outcomes, and study design (PICOS). | 2 |

Protocol and registration | 5 | Indicate if a review protocol exists, if and where it can be accessed (e.g., Web address), and, if available, provide registration information including registration number. | - |

Eligibility criteria | 6 | Specify study characteristics (e.g., PICOS, length of follow-up) and report characteristics (e.g., years considered, language, publication status) used as criteria for eligibility, giving rationale. | 2 |

Information sources | 7 | Describe all information sources (e.g., databases with dates of coverage, contact with study authors to identify additional studies) in the search and date last searched. | 2 |

Search | 8 | Present full electronic search strategy for at least one database, including any limits used, such that it could be repeated. | 2 |

Study selection | 9 | State the process for selecting studies (i.e., screening, eligibility, included in systematic review, and, if applicable, included in the meta-analysis). | 2 |

Data collection process | 10 | Describe method of data extraction from reports (e.g., piloted forms, independently, in duplicate) and any processes for obtaining and confirming data from investigators. | 2–3 |

Data items | 11 | List and define all variables for which data were sought (e.g., PICOS, funding sources) and any assumptions and simplifications made. | 2–3 |

Risk of bias in individual studies | 12 | Describe methods used for assessing risk of bias of individual studies (including specification of whether this was done at the study or outcome level), and how this information is to be used in any data synthesis. | 3 |

Summary measures | 13 | State the principal summary measures (e.g., risk ratio, difference in means). | 3 |

Synthesis of results | 14 | Describe the methods of handling data and combining results of studies, if done, including measures of consistency (e.g., I^{2}) for each meta-analysis. | 3 |

Risk of bias across studies | 15 | Specify any assessment of risk of bias that may affect the cumulative evidence (e.g., publication bias, selective reporting within studies). | 3 |

Additional analyses | 16 | Describe methods of additional analyses (e.g., sensitivity or subgroup analyses, meta-regression), if done, indicating which were pre-specified. | 3 |

Study selection | 17 | Give numbers of studies screened, assessed for eligibility, and included in the review, with reasons for exclusions at each stage, ideally with a flow diagram. | 3 |

Study characteristics | 18 | For each study, present characteristics for which data were extracted (e.g., study size, PICOS, follow-up period) and provide the citations. | 3–5 |

Risk of bias within studies | 19 | Present data on risk of bias of each study and, if available, any outcome level assessment (see item 12). | 5 |

Results of individual studies | 20 | For all outcomes considered (benefits or harms), present, for each study: (a) simple summary data for each intervention group (b) effect estimates and confidence intervals, ideally with a forest plot. | 5 |

Synthesis of results | 21 | Present results of each meta-analysis done, including confidence intervals and measures of consistency. | 5–7 |

Risk of bias across studies | 22 | Present results of any assessment of risk of bias across studies (see Item 15). | 7 |

Additional analysis | 23 | Give results of additional analyses, if done (e.g., sensitivity or subgroup analyses, meta-regression [see Item 16]). | 7 |

Summary of evidence | 24 | Summarize the main findings including the strength of evidence for each main outcome; consider their relevance to key groups (e.g., healthcare providers, users, and policy makers). | 7–8 |

Limitations | 25 | Discuss limitations at study and outcome level (e.g., risk of bias), and at review-level (e.g., incomplete retrieval of identified research, reporting bias). | 8 |

Conclusions | 26 | Provide a general interpretation of the results in the context of other evidence, and implications for future research. | 8 |

Funding | 27 | Describe sources of funding for the systematic review and other support (e.g., supply of data); role of funders for the systematic review. | 1 |

Search Strategy

--------------------------------------- |

#1 “Haigis” or “Hamed” or “hard contact lens” or “Ianchulev” or “Geggel” (Word variations have been searched) |

#2 “Actual K” or Awwad or BESSt or “Ray Tracing” or “Ferrara” (Word variations have been searched) |

#3 “Kim” or Leccisotti or Mackool or Maloney or “Maloney-Koch-Wang” (Word variations have been searched) |

#4 “Maloney/Koch/Wang” or “Razmjoo Regression” or Ronje or Saiki or “Seitz-Speicher-Savini” (Word variations have been searched) |

#5 “Seitz/Speicher/Savini” or “Savini-Barboni-Zannini” or “Savini/Barboni/Zannini” or Shammas or “Wang” (Word variations have been searched) |

#6 “Wang-Koch-Maloney” or “Wang/Koch/Maloney” or “Barrett True-K” or “Rosa” or “Sirius” (Word variations have been searched) |

#7 okulix or OCT or “optical coherence tomography” or Borasio or “Soper and Goffman” (Word variations have been searched) |

#8 “Soper-Goffman” or “Soper/Goffman” or SToP (Word variations have been searched) |

#9 “Optiwave Refractive Analysis” OR ORA OR “Total Corneal Power (Word variations have been searched)1” OR “Equivalent K-reading” OR EKR |

#10 “total corneal refractive power” OR “true net corneal power” OR “total mean power” (Word variations have been searched) |

#11 #1 or #2 or #3 or #4 or #5 or #6 or #7 or #8 or #9 or #10 |

#12 “intraocular lens power calculation” (Word variations have been searched) |

#13 formula* or calculate* (Word variations have been searched) |

#14 MeSH descriptor: [Corneal Surgery, Laser] explode all trees |

#15 cornea* or kerato* or “keratectomy” or Lase* (Word variations have been searched) |

#16 “refractive surgery” (Word variations have been searched) |

#17 #15 and #16 |

#18 #14 or #17 |

#19 MeSH descriptor: [Lenses, Intraocular] explode all trees |

#20 “intraocular lens” or IOL (Word variations have been searched) |

#21 MeSH descriptor: [Cataract] explode all trees |

#22 #19 or #20 or #21 |

#23 #22 and #13 |

#24 #12 or #23 |

#25 #11 and #24 and #18 |

‘Actual K’ Awwad BESSt ‘Ray Tracing’ Ferrara Feiz Haigis Hamed ‘Hard Contact Lens’ Ianchulev Geggel Kim Leccisotti Mackool Maloney ‘Maloney-Koch-Wang’ ‘Maloney/Koch/Wang’ ‘Razmjoo Regression’ Ronje Saiki ‘Seitz-Speicher-Savini’ ‘Seitz/Speicher/Savini’ ‘Savini-Barboni-Zannini’ ‘Savini/Barboni/Zannini’ Shammas Wang ‘Wang-Koch-Maloney’ ‘Wang/Koch/Maloney’ ‘Barrett True-K’ Rosa Sirius okulix OCT ‘optical coherence tomography’ Borasio ‘Soper and Goffman’ ‘Soper-Goffman’ ‘Soper/Goffman’ StoP ‘Optiwave Refractive Analysis’ ORA ‘Total Corneal Power 1’ ‘Equivalent K-reading’ EKR ‘total corneal refractive power’ ‘true net corneal power’ ‘total mean power’ OR/1-47 ‘Lenses, Intraocular’/exp ‘intraocular lens’ IOL ‘Cataract’/exp OR/49-52 formula* calculat* OR/54-55 53 AND 56 ‘intraocular lens power calculation’ OR/57-58 cornea* kerato* Keratectomy Lase* OR/60-63 ‘refractive surgery’ 64 AND 65 ‘Corneal Surgery, Laser’/exp 57 AND 58 48 AND 59 AND 68 |

Summary of studies included in the network meta-analysis

Study (Author, Year) | Country | Treatment | Age (Mean±SD, y) | Male | Total | Corneal Power (K, D) | Axial Length (mm) | Follow-up | Formula | No.Eye | Percentage of IOL Prediction Error (%) | MAE (D, Mean±SD) | MeAE (D) | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Within±0.50D | Within±1.00D | |||||||||||||

Abulafia 2016 | USA | LASIK/PRK | 58±7 | 26 | 25.69±1.25 | 3w | Shammas-PL | 30 | 50 | 80 | 0.63±0.48 | 0.53 | ||

Haigis-L | 30 | 46.7 | 76.7 | 0.68±0.45 | 0.62 | |||||||||

Barrett True-K | 30 | 63.3 | 80 | 0.52±0.43 | 0.41 | |||||||||

Cho 2018 | Korea | 54.6±9.37 | 21 | 56 | 39.73±2.23 | 27.08±2.50 | 3m | Wang/Koch/Maloney | 56 | 33.9 | 55.4 | 0.94±0.74 | ||

Shammas-PL | 56 | 37.5 | 58.9 | 0.92±0.74 | ||||||||||

Haigis-L | 56 | 58.9 | 85.7 | 0.51±0.44 | ||||||||||

TCRP 4mm (Haigis) | 56 | 42.6 | 70.37 | 0.82±0.70 | ||||||||||

Barrett True-K | 56 | 57.4 | 75.9 | 0.66±0.63 | ||||||||||

Huang 2013 | USA | LASIK/PRK/LASEK | 61.5±8.0 | 46 | OCT | 46 | 59 | 89 | 0.5 | |||||

Haigis-L | 46 | 46 | 78 | 0.67 | ||||||||||

Shammas-PL | 46 | 46 | 85 | 0.67 | ||||||||||

Ianchulev 2014 | USA | LASIK/PRK | 215 | Haigis-L | 246 | 48 | 80 | 0.65±0.58 | ||||||

ORA | 246 | 67 | 94 | 0.42±0.39 | ||||||||||

Shammas-PL | 246 | 50 | 87 | 0.59±0.52 | ||||||||||

Kang 2017 | Korea | LASIK/PRK/LASEK | 53.1±10.3 | 21 | 68 | 38.25±2.25 | 28.1±2.4 | Triple-S | 68 | 0.50 | ||||

Maloney (D-K SRK/T) | 68 | 0.56 | ||||||||||||

Shammas-PL | 68 | 0.72 | ||||||||||||

Barrett True-K | 68 | 0.66 | ||||||||||||

Haigis-L | 68 | 1.01 | ||||||||||||

Potvin 2015 | USA | LASIK/PRK | 77 | 40.92±2.26 | 25.83±1.36 | Haigis-L | 101 | 58 | 92 | |||||

Shammas-PL | 101 | 57 | 90 | |||||||||||

Hill-Potvin-Shammas | 101 | 66 | 91 | |||||||||||

Wang/Koch/Maloney | 101 | 50 | 86 | |||||||||||

Saiki 2013 | Japan | LASIK | 54.0±9.9 | 12 | 16 | 26.39±0.99 | 1m | Haigis-L | 23 | 26 | 52 | 0.95 | ||

Shammas-PL | 25 | 20 | 72 | 0.77 | ||||||||||

Saiki 2013 | Japan | LASIK | 54.1±9.8 | 14 | 19 | 26.19±1.06 | 1m | Haigis-L | 25 | 24 | 52 | 0.95 | ||

Shammas-PL | 28 | 25 | 71 | 0.77 | ||||||||||

Saiki 2014 | Japan | LASIK | 54.0±10.6 | 11 | 17 | 26.47±1.12 | 1m | OKULIX | 24 | 41.7 | 75 | 0.62 | ||

Shammas-PL | 24 | 20.8 | 66.9 | 0.8 | ||||||||||

Haigis-L | 21 | 18.8 | 43.1 | 1.13 | ||||||||||

Savini 2015 | Italy | PRK/LASIK | 27.82±1.78 | Shammas-PL | 6 | 83.3 | 0.31 | |||||||

Triple-S | 6 | 50 | 0.41 | |||||||||||

Rosa (R) | 6 | 0 | 1.05 | |||||||||||

Ferrara | 6 | 0 | 2.09 | |||||||||||

Savini 2018 | Italy | PRK | 56.4±8.3 | 22 | 26.7±1.7 | OKULIX | 22 | 63.6 | 90.9 | 0.31 | ||||

Shammas-PL | 22 | 36.4 | 68.2 | 0.79 | ||||||||||

TCP 1 | 22 | 54.5 | 86.4 | 0.39 | ||||||||||

Barrett True-K | 22 | 63.6 | 86.4 | 0.45 | ||||||||||

Savini 2019 | Italy | 58.2±7.9 | 50 | 42.80±1.72 | 27.17±1.57 | SToP (SRK/T) | 50 | 62 | 84 | 0.49 | 0.31 | |||

SToP (Holladay 1) | 50 | 60 | 78 | 0.55 | 0.45 | |||||||||

Shammas-PL | 50 | 54 | 76 | 0.68 | 0.48 | |||||||||

Barrett True-K | 50 | 52 | 88 | 0.57 | 0.49 | |||||||||

Triple-S | 50 | 70 | 96 | 0.4 | 0.31 | |||||||||

EKR 4.5mm (D-K Holladay1) | 50 | 44 | 82 | 0.61 | 0.59 | |||||||||

BESSt | 50 | 68 | 92 | 0.42 | 0.37 | |||||||||

Tang 2012 | USA | myopic LASIK/PRK | 59.4±11.9 | 16 | 1m | Haigis-L | 22 | 72.7 | 0.73 | |||||

OCT | 22 | 81.8 | 0.57 | |||||||||||

Wang 2010 | USA | PRK/LASIK | 58±8 | 57 | 26.19±1.55 | 3w | Wang/Koch/Maloney | 72 | 58 | 96 | 0.66±0.48 | |||

Shammas-PL | 72 | 60 | 90 | 0.69±0.49 | ||||||||||

Haigis-L | 72 | 60 | 94 | 0.65±0.51 | ||||||||||

Wang 2015 | USA | LASIK/PRK | 63±7 | 80 | 25.46±1.30 | 3w | OCT | 104 | 68.3 | 92.3 | 0.35 | |||

Barrett True-K | 104 | 58.7 | 90.4 | 0.42 | ||||||||||

Wang/Koch/Maloney | 84 | 50 | 86.9 | 0.51 | ||||||||||

Shammas-PL | 104 | 52.9 | 88.5 | 0.48 | ||||||||||

Haigis-L | 104 | 55.8 | 90.4 | 0.49 | ||||||||||

Wang 2019 | USA | myopic LASIK/PRK | 64.5±7.1 | 37 | 25.72±1.64 | 3w | Haigis-L | 53 | 45.3 | 81.1 | 0.61 | 0.53 | ||

Barrett True-K | 53 | 52.8 | 92.5 | 0.54 | 0.37 | |||||||||

Wu 2017 | China | LASIK | 50.3±9.0 | 2 | 10 | 36.35±0.77 | 30.06±2.87 | 3m | Haigis-L | 10 | 60 | 80 | 0.604 | 0.465 |

K-M (Haigis) | 10 | 50 | 90 | 0.557 | 0.51 | |||||||||

Shammas-PL | 10 | 50 | 90 | 0.558 | 0.519 | |||||||||

Yang 2013 | USA | PRK/LASIK | 61.27±6.79 | 33 | 40.08±2.58 | 25.98±1.55 | 3–6m | Wang/Koch/Maloney | 62 | 50 | 68 | 0.94±0.48 | ||

40.20±2.44 | Shammas-PL | 62 | 45 | 71 | 1.01±0.40 | |||||||||

40.53±2.40 | Haigis-L | 62 | 40 | 68 | 1.10±0.44 | |||||||||

Vrijman 2019 | Netherlands | LASIK/PRK/LASEK | 36 | 25.28±1.40 | Shammas-PL | 64 | 50 | 86.1 | 0.63±0.60 | 0.52 | ||||

Haigis-L | 64 | 55.6 | 86.1 | 0.58±0.56 | 0.45 | |||||||||

Barrett True-K | 64 | 69.4 | 88.9 | 0.46±0.48 | 0.33 |

The number of trials and eyes involved in each formula

Name | Number of Studies | Number of Eyes |
---|---|---|

Barrett True-K | 8 | 447 |

BESSt | 1 | 50 |

EKR 4.5mm (D-K Holladay1) | 1 | 50 |

Ferrara | 1 | 6 |

OCT | 3 | 172 |

Haigis-L | 16 | 1003 |

Hill-Potvin-Shammas | 1 | 101 |

K-M (Haigis) | 1 | 10 |

Maloney (D-K SRK/T) | 1 | 68 |

Rosa (R) | 1 | 6 |

Okulix | 2 | 46 |

ORA | 1 | 246 |

Triple-S | 3 | 124 |

Shammas-PL | 17 | 994 |

SToP (Holladay 1) | 1 | 50 |

SToP (SRK/T) | 1 | 50 |

TCP 1 | 1 | 22 |

TCRP 4mm (Haigis) | 1 | 56 |

Wang/Koch/Maloney | 5 | 375 |

Results of direct-comparison meta-analysis in percentage of eyes within ±0.50 D of prediction

Name | Number of Studies | Odds Ratio (95% CI) | I^{2} |
---|---|---|---|

Haigis-L vs Shammas-PL | 13 | 1.062 (0.876,1.287) | 0.00% |

Haigis-L vs Okulix | 1 | 0.329 (0.085,1.281) | .% |

Shammas-PL vs Okulix | 2 | 0.346 (0.143,0.839) | 0.00% |

Shammas-PL vs Triple-S | 2 | 1.099 (0.13,9.313) | 61.40% |

Shammas-PL vs Rosa (R) | 1 | 47.667 (1.597,1422.695) | .% |

Shammas-PL vs Ferrara | 1 | 47.667 (1.597,1422.695) | .% |

Triple-S vs Rosa (R) | 1 | 13 (0.511,330.477) | .% |

Triple-S vs Ferrara | 1 | 13 (0.511,330.477) | .% |

Haigis-L vs Wang/Koch/Maloney | 5 | 1.267 (0.857,1.872) | 46.30% |

Shammas-PL vs Wang/Koch/Maloney | 5 | 1.109 (0.836,1.47) | 0.00% |

Haigis-L vs K-M (Haigis) | 1 | 1.5 (0.255,8.817) | .% |

Shammas-PL vs K-M (Haigis) | 1 | 1 (0.173,5.772) | .% |

Haigis-L vs Barrett True-K | 5 | 0.776 (0.563,1.071) | 0.00% |

Shammas-PL vs Barrett True-K | 6 | 0.622 (0.452,0.857) | 3.20% |

Haigis-L vs OCT | 2 | 0.588 (0.368,0.937) | 0.00% |

Shammas-PL vs OCT | 2 | 0.543 (0.341,0.865) | 0.00% |

OCT vs Wang/Koch/Maloney | 1 | 2.152 (1.224,3.782) | .% |

OCT vs Barrett True-K | 1 | 1.517 (0.859,2.677) | .% |

Wang/Koch/Maloney vs Barrett True-K | 2 | 0.554 (0.31,0.99) | 36.90% |

Haigis-L vs ORA | 1 | 0.453 (0.314,0.652) | .% |

Shammas-PL vs ORA | 1 | 0.491 (0.341,0.707) | .% |

Haigis-L vs Hill-Potvin-Shammas | 1 | 0.713 (0.402,1.263) | .% |

Shammas-PL vs Hill-Potvin-Shammas | 1 | 0.684 (0.387,1.211) | .% |

Wang/Koch/Maloney vs Hill-Potvin-Shammas | 1 | 0.518 (0.293,0.913) | .% |

Haigis-L vs TCRP 4mm (Haigis) | 1 | 1.913 (0.903,4.053) | .% |

Shammas-PL vs TCRP 4mm (Haigis) | 1 | 0.8 (0.375,1.705) | .% |

Wang/Koch/Maloney vs TCRP 4mm (Haigis) | 1 | 0.685 (0.318,1.472) | .% |

Barrett True-K vs TCRP 4mm (Haigis) | 1 | 1.778 (0.841,3.758) | .% |

Shammas-PL vs TCP 1 | 1 | 0.476 (0.142,1.593) | .% |

Okulix vs TCP 1 | 1 | 1.458 (0.436,4.88) | .% |

Okulix vs Barrett True-K | 1 | 1 (0.293,3.416) | .% |

TCP 1 vs Barrett True-K | 1 | 0.686 (0.205,2.295) | .% |

SToP (SRK/T) vs SToP (Holladay 1) | 1 | 1.088 (0.487,2.43) | .% |

SToP (SRK/T) vs EKR 4.5mm (D-K Holladay1) | 1 | 2.077 (0.934,4.615) | .% |

SToP (SRK/T) vs BESSt | 1 | 0.768 (0.337,1.75) | .% |

SToP (SRK/T) vs Shammas-PL | 1 | 1.39 (0.626,3.084) | .% |

SToP (SRK/T) vs Triple-S | 1 | 0.699 (0.304,1.607) | .% |

SToP (SRK/T) vs Barrett True-K | 1 | 1.506 (0.679,3.339) | .% |

SToP (Holladay 1) vs EKR 4.5mm (D-K Holladay1) | 1 | 1.909 (0.862,4.227) | .% |

SToP (Holladay 1) vs BESSt | 1 | 0.706 (0.311,1.603) | .% |

SToP (Holladay 1) vs Shammas-PL | 1 | 1.278 (0.578,2.825) | .% |

SToP (Holladay 1) vs Triple-S | 1 | 0.643 (0.281,1.472) | .% |

SToP (Holladay 1) vs Barrett True-K | 1 | 1.385 (0.627,3.058) | .% |

EKR 4.5mm (D-K Holladay1) vs BESSt | 1 | 0.37 (0.164,0.836) | .% |

EKR 4.5mm (D-K Holladay1) vs Shammas-PL | 1 | 0.669 (0.304,1.472) | .% |

EKR 4.5mm (D-K Holladay1) vs Triple-S | 1 | 0.337 (0.148,0.767) | .% |

EKR 4.5mm (D-K Holladay1) vs Barrett True-K | 1 | 0.725 (0.33,1.594) | .% |

BESSt vs Shammas-PL | 1 | 1.81 (0.802,4.085) | .% |

BESSt vs Triple-S | 1 | 0.911 (0.39,2.126) | .% |

BESSt vs Barrett True-K | 1 | 1.962 (0.87,4.422) | .% |

Triple-S vs Barrett True-K | 1 | 2.154 (0.948,4.894) | .% |

Results of direct-comparison meta-analysis in percentage of eyes within ±1.00 D of prediction

Name | Number of Studies | Odds Ratio (95% CI) | I^{2} |
---|---|---|---|

Haigis-L vs Shammas-PL | 13 | 0.885 (0.611,1.281) | 43.50% |

Haigis-L vs Okulix | 1 | 0.25 (0.071,0.886) | .% |

Shammas-PL vs Okulix | 2 | 0.441 (0.151,1.288) | 9.50% |

Haigis-L vs OCT | 3 | 0.612 (0.316,1.186) | 0.00% |

Haigis-L vs Wang/Koch/Maloney | 5 | 1.667 (0.909,3.059) | 51.30% |

Shammas-PL vs Wang/Koch/Maloney | 5 | 1.128 (0.77,1.655) | 0.00% |

Haigis-L vs K-M (Haigis) | 1 | 0.444 (0.034,5.88) | .% |

Shammas-PL vs K-M (Haigis) | 1 | 1 (0.054,18.574) | .% |

Haigis-L vs Barrett True-K | 5 | 0.897 (0.544,1.479) | 9.80% |

Shammas-PL vs Barrett True-K | 6 | 0.588 (0.385,0.897) | 0.00% |

Shammas-PL vs OCT | 2 | 0.654 (0.31,1.378) | 0.00% |

OCT vs Wang/Koch/Maloney | 1 | 1.867 (0.748,4.661) | .% |

OCT vs Barrett True-K | 1 | 1.277 (0.483,3.375) | .% |

Wang/Koch/Maloney vs Barrett True-K | 2 | 0.498 (0.275,0.899) | 0.00% |

Haigis-L vs ORA | 1 | 0.261 (0.142,0.48) | .% |

Shammas-PL vs ORA | 1 | 0.434 (0.229,0.824) | .% |

Haigis-L vs Hill-Potvin-Shammas | 1 | 1.137 (0.42,3.076) | .% |

Shammas-PL vs Hill-Potvin-Shammas | 1 | 0.89 (0.346,2.293) | .% |

Wang/Koch/Maloney vs Hill-Potvin-Shammas | 1 | 0.608 (0.25,1.476) | .% |

Haigis-L vs TCRP 4mm (Haigis) | 1 | 2.615 (1.021,6.699) | .% |

Shammas-PL vs TCRP 4mm (Haigis) | 1 | 0.625 (0.287,1.364) | .% |

Wang/Koch/Maloney vs TCRP 4mm (Haigis) | 1 | 0.541 (0.249,1.174) | .% |

Barrett True-K vs TCRP 4mm (Haigis) | 1 | 1.442 (0.621,3.347) | .% |

Shammas-PL vs TCP 1 | 1 | 0.338 (0.075,1.535) | .% |

Okulix vs TCP 1 | 1 | 1.579 (0.237,10.516) | .% |

Okulix vs Barrett True-K | 1 | 1.579 (0.237,10.516) | .% |

TCP 1 vs Barrett True-K | 1 | 1 (0.179,5.596) | .% |

SToP (SRK/T) vs SToP (Holladay 1) | 1 | 1.481 (0.54,4.064) | .% |

SToP (SRK/T) vs Triple-S | 1 | 0.219 (0.044,1.088) | .% |

SToP (SRK/T) vs EKR 4.5mm (D-K Holladay1) | 1 | 1.152 (0.405,3.277) | .% |

SToP (SRK/T) vs BESSt | 1 | 0.457 (0.128,1.627) | .% |

SToP (SRK/T) vs Shammas-PL | 1 | 1.658 (0.612,4.491) | .% |

SToP (SRK/T) vs Barrett True-K | 1 | 0.716 (0.229,2.238) | .% |

SToP (Holladay 1) vs Triple-S | 1 | 0.148 (0.031,0.706) | .% |

SToP (Holladay 1) vs EKR 4.5mm (D-K Holladay1) | 1 | 0.778 (0.291,2.082) | .% |

SToP (Holladay 1) vs BESSt | 1 | 0.308 (0.091,1.046) | .% |

SToP (Holladay 1) vs Shammas-PL | 1 | 1.12 (0.441,2.844) | .% |

SToP (Holladay 1) vs Barrett True-K | 1 | 0.483 (0.164,1.43) | .% |

Triple-S vs EKR 4.5mm (D-K Holladay1) | 1 | 5.268 (1.077,25.779) | .% |

Triple-S vs BESSt | 1 | 2.087 (0.365,11.948) | .% |

Triple-S vs Shammas-PL | 1 | 7.579 (1.599,35.933) | .% |

Triple-S vs Barrett True-K | 1 | 3.273 (0.627,17.071) | .% |

EKR 4.5mm (D-K Holladay1) vs BESSt | 1 | 0.396 (0.113,1.384) | .% |

EKR 4.5mm (D-K Holladay1 vs Shammas-PL | 1 | 1.439 (0.545,3.797) | .% |

EKR 4.5mm (D-K Holladay1) vs Barrett True-K | 1 | 0.621 (0.203,1.899) | .% |

BESSt vs Shammas-PL | 1 | 3.632 (1.082,12.183) | .% |

BESSt vs Barrett True-K | 1 | 1.568 (0.414,5.935) | .% |

Results of direct-comparison meta-analysis in respect of mean absolute error

Name | Number of Studies | Weighted Mean Differences (95% CI) | I^{2} |
---|---|---|---|

Haigis-L vs OCT | 2 | 0.167 (−0.028,0.362) | 0.00% |

Haigis-L vs Shammas-PL | 8 | −0.027 (−0.132,0.079) | 56.90% |

Haigis-L vs Wang/Koch/Maloney | 3 | −0.084 (−0.392,0.224) | 88.50% |

Shammas-PL vs Wang/Koch/Maloney | 3 | 0.04 (−0.062,0.143) | 0.00% |

Haigis-L vs K-M (Haigis) | 1 | 0.047 (−0.576,0.67) | .% |

Shammas-PL vs K-M (Haigis) | 1 | 0.001 (−0.718,0.72) | .% |

Haigis-L vs Barrett True-K | 4 | 0.048 (−0.091,0.187) | 43.70% |

Shammas-PL vs Barrett True-K | 4 | 0.164 (0.048,0.28) | 0.00% |

Shammas-PL vs OCT | 1 | 0.17 (−0.12,0.46) | .% |

Haigis-L vs ORA | 1 | 0.23 (0.143,0.317) | .% |

Shammas-PL vs ORA | 1 | 0.17 (0.089,0.251) | .% |

Haigis-L vs TCRP 4mm (Haigis) | 1 | −0.31 (−0.527,−0.093) | .% |

Shammas-PL vs TCRP 4mm (Haigis) | 1 | 0.1 (−0.167,0.367) | .% |

Wang/Koch/Maloney vs Barrett True-K | 1 | 0.28 (0.025,0.535) | .% |

Wang/Koch/Maloney vs TCRP 4mm (Haigis) | 1 | 0.12 (−0.147,0.387) | .% |

Barrett True-K vs TCRP 4mm (Haigis) | 1 | −0.16 (−0.407,0.087) | .% |

SToP (SRK/T) vs SToP (Holladay 1) | 1 | −0.06 (−0.381,0.261) | .% |

SToP (SRK/T) vs Shammas-PL | 1 | −0.19 (−0.511,0.131) | .% |

SToP (SRK/T) vs Barrett True-K | 1 | −0.08 (−0.372,0.212) | .% |

SToP (SRK/T) vs BESSt | 1 | 0.07 (−0.251,0.391) | .% |

SToP (SRK/T) vs Triple-S | 1 | 0.09 (−0.231,0.411) | .% |

SToP (Holladay 1) vs Shammas-PL | 1 | −0.13 (−0.451,0.191) | .% |

SToP (Holladay 1) vs Barrett True-K | 1 | −0.02 (−0.312,0.272) | .% |

SToP (Holladay 1) vs BESSt | 1 | 0.13 (−0.191,0.451) | .% |

SToP (Holladay 1) vs Triple-S | 1 | 0.15 (−0.171,0.471) | .% |

Shammas-PL vs BESSt | 1 | 0.26 (−0.061,0.581) | .% |

Shammas-PL vs Triple-S | 1 | 0.28 (−0.041,0.601) | .% |

Barrett True-K vs BESSt | 1 | 0.15 (−0.142,0.442) | .% |

Barrett True-K vs Triple-S | 1 | 0.17 (−0.122,0.462) | .% |

BESSt vs Triple-S | 1 | 0.02 (−0.301,0.341) | .% |

A descriptive analysis for median absolute error

Name | Number of Studies | Range |
---|---|---|

SToP (SRK/T) | 1 | 0.31 |

ORA | 1 | 0.35 |

OCT | 1 | 0.35 |

BESSt | 1 | 0.37 |

TCP 1 | 1 | 0.39 |

Triple-S | 3 | 0.31–0.5 |

SToP (Holladay 1) | 1 | 0.45 |

Okulix | 2 | 0.31–0.62 |

Barrett True K | 7 | 0.33–0.66 |

K-M (Haigis) | 1 | 0.51 |

Wang/Koch/Maloney | 1 | 0.51 |

Shammas-PL | 12 | 0.31–0.8 |

Maloney (D-K SRK/T) | 1 | 0.56 |

EKR 4.5mm (D-K Holladay1) | 1 | 0.59 |

Haigis-L | 9 | 0.39–1.13 |

Rosa (R) | 1 | 1.05 |

Ferrara | 1 | 2.09 |

Results of network rank test in percentage of eyes within ±0.50 D of the prediction error

Name | SUCRA value (%) | PrBest (%) |
---|---|---|

Okulix | 85.1 | 32.7 |

ORA | 82.7 | 9.5 |

BESSt | 80 | 16.1 |

Triple-S | 78.8 | 14 |

OCT | 74.5 | 3.6 |

SToP (SRK/T) | 65.9 | 3.8 |

Hill-Potvin-Shammas | 62.1 | 1.3 |

SToP (Holladay 1) | 60.1 | 2.5 |

TCP 1 | 59.3 | 8.8 |

Barrett True-K | 58 | 0 |

Haigis-L | 36.5 | 0 |

K-M (Haigis) | 35.9 | 6 |

Shammas-PL | 32 | 0 |

TCRP 4mm (Haigis) | 29.2 | 0 |

Wang/Koch/Maloney | 23.6 | 0 |

EKR 4.5mm (D-K Holladay1) | 23.3 | 0 |

Ferrara | 6.8 | 0.9 |

Rosa (R) | 6.2 | 0.8 |

Results of network rank test in percentage of eyes within ±1.00 D of the prediction error

Name | SUCRA value (%) | PrBest (%) |
---|---|---|

Triple-S | 92 | 57.1 |

ORA | 80 | 4.7 |

BESSt | 79.6 | 9.5 |

Okulix | 74.8 | 5.7 |

TCP 1 | 64.8 | 7.9 |

OCT | 55.5 | 0 |

Barrett True-K | 54.5 | 0 |

K-M (Haigis) | 53.3 | 14.6 |

SToP (SRK/T) | 48.7 | 0.3 |

EKR 4.5mm (D-K Holladay1) | 41.2 | 0.1 |

Hill-Potvin-Shammas | 33.4 | 0.1 |

TCRP 4mm (Haigis) | 33.4 | 0 |

Shammas-PL | 29.9 | 0 |

SToP (Holladay 1) | 27.7 | 0 |

Haigis-L | 20.8 | 0 |

Wang/Koch/Maloney | 10.5 | 0 |

Results of network rank test in mean absolute error

Name | SUCRA value (%) | PrWorst (%) |
---|---|---|

Triple-S | 21.9 | 26.4 |

BESSt | 23.7 | 23.9 |

ORA | 28.3 | 10.1 |

OCT | 35.3 | 8.7 |

SToP (SRK/T) | 35.4 | 11.5 |

Barrett True-K | 44.7 | 0.2 |

SToP (Holladay 1) | 46.3 | 5.6 |

K-M (Haigis) | 59.1 | 13.4 |

Haigis-L | 69.3 | 0 |

Shammas-PL | 75.7 | 0 |

Wang/Koch/Maloney | 77.6 | 0 |

TCRP 4mm (Haigis) | 82.8 | 0.2 |

Node-splitting analysis of inconsistency in percentage of eyes within ±0.50 D of the prediction error

Name | Direct estimate (95% Cl) | Indirect estimate (95% Cl) | Overall (95% Cl) | ||||
---|---|---|---|---|---|---|---|

Coefficient | SE | Coefficient | SE | Coefficient | SE | ||

SToP (SRK/T) vs Shammas-PL | −0.3292036 | 0.4066998 | −0.7195798 | 0.4248766 | 39.04% | 0.4196981 | 0.35 |

SToP (SRK/T) vs Triple-S | 0.3577514 | 0.4244143 | −1.871226 | 1.244914 | 2.228978 | 1.249064 | 0.07 |

SToP (SRK/T) vs Barrett True-K | −0.4095051 | 0.4062235 | 0.241206 | 0.4281203 | −0.650711 | 0.4225238 | 0.12 |

SToP (Holladay 1) vs Shammas-PL | −0.2451225 | 0.4047822 | −0.6354986 | 0.423042 | 39.04% | 0.4196981 | 0.35 |

SToP (Holladay 1) vs Triple-S | 0.4418328 | 0.4225771 | −1.787145 | 1.244289 | 2.228978 | 1.249064 | 0.07 |

SToP (Holladay 1) vs Barrett True-K | −0.3254224 | 0.4043038 | 0.3252886 | 0.4262998 | −0.650711 | 0.4225238 | 0.12 |

Haigis-L vs Shammas-PL | −0.0626208 | 0.0974955 | 0.1964565 | 0.3539498 | −0.2590774 | 0.3553641 | 0.47 |

Haigis-L vs Okulix | 1.019808 | 0.5596409 | 0.6998357 | 0.55165 | 0.3199726 | 7.81E-01 | 0.68 |

Haigis-L vs Barrett True-K | 0.3660999 | 0.1487203 | 0.1676605 | 0.3402155 | 19.84% | 0.360515 | 0.58 |

EKR 4.5mm (D-K Holladay1) vs Shammas-PL | 0.4015047 | 0.4020997 | 0.0111286 | 0.4204759 | 39.04% | 0.4196981 | 0.35 |

EKR 4.5mm (D-K Holladay1) vs Triple-S | 1.08846 | 0.4200082 | −1.140518 | 1.243419 | 222.90% | 1.249064 | 0.07 |

EKR 4.5mm (D-K Holladay1) vs Barrett True-K | 0.3212048 | 0.401618 | 0.9719158 | 0.4237534 | −65.07% | 0.4225238 | 0.12 |

BESSt vs Shammas-PL | −0.5934292 | 0.4152434 | −0.9838053 | 0.4330623 | 39.04% | 0.4196981 | 0.35 |

BESSt vs Triple-S | 0.0935261 | 0.4326082 | −2.135452 | 1.247732 | 2.228978 | 1.249064 | 0.07 |

BESSt vs Barrett True-K | −6.74E-01 | 0.414777 | −0.023018 | 0.4362453 | −0.650711 | 0.4225238 | 0.12 |

Shammas-PL vs Barrett True-K | 0.3941931 | 0.1445579 | 0.3531116 | 0.401653 | 0.0410815 | 0.4175382 | 0.92 |

Okulix vs Barrett True-K | 1.41E-02 | 0.5814966 | −0.7427426 | 0.4381473 | 0.7568075 | 0.597749 | 0.21 |

TCP 1 vs Barrett True-K | 0.3772942 | 0.6162483 | −0.3795132 | 0.586693 | 0.7568075 | 0.597749 | 0.21 |

Triple-S vs Barrett True-K | −0.6487058 | 0.4119247 | 0.0020052 | 0.4223041 | −0.650711 | 0.4225238 | 0.12 |

OCT vs Wang/Koch/Maloney | −0.7360065 | 0.2694971 | −0.7904397 | 0.2477312 | 0.0544332 | 0.2689849 | 0.84 |

OCT vs Barrett True-K | −0.4007618 | 0.2716629 | −0.1198618 | 0.2552917 | −0.2809 | 0.2778881 | 0.31 |

Wang/Koch/Maloney vs Barrett True-K | 0.4527866 | 0.2027306 | 0.6096828 | 0.2200616 | −0.1568961 | 0.261623 | 0.55 |

Node-splitting analysis of inconsistency in percentage of eyes within ±1.00 D of the prediction error

Name | Direct estimate (95% Cl) | Indirect estimate (95% Cl) | Overall (95% Cl) | ||||
---|---|---|---|---|---|---|---|

Coefficient | SE | Coefficient | SE | Coefficient | SE | ||

SToP (SRK/T) vs SToP (Holladay 1) | −0.3925617 | 0.5634306 | 0.1091558 | 416.0742 | −0.5017175 | 416.0746 | 0.999 |

SToP (SRK/T) vs Triple-S | 1.519826 | 0.849551 | 2.01394 | 402.9404 | −0.4941143 | 402.9404 | 0.999 |

SToP (SRK/T) vs EKR 4.5mm (D-K Holladay1) | −0.1418806 | 0.5800042 | 0.3681856 | 394.6931 | −0.5100662 | 394.6935 | 0.999 |

SToP (SRK/T) vs BESSt | 0.784119 | 0.6874901 | 1.288312 | 420.4081 | −0.5041929 | 420.4084 | 0.999 |

SToP (SRK/T) vs Shammas-PL | −0.505549 | 0.5596836 | 0.5103421 | 1.17822 | −1.015891 | 1.274021 | 0.425 |

SToP (SRK/T) vs Barrett True-K | 0.3342011 | 0.6268902 | −0.6816827 | 1.071906 | 1.015884 | 1.274025 | 0.425 |

SToP (Holladay 1) vs Shammas-PL | −0.1129869 | 0.5300835 | 0.3949672 | 0.6424125 | −0.5079541 | 0.6370187 | 0.425 |

SToP (Holladay 1) vs Barrett True-K | 0.7267638 | 0.6006106 | 0.2188107 | 0.577018 | 0.507953 | 0.6370193 | 0.425 |

Triple-S vs Shammas-PL | −2.025374 | 0.8278114 | −1.51742 | 0.9038679 | −0.5079541 | 0.6370187 | 0.425 |

Triple-S vs Barrett True-K | −1.185624 | 0.8746521 | −1.693577 | 0.8586227 | 0.507953 | 0.6370193 | 0.425 |

EKR 4.5mm (D-K Holladay1) vs Shammas-PL | −0.363668 | 0.5476676 | 0.1442861 | 0.656997 | −0.5079541 | 0.6370187 | 0.425 |

EKR 4.5mm (D-K Holladay1) vs Barrett True-K | 0.4760827 | 0.6161853 | −0.0318704 | 0.5932124 | 0.507953 | 0.6370193 | 0.425 |

Haigis-L vs Shammas-PL | 0.1519857 | 0.1506452 | −0.5034617 | 0.4992055 | 0.6554474 | 0.4996184 | 0.19 |

Haigis-L vs Okulix | 0.9501891 | 0.6041028 | 1.41422 | 0.8664039 | −0.4640312 | 1.046748 | 0.658 |

Haigis-L vs Barrett True-K | 0.4205992 | 0.234029 | 1.020637 | 0.4914459 | −0.6000377 | 0.524455 | 0.253 |

BESSt vs Shammas-PL | −1.289667 | 0.6604374 | −0.7817134 | 0.7535801 | −0.5079541 | 0.6370187 | 0.425 |

BESSt vs Barrett True-K | −0.4499169 | 0.7182772 | −0.9578699 | 0.6986693 | 0.507953 | 0.6370193 | 0.425 |

Shammas-PL vs OCT | 0.4468762 | 0.3645876 | 0.4044012 | 0.7852912 | 0.042475 | 0.8522482 | 0.96 |

Shammas-PL vs Barrett True-K | 3.50E-01 | 0.2206134 | 0.9449886 | 0.68828 | −0.5950868 | 0.7103494 | 0.402 |

Okulix vs Barrett True-K | −0.10476 | 0.8412185 | −0.6904725 | 0.5413448 | 0.5857125 | 0.8053155 | 0.467 |

TCP 1 vs Barrett True-K | 1.95E-12 | 0.9087677 | −0.5857125 | 0.8053155 | 0.5857125 | 0.8053155 | 0.467 |

OCT vs Wang/Koch/Maloney | −0.6620631 | 0.4678593 | −0.8022948 | 0.398238 | 0.1402317 | 0.4551211 | 0.758 |

OCT vs Barrett True-K | −0.3251335 | 0.4870553 | 0.0919754 | 0.3956174 | −0.4171089 | 0.4764846 | 0.381 |

Wang/Koch/Maloney vs Barrett True-K | 0.5799617 | 0.322668 | 0.8592821 | 0.3397657 | −0.2793204 | 0.4116233 | 0.497 |

Node-splitting analysis of inconsistency in mean absolute error

Name | Direct estimate (95% Cl) | Indirect estimate (95% Cl) | Overall (95% Cl) | ||||
---|---|---|---|---|---|---|---|

Coefficient | SE | Coefficient | SE | Coefficient | SE | ||

SToP (SRK/T) vs Shammas-PL | 0.189999 | 0.1992685 | 0.2116316 | 0.202537 | −0.0216326 | 0.2025379 | 0.915 |

SToP (SRK/T) vs Barrett True-K | 0.0799985 | 0.1870084 | 0.0583617 | 0.21391 | 0.0216368 | 0.2025387 | 0.915 |

SToP (Holladay 1) vs Shammas-PL | 0.13 | 0.1992688 | 0.1516326 | 0.2025379 | −0.0216326 | 0.2025379 | 0.915 |

SToP (Holladay 1) vs Barrett True-K | 0.0200001 | 0.1870087 | −0.0016367 | 0.213911 | 0.0216368 | 0.2025387 | 0.915 |

Haigis-L vs Shammas-PL | 0.033825 | 0.0547851 | 0.0121921 | 0.2006475 | 0.0216329 | 0.2025397 | 0.915 |

Haigis-L vs Barrett True-K | −0.0978088 | 0.0727115 | −0.0761741 | 0.1948677 | −0.0216346 | 0.2025386 | 0.915 |

Shammas-PL vs OCT | −0.189883 | 0.1515766 | −0.1928339 | 0.2148565 | 0.0029509 | 0.2561543 | 0.991 |

Shammas-PL vs Barrett True-K | −0.1326214 | 0.0759552 | −0.1014412 | 0.1750405 | −0.0311802 | 0.1832793 | 0.865 |

Wang/Koch/Maloney vs Barrett True-K | −0.0984054 | 0.145714 | −0.1430995 | 0.1050655 | 0.0446941 | 0.1553571 | 0.774 |

Meta-analysis results in subgroup analysis

0.5 D: | 0.5 D: NA | 0.5 D: | 0.5 D: 0.776 (0.563,1.071) | |

1.0 D: | 1.0 D: 1.277 (0.483,3.375) | 1.0 D: | 1.0 D: 0.897 (0.544,1.479) | |

MAE: | MAE: NA | MAE: | MAE: 0.048 (−0.091,0.187) | |

0.5 D: | 0.5 D: NA | 0.5 D: 1.109 (0.836,1.47) | 0.5 D: 1.267 (0.857,1.872) | |

1.0 D: | 1.0 D: 1.867 (0.748,4.661) | 1.0 D: 1.128 (0.77,1.655) | 1.0 D: 1.667 (0.909,3.059) | |

MAE: −0.13 (−0.32,0.06) | MAE: NA | MAE: 0.04 (−0.062,0.143) | MAE: −0.08 (−0.392,0.224) | |

0.5 D: NA | 0.5 D: NA | 0.5 D: NA | 0.5 D: NA | |

1.0 D: 0.96 (0.47,1.97) | 1.0 D: | 1.0 D: 0.654 (0.31,1.378) | 1.0 D: 0.612 (0.316,1.186) | |

MAE: NA | MAE: NA | MAE: NA | MAE: NA | |

0.5 D: | 0.5 D: 0.88 (0.68,1.14) | 0.5 D: NA | 0.5 D: 0.5 (0.876,1.287) | |

1.0 D: 1.49 (0.98,2.27) | 1.0 D: 0.73 (0.49,1.09) | 1.0 D: 1.55 (0.81,2.98) | 1.0 D: 0.885 (0.611,1.281) | |

MAE: −0.13 (−0.27,0.01) | MAE: 0.00 (−0.15,0.16) | MAE: NA | MAE: −0.027 (−0.13,0.079) | |

0.5 D: | 0.5 D: 0.83 (0.64,1.08) | 0.5 D: NA | 0.5 D: 0.95 (0.78,1.14) | |

1.0 D: | 1.0 D: 0.83 (0.55,1.24) | 1.0 D: 1.75 (0.92,3.33) | 1.0 D: 1.13 (0.84,1.52) | |

MAE: −0.10 (−0.23,0.04) | MAE: 0.03 (−0.12,0.19) | MAE: NA | MAE: 0.03 (−0.07,0.14) | |

Results of network rank test in percentage of eyes within ±0.50 D of the prediction error in subgroup analysis

Name | SUCRA value (%) | PrBest (%) |
---|---|---|

Barrett True-K | 99.5 | 98.7 |

Haigis-L | 54 | 1.1 |

Shammas-PL | 37.5 | 0.2 |

Wang/Koch/Maloney | 9 | 0 |

Results of network rank test in percentage of eyes within ±1.00 D of the prediction error in subgroup analysis

Name | SUCRA value (%) | PrBest (%) |
---|---|---|

OCT | 85.2 | 54.9 |

Barrett True-K | 85.1 | 44.6 |

Shammas-PL | 46.6 | 0.4 |

Haigis-L | 26.3 | 0.1 |

Wang/Koch/Maloney | 6.8 | 0 |

Results of network rank test in mean absolute error in subgroup analysis

Name | SUCRA value (%) | PrWorst (%) |
---|---|---|

Barrett True-K | 6.8 | 84.9 |

Haigis-L | 49.7 | 5.7 |

Wang/Koch/Maloney | 70.6 | 7 |

Shammas-PL | 72.8 | 2.4 |

Node-splitting analysis of inconsistency in subgroup analysis

Name | Outcome | Direct estimate (95% Cl) | Indirect estimate (95% Cl) | Overall (95% Cl) | ||||
---|---|---|---|---|---|---|---|---|

Coefficient | SE | Coefficient | SE | Coefficient | SE | |||

Haigis-L vs Shammas-PL | ±0.50 D | −0.0624174 | 0.0975058 | 0.1008445 | 0.3692068 | −0.16326 | 0.370925 | 0.66 |

Haigis-L vs Barrett True-K | ±0.50 D | 0.3686869 | 0.1493119 | 0.2054248 | 0.3514641 | 0.163262 | 0.370925 | 0.66 |

Shammas-PL vs Barrett True-K | ±0.50 D | 0.4082251 | 0.1457697 | 0.3569623 | 0.4016674 | 0.051263 | 0.418037 | 0.902 |

Wang/Koch/Maloney vs Barrett True-K | ±0.50 D | 0.4552668 | 0.2030435 | 0.6236713 | 0.2218308 | −0.1684 | 0.263861 | 0.523 |

Haigis-L vs Shammas-PL | ±1.00 D | 0.150802 | 0.1520639 | −0.5023516 | 0.5321101 | 0.6531536 | 0.532744 | 0.22 |

Haigis-L vs Barrett True-K | ±1.00 D | 0.4231642 | 0.2349161 | 1.076318 | 0.500621 | −0.6531534 | 0.532744 | 0.22 |

Shammas-PL vs OCT | ±1.00 D | 0.446921 | 0.3663693 | 0.4019853 | 0.7876763 | 0.0449357 | 0.855038 | 0.958 |

Shammas-PL vs Barrett True-K | ±1.00 D | 0.3554842 | 0.2221465 | 0.9426624 | 0.6908429 | −0.5871782 | 0.713269 | 0.41 |

OCT vs Wang/Koch/Maloney | ±1.00 D | −0.6610051 | 0.4709804 | −0.8020179 | 0.4005051 | 0.1410127 | 0.45862 | 0.758 |

OCT vs Barrett True-K | ±1.00 D | −0.3248179 | 0.4894786 | 0.1006259 | 0.3976941 | −0.4254438 | 0.479357 | 0.375 |

Wang/Koch/Maloney vs Barrett True-K | ±1.00 D | 0.5790156 | 0.3248248 | 0.8724429 | 0.3425536 | −0.2934273 | 0.414773 | 0.479 |

Haigis-L vs Shammas-PL | MAE | 0.0343988 | 0.0564512 | 0.0120096 | 0.2042139 | 0.022389 | 0.206164 | 0.914 |

Haigis-L vs Barrett True-K | MAE | −0.0979904 | 0.0745031 | −0.0756012 | 0.1983416 | −0.02239 | 0.206164 | 0.914 |

Shammas-PL vs Barrett True-K | MAE | −0.1332382 | 0.0777479 | −0.1019118 | 0.1789881 | −0.03133 | 0.187368 | 0.867 |

Wang/Koch/Maloney vs Barrett True-K | MAE | −0.1011311 | 0.1489445 | −0.1435984 | 0.1078104 | 0.042467 | 0.158915 | 0.789 |