Journal of Refractive Surgery

Original Article Supplemental DataOpen Access

Network Meta-analysis of No-History Methods to Calculate Intraocular Lens Power in Eyes With Previous Myopic Laser Refractive Surgery

Daizong Wen, MD; Jinjin Yu, MD; Zhenhai Zeng, MD; Colm McAlinden, PhD; Liang Hu, MD; Ke Feng, MD; Yiran Wang, MD; Benhao Song, MD; Sisi Chen, MD; Rui Ning, MD; Yili Jin, MD; Qinmei Wang, MD; A-Yong Yu, MD, PhD; Jinhai Huang, MD, PhD

  • Journal of Refractive Surgery. 2020;36(7):481-490
  • https://doi.org/10.3928/1081597X-20200519-04
  • Posted July 10, 2020

Abstract

PURPOSE:

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

METHODS:

PubMed, Embase, the Cochrane Library, and the U.S. trial registry (www.ClinicalTrial.gov) were used to systematically search trials published up to August 2019. Included were case series studies reporting the following outcomes in patients with cataract undergoing phacoemulsification after laser refractive surgery: 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). A network meta-analysis was conducted using the STATA software version 13.1 (STATACorp LLC).

RESULTS:

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.

CONCLUSIONS:

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.]

Abstract

PURPOSE:

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

METHODS:

PubMed, Embase, the Cochrane Library, and the U.S. trial registry (www.ClinicalTrial.gov) were used to systematically search trials published up to August 2019. Included were case series studies reporting the following outcomes in patients with cataract undergoing phacoemulsification after laser refractive surgery: 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). A network meta-analysis was conducted using the STATA software version 13.1 (STATACorp LLC).

RESULTS:

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.

CONCLUSIONS:

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

PRISMA 2009 ChecklistPRISMA 2009 Checklist

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.

Search StrategySearch StrategySearch StrategySearch StrategySearch StrategySearch StrategySearch Strategy

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 I2 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 studies3,6,14–30 were included in the network meta-analysis.

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

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.3,35Table 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.

Summary of studies included in the network meta-analysisSummary of studies included in the network meta-analysisSummary of studies included in the network meta-analysis

Table C:

Summary of studies included in the network meta-analysis

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

Table 1:

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

The number of trials and eyes involved in each formula

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.

The risk of bias of the trials included in the current study.

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 EG (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).

Network of direct comparison for the intraocular lens power formulas. Each node represents 1 formula. The size of the node is proportional to the number of eyes included in the formula. The edges represent direct comparisons, and the width of the edge is proportional to the number of trials. OCT: Fourier-domain OCT-based formula; ORA: Optiwave Refractive Analysis; Rosa (R): modified Rosa's method; Triple-S: Seitz/Speicher/Savini; D-K SRK/T: the SRK/T formula with the double-K method; D-K Holladay1: the Holladay 1 formula with the double-K method; K-M: Koch-Maloney; TCP: Total Corneal Power; EKR: Equivalent K-reading; TCRP: total corneal refractive power.

Figure C.

Network of direct comparison for the intraocular lens power formulas. Each node represents 1 formula. The size of the node is proportional to the number of eyes included in the formula. The edges represent direct comparisons, and the width of the edge is proportional to the number of trials. OCT: Fourier-domain OCT-based formula; ORA: Optiwave Refractive Analysis; Rosa (R): modified Rosa's method; Triple-S: Seitz/Speicher/Savini; D-K SRK/T: the SRK/T formula with the double-K method; D-K Holladay1: the Holladay 1 formula with the double-K method; K-M: Koch-Maloney; TCP: Total Corneal Power; EKR: Equivalent K-reading; TCRP: total corneal refractive power.

Meta-analysis results comparing all formulas without prior date. The upper right showed the direct comparisons meta-analysis between each pair of formulas and the bottom left showed the network meta-analysis between each pair of formulas. Weighted mean differences and odds ratios (95% confidence intervals) are calculated by column. 0.50 diopters (D): percentage of eyes within ±0.50 D of the prediction refractive error; 1.00 D: percentage of eyes within ±1.00 D of the prediction refractive error; MAE: mean absolute error; NA: not available; OCT: Fourier-domain OCT-Based Formula; ORA: Optiwave Refractive Analysis; Rosa (R): modified Rosa's method; Triple-S: Seitz/Speicher/Savini; D-K Holladay1: the Holladay 1 formula with the double-K method; K-M: Koch-Maloney; TCP: Total Corneal Power; EKR: Equivalent K-reading; TCRP: total corneal refractive power. The underlined data indicate that there are statistically significant effects (P < .05).

Figure D.

Meta-analysis results comparing all formulas without prior date. The upper right showed the direct comparisons meta-analysis between each pair of formulas and the bottom left showed the network meta-analysis between each pair of formulas. Weighted mean differences and odds ratios (95% confidence intervals) are calculated by column. 0.50 diopters (D): percentage of eyes within ±0.50 D of the prediction refractive error; 1.00 D: percentage of eyes within ±1.00 D of the prediction refractive error; MAE: mean absolute error; NA: not available; OCT: Fourier-domain OCT-Based Formula; ORA: Optiwave Refractive Analysis; Rosa (R): modified Rosa's method; Triple-S: Seitz/Speicher/Savini; D-K Holladay1: the Holladay 1 formula with the double-K method; K-M: Koch-Maloney; TCP: Total Corneal Power; EKR: Equivalent K-reading; TCRP: total corneal refractive power. The underlined data indicate that there are statistically significant effects (P < .05).

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

Table E:

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

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

Table F:

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

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

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.

A descriptive analysis for median absolute error

Table H:

A descriptive analysis for median absolute error

Formula rank in median absolute error. OCT = Fourier-Domain OCT-Based formula; ORA = Optiwave Refractive Analysis; Rosa (R) = modified Rosa formula; Triple-S = Seitz/Speicher/Savini; D-K SRK/T = the SRK/T formula with the Double-K formula; D-K Holladay1 = the Holladay 1 formula with the Double-K formula; K-M = Koch-Maloney; TCP = Total Corneal Power; EKR = Equivalent K-Reading; TCRP = Total Corneal Refractive Power; D = diopters

Figure 1.

Formula rank in median absolute error. OCT = Fourier-Domain OCT-Based formula; ORA = Optiwave Refractive Analysis; Rosa (R) = modified Rosa formula; Triple-S = Seitz/Speicher/Savini; D-K SRK/T = the SRK/T formula with the Double-K formula; D-K Holladay1 = the Holladay 1 formula with the Double-K formula; K-M = Koch-Maloney; TCP = Total Corneal Power; EKR = Equivalent K-Reading; TCRP = Total Corneal Refractive Power; D = diopters

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 IK (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.

Ranking probability results in the predictability and accuracy outcome measures. (A) The SUCRA and PrBest for the outcome: prediction error within ±0.50 diopters (D). (B) The SUCRA and PrBest for the outcome: prediction error within ±1.00 D/(C) The SUCRA and PrWorst for the outcome: mean absolute error. SUCRA = surface under the cumulative ranking curve; OCT = Fourier-Domain OCT-Based formula; ORA = Optiwave Refractive Analysis; Rosa (R) = modified Rosa formula; Triple-S = Seitz/Speicher/Savini; D-K Holladay1 = Holladay 1 formula with the Double-K formula; K-M = Koch-Maloney; TCP = Total Corneal Power; EKR = Equivalent K-Reading; TCRP = Total Corneal Refractive Power

Figure 2.

Ranking probability results in the predictability and accuracy outcome measures. (A) The SUCRA and PrBest for the outcome: prediction error within ±0.50 diopters (D). (B) The SUCRA and PrBest for the outcome: prediction error within ±1.00 D/(C) The SUCRA and PrWorst for the outcome: mean absolute error. SUCRA = surface under the cumulative ranking curve; OCT = Fourier-Domain OCT-Based formula; ORA = Optiwave Refractive Analysis; Rosa (R) = modified Rosa formula; Triple-S = Seitz/Speicher/Savini; D-K Holladay1 = Holladay 1 formula with the Double-K formula; K-M = Koch-Maloney; TCP = Total Corneal Power; EKR = Equivalent K-Reading; TCRP = Total Corneal Refractive Power

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

Table I:

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

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

Table J:

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

Results of network rank test in mean absolute 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 LN, 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 EG).

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

Table L:

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

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

Table M:

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

Node-splitting analysis of inconsistency in mean absolute error

Table N:

Node-splitting analysis of inconsistency in mean absolute error

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

Figure E.

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

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

Figure F.

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

The funnel plot in mean absolute error.

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 OS and Figures HJ (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).

Meta-analysis results in subgroup analysis

Table O:

Meta-analysis results in subgroup analysis

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

Results of network rank test in percentage of eyes within ±1.00 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

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

Table R:

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

Node-splitting analysis of inconsistency in subgroup analysis

Table S:

Node-splitting analysis of inconsistency in subgroup analysis

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

Figure H.

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

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

Figure I.

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

The funnel plot of the mean absolute error 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 al43 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 Kingdom45 and Swedish National Cataract Register Study46). 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

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

FormulaAbbreviationBrief Descriptiona
Barrett Universal II
  Barrett True-KBased on an unpublished modification of Barrett Universal II formula.
Double-K
  BESStModifies corneal power measurements obtained by a rotating Scheimpflug camera. The calculated value can then be entered into a Double-K formula.8,19,31,49
  Total Corneal Power 1TCP 1The value provided by the option Total Corneal Power 1 uses the Double-K Holladay 1 formula.17
  Equivalent K Reading at 4.5 mm using the Double-K Holladay 1EKR 4.5 mm (D-K Holladay 1)Calculated by the Scheimpflug camera and then entered into the Double-K Holladay 1 formula.8,19,32
  Wang/Koch/MaloneyModified Maloney method and uses the Double-K Holladay 1 formula.3,50
  Maloney with Double-K SRK/TMaloney (D-K SRK/T)The adjusted corneal power is entered into the Double-K SRK/T formula.25
  Seitz/Speicher/Savini (with Double-K SRK/T)Triple-SModifies the measured post-laser refractive surgery keratometryand uses the Double-K SRK/T formula.19,38,49
SRK/T
  FerraraUses a variable index, correlated to the axial length, to calculate corneal power, and is entered into the SRK/T formula.33
OCT system
  Fourier-Domain OCT-BasedOCTBased on a Gaussian optical vergence model of the eye.34
Haigis
  Haigis-LModifies the measured anterior corneal radius.2
  Total Corneal Refractive Power at 4 mm with the HaigisTCRP 4 mm (Haigis)The corneal power at 4 mm is calculated by ray-tracing through both anterior corneal surfaces, based on a Scheimpflug camera.27
  Koch-Maloney with HaigisK-M (Haigis)Modified version of the original Maloney method.30,50
Shammas
  Hill-Potvin-ShammasBased on the “true net power” in the 4-mm zone.26
  Shammas-PLAdjusted corneal power and then entered into the Shammas-PL formula.39
Rosa
  Modified RosaRosa (R)Modifies the original Rosa formula and uses a regression formula based on axial length and keratometry.36
Ray-tracing
  Ray-tracing (Okulix)OkulixUsing ray-tracing based on corneal topography.37
Aberrometry
  Intraoperative aberrometry (Optiwave Refractive Analysis)ORABased on the measurements of the intraoperative aphakic refraction.24
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.40–42

PRISMA 2009 Checklist

Section/topic#Checklist itemReported on page #
TITLE
Title1Identify the report as a systematic review, meta-analysis, or both.1
ABSTRACT
Structured summary2Provide 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
INTRODUCTION
Rationale3Describe the rationale for the review in the context of what is already known.2
Objectives4Provide an explicit statement of questions being addressed with reference to participants, interventions, comparisons, outcomes, and study design (PICOS).2
METHODS
Protocol and registration5Indicate 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 criteria6Specify 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 sources7Describe 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
Search8Present full electronic search strategy for at least one database, including any limits used, such that it could be repeated.2
Study selection9State the process for selecting studies (i.e., screening, eligibility, included in systematic review, and, if applicable, included in the meta-analysis).2
Data collection process10Describe 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 items11List 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 studies12Describe 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 measures13State the principal summary measures (e.g., risk ratio, difference in means).3
Synthesis of results14Describe the methods of handling data and combining results of studies, if done, including measures of consistency (e.g., I2) for each meta-analysis.3
Risk of bias across studies15Specify any assessment of risk of bias that may affect the cumulative evidence (e.g., publication bias, selective reporting within studies).3
Additional analyses16Describe methods of additional analyses (e.g., sensitivity or subgroup analyses, meta-regression), if done, indicating which were pre-specified.3
RESULTS
Study selection17Give 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 characteristics18For 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 studies19Present data on risk of bias of each study and, if available, any outcome level assessment (see item 12).5
Results of individual studies20For 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 results21Present results of each meta-analysis done, including confidence intervals and measures of consistency.5–7
Risk of bias across studies22Present results of any assessment of risk of bias across studies (see Item 15).7
Additional analysis23Give results of additional analyses, if done (e.g., sensitivity or subgroup analyses, meta-regression [see Item 16]).7
DISCUSSION
Summary of evidence24Summarize 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
Limitations25Discuss 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
Conclusions26Provide a general interpretation of the results in the context of other evidence, and implications for future research.8
FUNDING
Funding27Describe 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

MEDLINE (PubMed)(“Actual K” OR Awwad OR BESSt OR “Ray Tracing” OR Ferrara OR Feiz OR Haigis OR Hamed OR “Hard Contact Lens” OR Ianchulev OR Geggel OR Kim OR Leccisotti OR Mackool OR Maloney OR “Maloney-Koch-Wang” OR “Maloney/Koch/Wang” OR “Razmjoo Regression” OR Ronje OR Saiki OR “Seitz-Speicher-Savini” OR “Seitz/Speicher/Savini” OR “Savini-Barboni-Zannini” OR “Savini/Barboni/Zannini” OR Shammas OR Wang OR “Wang-Koch-Maloney” OR “Wang/Koch/Maloney” OR “Koch-Maloney” OR “Koch/Maloney” OR “Barrett True-K” OR Rosa OR Sirius OR okulix OR OCT OR “optical coherence tomography” OR Borasio OR “Soper and Goffman” OR “Soper-Goffman” OR “Soper/Goffman” OR SToP OR “Optiwave Refractive Analysis” OR ORA OR “Total Corneal Power 1” OR “Equivalent K-reading” OR EKR OR “total corneal refractive power” OR “true net corneal power” OR “total mean power”) AND (“intraocular lens power calculation” OR ((“Lenses, Intraocular”[Mesh] OR “intraocular lens” OR IOL OR “Cataract”[Mesh]) AND (formula* OR calculat*))) AND (“Corneal Surgery, Laser”[Mesh] OR ((cornea* OR kerato* OR Keratectomy OR Lase*) AND (“refractive surgery”)))
---------------------------------------
Cochrane Central Register of Controlled Trials (CENTRAL) in The Cochrane Library (Wiley)
#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

EMBASE

‘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


ClinicalTrials.gov search strategy“intraocular lens power calculation” OR ((“intraocular lens” OR IOL OR Cataract) AND (formula* OR calculat*))

Summary of studies included in the network meta-analysis

Study (Author, Year)CountryTreatmentAge (Mean±SD, y)MaleTotalCorneal Power (K, D)Axial Length (mm)Follow-upFormulaNo.Eye Percentage of IOL Prediction Error (%)MAE (D, Mean±SD)MeAE (D)

Within±0.50DWithin±1.00D
Abulafia 2016USALASIK/PRK58±72625.69±1.253wShammas-PL3050800.63±0.480.53
Haigis-L3046.776.70.68±0.450.62
Barrett True-K3063.3800.52±0.430.41
Cho 2018Korea54.6±9.37215639.73±2.2327.08±2.503mWang/Koch/Maloney5633.955.40.94±0.74
Shammas-PL5637.558.90.92±0.74
Haigis-L5658.985.70.51±0.44
TCRP 4mm (Haigis)5642.670.370.82±0.70
Barrett True-K5657.475.90.66±0.63
Huang 2013USALASIK/PRK/LASEK61.5±8.046OCT4659890.5
Haigis-L4646780.67
Shammas-PL4646850.67
Ianchulev 2014USALASIK/PRK215Haigis-L24648800.65±0.58
ORA24667940.42±0.39
Shammas-PL24650870.59±0.52
Kang 2017KoreaLASIK/PRK/LASEK53.1±10.3216838.25±2.2528.1±2.4Triple-S680.50
Maloney (D-K SRK/T)680.56
Shammas-PL680.72
Barrett True-K680.66
Haigis-L681.01
Potvin 2015USALASIK/PRK7740.92±2.2625.83±1.36Haigis-L1015892
Shammas-PL1015790
Hill-Potvin-Shammas1016691
Wang/Koch/Maloney1015086
Saiki 2013JapanLASIK54.0±9.9121626.39±0.991mHaigis-L2326520.95
Shammas-PL2520720.77
Saiki 2013JapanLASIK54.1±9.8141926.19±1.061mHaigis-L2524520.95
Shammas-PL2825710.77
Saiki 2014JapanLASIK54.0±10.6111726.47±1.121mOKULIX2441.7750.62
Shammas-PL2420.866.90.8
Haigis-L2118.843.11.13
Savini 2015ItalyPRK/LASIK27.82±1.78Shammas-PL683.30.31
Triple-S6500.41
Rosa (R)601.05
Ferrara602.09
Savini 2018ItalyPRK56.4±8.32226.7±1.7OKULIX2263.690.90.31
Shammas-PL2236.468.20.79
TCP 12254.586.40.39
Barrett True-K2263.686.40.45
Savini 2019Italy58.2±7.95042.80±1.7227.17±1.57SToP (SRK/T)5062840.490.31
SToP (Holladay 1)5060780.550.45
Shammas-PL5054760.680.48
Barrett True-K5052880.570.49
Triple-S5070960.40.31
EKR 4.5mm (D-K Holladay1)5044820.610.59
BESSt5068920.420.37
Tang 2012USAmyopic LASIK/PRK59.4±11.9161mHaigis-L2272.70.73
OCT2281.80.57
Wang 2010USAPRK/LASIK58±85726.19±1.553wWang/Koch/Maloney7258960.66±0.48
Shammas-PL7260900.69±0.49
Haigis-L7260940.65±0.51
Wang 2015USALASIK/PRK63±78025.46±1.303wOCT10468.392.30.35
Barrett True-K10458.790.40.42
Wang/Koch/Maloney845086.90.51
Shammas-PL10452.988.50.48
Haigis-L10455.890.40.49
Wang 2019USAmyopic LASIK/PRK64.5±7.13725.72±1.643wHaigis-L5345.381.10.610.53
Barrett True-K5352.892.50.540.37
Wu 2017ChinaLASIK50.3±9.021036.35±0.7730.06±2.873mHaigis-L1060800.6040.465
K-M (Haigis)1050900.5570.51
Shammas-PL1050900.5580.519
Yang 2013USAPRK/LASIK61.27±6.793340.08±2.5825.98±1.553–6mWang/Koch/Maloney6250680.94±0.48
40.20±2.44Shammas-PL6245711.01±0.40
40.53±2.40Haigis-L6240681.10±0.44
Vrijman 2019NetherlandsLASIK/PRK/LASEK3625.28±1.40Shammas-PL645086.10.63±0.600.52
Haigis-L6455.686.10.58±0.560.45
Barrett True-K6469.488.90.46±0.480.33

The number of trials and eyes involved in each formula

NameNumber of StudiesNumber of Eyes
Barrett True-K8447
BESSt150
EKR 4.5mm (D-K Holladay1)150
Ferrara16
OCT3172
Haigis-L161003
Hill-Potvin-Shammas1101
K-M (Haigis)110
Maloney (D-K SRK/T)168
Rosa (R)16
Okulix246
ORA1246
Triple-S3124
Shammas-PL17994
SToP (Holladay 1)150
SToP (SRK/T)150
TCP 1122
TCRP 4mm (Haigis)156
Wang/Koch/Maloney5375

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

NameNumber of StudiesOdds Ratio (95% CI)I2
Haigis-L vs Shammas-PL131.062 (0.876,1.287)0.00%
Haigis-L vs Okulix10.329 (0.085,1.281).%
Shammas-PL vs Okulix20.346 (0.143,0.839)0.00%
Shammas-PL vs Triple-S21.099 (0.13,9.313)61.40%
Shammas-PL vs Rosa (R)147.667 (1.597,1422.695).%
Shammas-PL vs Ferrara147.667 (1.597,1422.695).%
Triple-S vs Rosa (R)113 (0.511,330.477).%
Triple-S vs Ferrara113 (0.511,330.477).%
Haigis-L vs Wang/Koch/Maloney51.267 (0.857,1.872)46.30%
Shammas-PL vs Wang/Koch/Maloney51.109 (0.836,1.47)0.00%
Haigis-L vs K-M (Haigis)11.5 (0.255,8.817).%
Shammas-PL vs K-M (Haigis)11 (0.173,5.772).%
Haigis-L vs Barrett True-K50.776 (0.563,1.071)0.00%
Shammas-PL vs Barrett True-K60.622 (0.452,0.857)3.20%
Haigis-L vs OCT20.588 (0.368,0.937)0.00%
Shammas-PL vs OCT20.543 (0.341,0.865)0.00%
OCT vs Wang/Koch/Maloney12.152 (1.224,3.782).%
OCT vs Barrett True-K11.517 (0.859,2.677).%
Wang/Koch/Maloney vs Barrett True-K20.554 (0.31,0.99)36.90%
Haigis-L vs ORA10.453 (0.314,0.652).%
Shammas-PL vs ORA10.491 (0.341,0.707).%
Haigis-L vs Hill-Potvin-Shammas10.713 (0.402,1.263).%
Shammas-PL vs Hill-Potvin-Shammas10.684 (0.387,1.211).%
Wang/Koch/Maloney vs Hill-Potvin-Shammas10.518 (0.293,0.913).%
Haigis-L vs TCRP 4mm (Haigis)11.913 (0.903,4.053).%
Shammas-PL vs TCRP 4mm (Haigis)10.8 (0.375,1.705).%
Wang/Koch/Maloney vs TCRP 4mm (Haigis)10.685 (0.318,1.472).%
Barrett True-K vs TCRP 4mm (Haigis)11.778 (0.841,3.758).%
Shammas-PL vs TCP 110.476 (0.142,1.593).%
Okulix vs TCP 111.458 (0.436,4.88).%
Okulix vs Barrett True-K11 (0.293,3.416).%
TCP 1 vs Barrett True-K10.686 (0.205,2.295).%
SToP (SRK/T) vs SToP (Holladay 1)11.088 (0.487,2.43).%
SToP (SRK/T) vs EKR 4.5mm (D-K Holladay1)12.077 (0.934,4.615).%
SToP (SRK/T) vs BESSt10.768 (0.337,1.75).%
SToP (SRK/T) vs Shammas-PL11.39 (0.626,3.084).%
SToP (SRK/T) vs Triple-S10.699 (0.304,1.607).%
SToP (SRK/T) vs Barrett True-K11.506 (0.679,3.339).%
SToP (Holladay 1) vs EKR 4.5mm (D-K Holladay1)11.909 (0.862,4.227).%
SToP (Holladay 1) vs BESSt10.706 (0.311,1.603).%
SToP (Holladay 1) vs Shammas-PL11.278 (0.578,2.825).%
SToP (Holladay 1) vs Triple-S10.643 (0.281,1.472).%
SToP (Holladay 1) vs Barrett True-K11.385 (0.627,3.058).%
EKR 4.5mm (D-K Holladay1) vs BESSt10.37 (0.164,0.836).%
EKR 4.5mm (D-K Holladay1) vs Shammas-PL10.669 (0.304,1.472).%
EKR 4.5mm (D-K Holladay1) vs Triple-S10.337 (0.148,0.767).%
EKR 4.5mm (D-K Holladay1) vs Barrett True-K10.725 (0.33,1.594).%
BESSt vs Shammas-PL11.81 (0.802,4.085).%
BESSt vs Triple-S10.911 (0.39,2.126).%
BESSt vs Barrett True-K11.962 (0.87,4.422).%
Triple-S vs Barrett True-K12.154 (0.948,4.894).%

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

NameNumber of StudiesOdds Ratio (95% CI)I2
Haigis-L vs Shammas-PL130.885 (0.611,1.281)43.50%
Haigis-L vs Okulix10.25 (0.071,0.886).%
Shammas-PL vs Okulix20.441 (0.151,1.288)9.50%
Haigis-L vs OCT30.612 (0.316,1.186)0.00%
Haigis-L vs Wang/Koch/Maloney51.667 (0.909,3.059)51.30%
Shammas-PL vs Wang/Koch/Maloney51.128 (0.77,1.655)0.00%
Haigis-L vs K-M (Haigis)10.444 (0.034,5.88).%
Shammas-PL vs K-M (Haigis)11 (0.054,18.574).%
Haigis-L vs Barrett True-K50.897 (0.544,1.479)9.80%
Shammas-PL vs Barrett True-K60.588 (0.385,0.897)0.00%
Shammas-PL vs OCT20.654 (0.31,1.378)0.00%
OCT vs Wang/Koch/Maloney11.867 (0.748,4.661).%
OCT vs Barrett True-K11.277 (0.483,3.375).%
Wang/Koch/Maloney vs Barrett True-K20.498 (0.275,0.899)0.00%
Haigis-L vs ORA10.261 (0.142,0.48).%
Shammas-PL vs ORA10.434 (0.229,0.824).%
Haigis-L vs Hill-Potvin-Shammas11.137 (0.42,3.076).%
Shammas-PL vs Hill-Potvin-Shammas10.89 (0.346,2.293).%
Wang/Koch/Maloney vs Hill-Potvin-Shammas10.608 (0.25,1.476).%
Haigis-L vs TCRP 4mm (Haigis)12.615 (1.021,6.699).%
Shammas-PL vs TCRP 4mm (Haigis)10.625 (0.287,1.364).%
Wang/Koch/Maloney vs TCRP 4mm (Haigis)10.541 (0.249,1.174).%
Barrett True-K vs TCRP 4mm (Haigis)11.442 (0.621,3.347).%
Shammas-PL vs TCP 110.338 (0.075,1.535).%
Okulix vs TCP 111.579 (0.237,10.516).%
Okulix vs Barrett True-K11.579 (0.237,10.516).%
TCP 1 vs Barrett True-K11 (0.179,5.596).%
SToP (SRK/T) vs SToP (Holladay 1)11.481 (0.54,4.064).%
SToP (SRK/T) vs Triple-S10.219 (0.044,1.088).%
SToP (SRK/T) vs EKR 4.5mm (D-K Holladay1)11.152 (0.405,3.277).%
SToP (SRK/T) vs BESSt10.457 (0.128,1.627).%
SToP (SRK/T) vs Shammas-PL11.658 (0.612,4.491).%
SToP (SRK/T) vs Barrett True-K10.716 (0.229,2.238).%
SToP (Holladay 1) vs Triple-S10.148 (0.031,0.706).%
SToP (Holladay 1) vs EKR 4.5mm (D-K Holladay1)10.778 (0.291,2.082).%
SToP (Holladay 1) vs BESSt10.308 (0.091,1.046).%
SToP (Holladay 1) vs Shammas-PL11.12 (0.441,2.844).%
SToP (Holladay 1) vs Barrett True-K10.483 (0.164,1.43).%
Triple-S vs EKR 4.5mm (D-K Holladay1)15.268 (1.077,25.779).%
Triple-S vs BESSt12.087 (0.365,11.948).%
Triple-S vs Shammas-PL17.579 (1.599,35.933).%
Triple-S vs Barrett True-K13.273 (0.627,17.071).%
EKR 4.5mm (D-K Holladay1) vs BESSt10.396 (0.113,1.384).%
EKR 4.5mm (D-K Holladay1 vs Shammas-PL11.439 (0.545,3.797).%
EKR 4.5mm (D-K Holladay1) vs Barrett True-K10.621 (0.203,1.899).%
BESSt vs Shammas-PL13.632 (1.082,12.183).%
BESSt vs Barrett True-K11.568 (0.414,5.935).%

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

NameNumber of StudiesWeighted Mean Differences (95% CI)I2
Haigis-L vs OCT20.167 (−0.028,0.362)0.00%
Haigis-L vs Shammas-PL8−0.027 (−0.132,0.079)56.90%
Haigis-L vs Wang/Koch/Maloney3−0.084 (−0.392,0.224)88.50%
Shammas-PL vs Wang/Koch/Maloney30.04 (−0.062,0.143)0.00%
Haigis-L vs K-M (Haigis)10.047 (−0.576,0.67).%
Shammas-PL vs K-M (Haigis)10.001 (−0.718,0.72).%
Haigis-L vs Barrett True-K40.048 (−0.091,0.187)43.70%
Shammas-PL vs Barrett True-K40.164 (0.048,0.28)0.00%
Shammas-PL vs OCT10.17 (−0.12,0.46).%
Haigis-L vs ORA10.23 (0.143,0.317).%
Shammas-PL vs ORA10.17 (0.089,0.251).%
Haigis-L vs TCRP 4mm (Haigis)1−0.31 (−0.527,−0.093).%
Shammas-PL vs TCRP 4mm (Haigis)10.1 (−0.167,0.367).%
Wang/Koch/Maloney vs Barrett True-K10.28 (0.025,0.535).%
Wang/Koch/Maloney vs TCRP 4mm (Haigis)10.12 (−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-PL1−0.19 (−0.511,0.131).%
SToP (SRK/T) vs Barrett True-K1−0.08 (−0.372,0.212).%
SToP (SRK/T) vs BESSt10.07 (−0.251,0.391).%
SToP (SRK/T) vs Triple-S10.09 (−0.231,0.411).%
SToP (Holladay 1) vs Shammas-PL1−0.13 (−0.451,0.191).%
SToP (Holladay 1) vs Barrett True-K1−0.02 (−0.312,0.272).%
SToP (Holladay 1) vs BESSt10.13 (−0.191,0.451).%
SToP (Holladay 1) vs Triple-S10.15 (−0.171,0.471).%
Shammas-PL vs BESSt10.26 (−0.061,0.581).%
Shammas-PL vs Triple-S10.28 (−0.041,0.601).%
Barrett True-K vs BESSt10.15 (−0.142,0.442).%
Barrett True-K vs Triple-S10.17 (−0.122,0.462).%
BESSt vs Triple-S10.02 (−0.301,0.341).%

A descriptive analysis for median absolute error

NameNumber of StudiesRange
SToP (SRK/T)10.31
ORA10.35
OCT10.35
BESSt10.37
TCP 110.39
Triple-S30.31–0.5
SToP (Holladay 1)10.45
Okulix20.31–0.62
Barrett True K70.33–0.66
K-M (Haigis)10.51
Wang/Koch/Maloney10.51
Shammas-PL120.31–0.8
Maloney (D-K SRK/T)10.56
EKR 4.5mm (D-K Holladay1)10.59
Haigis-L90.39–1.13
Rosa (R)11.05
Ferrara12.09

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

NameSUCRA value (%)PrBest (%)
Okulix85.132.7
ORA82.79.5
BESSt8016.1
Triple-S78.814
OCT74.53.6
SToP (SRK/T)65.93.8
Hill-Potvin-Shammas62.11.3
SToP (Holladay 1)60.12.5
TCP 159.38.8
Barrett True-K580
Haigis-L36.50
K-M (Haigis)35.96
Shammas-PL320
TCRP 4mm (Haigis)29.20
Wang/Koch/Maloney23.60
EKR 4.5mm (D-K Holladay1)23.30
Ferrara6.80.9
Rosa (R)6.20.8

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

NameSUCRA value (%)PrBest (%)
Triple-S9257.1
ORA804.7
BESSt79.69.5
Okulix74.85.7
TCP 164.87.9
OCT55.50
Barrett True-K54.50
K-M (Haigis)53.314.6
SToP (SRK/T)48.70.3
EKR 4.5mm (D-K Holladay1)41.20.1
Hill-Potvin-Shammas33.40.1
TCRP 4mm (Haigis)33.40
Shammas-PL29.90
SToP (Holladay 1)27.70
Haigis-L20.80
Wang/Koch/Maloney10.50

Results of network rank test in mean absolute error

NameSUCRA value (%)PrWorst (%)
Triple-S21.926.4
BESSt23.723.9
ORA28.310.1
OCT35.38.7
SToP (SRK/T)35.411.5
Barrett True-K44.70.2
SToP (Holladay 1)46.35.6
K-M (Haigis)59.113.4
Haigis-L69.30
Shammas-PL75.70
Wang/Koch/Maloney77.60
TCRP 4mm (Haigis)82.80.2

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

NameDirect estimate (95% Cl)Indirect estimate (95% Cl)Overall (95% Cl)P-value



CoefficientSECoefficientSECoefficientSE
SToP (SRK/T) vs Shammas-PL−0.32920360.4066998−0.71957980.424876639.04%0.41969810.35
SToP (SRK/T) vs Triple-S0.35775140.4244143−1.8712261.2449142.2289781.2490640.07
SToP (SRK/T) vs Barrett True-K−0.40950510.40622350.2412060.4281203−0.6507110.42252380.12
SToP (Holladay 1) vs Shammas-PL−0.24512250.4047822−0.63549860.42304239.04%0.41969810.35
SToP (Holladay 1) vs Triple-S0.44183280.4225771−1.7871451.2442892.2289781.2490640.07
SToP (Holladay 1) vs Barrett True-K−0.32542240.40430380.32528860.4262998−0.6507110.42252380.12
Haigis-L vs Shammas-PL−0.06262080.09749550.19645650.3539498−0.25907740.35536410.47
Haigis-L vs Okulix1.0198080.55964090.69983570.551650.31997267.81E-010.68
Haigis-L vs Barrett True-K0.36609990.14872030.16766050.340215519.84%0.3605150.58
EKR 4.5mm (D-K Holladay1) vs Shammas-PL0.40150470.40209970.01112860.420475939.04%0.41969810.35
EKR 4.5mm (D-K Holladay1) vs Triple-S1.088460.4200082−1.1405181.243419222.90%1.2490640.07
EKR 4.5mm (D-K Holladay1) vs Barrett True-K0.32120480.4016180.97191580.4237534−65.07%0.42252380.12
BESSt vs Shammas-PL−0.59342920.4152434−0.98380530.433062339.04%0.41969810.35
BESSt vs Triple-S0.09352610.4326082−2.1354521.2477322.2289781.2490640.07
BESSt vs Barrett True-K−6.74E-010.414777−0.0230180.4362453−0.6507110.42252380.12
Shammas-PL vs Barrett True-K0.39419310.14455790.35311160.4016530.04108150.41753820.92
Okulix vs Barrett True-K1.41E-020.5814966−0.74274260.43814730.75680750.5977490.21
TCP 1 vs Barrett True-K0.37729420.6162483−0.37951320.5866930.75680750.5977490.21
Triple-S vs Barrett True-K−0.64870580.41192470.00200520.4223041−0.6507110.42252380.12
OCT vs Wang/Koch/Maloney−0.73600650.2694971−0.79043970.24773120.05443320.26898490.84
OCT vs Barrett True-K−0.40076180.2716629−0.11986180.2552917−0.28090.27788810.31
Wang/Koch/Maloney vs Barrett True-K0.45278660.20273060.60968280.2200616−0.15689610.2616230.55

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

NameDirect estimate (95% Cl)Indirect estimate (95% Cl)Overall (95% Cl)P-value



CoefficientSECoefficientSECoefficientSE
SToP (SRK/T) vs SToP (Holladay 1)−0.39256170.56343060.1091558416.0742−0.5017175416.07460.999
SToP (SRK/T) vs Triple-S1.5198260.8495512.01394402.9404−0.4941143402.94040.999
SToP (SRK/T) vs EKR 4.5mm (D-K Holladay1)−0.14188060.58000420.3681856394.6931−0.5100662394.69350.999
SToP (SRK/T) vs BESSt0.7841190.68749011.288312420.4081−0.5041929420.40840.999
SToP (SRK/T) vs Shammas-PL−0.5055490.55968360.51034211.17822−1.0158911.2740210.425
SToP (SRK/T) vs Barrett True-K0.33420110.6268902−0.68168271.0719061.0158841.2740250.425
SToP (Holladay 1) vs Shammas-PL−0.11298690.53008350.39496720.6424125−0.50795410.63701870.425
SToP (Holladay 1) vs Barrett True-K0.72676380.60061060.21881070.5770180.5079530.63701930.425
Triple-S vs Shammas-PL−2.0253740.8278114−1.517420.9038679−0.50795410.63701870.425
Triple-S vs Barrett True-K−1.1856240.8746521−1.6935770.85862270.5079530.63701930.425
EKR 4.5mm (D-K Holladay1) vs Shammas-PL−0.3636680.54766760.14428610.656997−0.50795410.63701870.425
EKR 4.5mm (D-K Holladay1) vs Barrett True-K0.47608270.6161853−0.03187040.59321240.5079530.63701930.425
Haigis-L vs Shammas-PL0.15198570.1506452−0.50346170.49920550.65544740.49961840.19
Haigis-L vs Okulix0.95018910.60410281.414220.8664039−0.46403121.0467480.658
Haigis-L vs Barrett True-K0.42059920.2340291.0206370.4914459−0.60003770.5244550.253
BESSt vs Shammas-PL−1.2896670.6604374−0.78171340.7535801−0.50795410.63701870.425
BESSt vs Barrett True-K−0.44991690.7182772−0.95786990.69866930.5079530.63701930.425
Shammas-PL vs OCT0.44687620.36458760.40440120.78529120.0424750.85224820.96
Shammas-PL vs Barrett True-K3.50E-010.22061340.94498860.68828−0.59508680.71034940.402
Okulix vs Barrett True-K−0.104760.8412185−0.69047250.54134480.58571250.80531550.467
TCP 1 vs Barrett True-K1.95E-120.9087677−0.58571250.80531550.58571250.80531550.467
OCT vs Wang/Koch/Maloney−0.66206310.4678593−0.80229480.3982380.14023170.45512110.758
OCT vs Barrett True-K−0.32513350.48705530.09197540.3956174−0.41710890.47648460.381
Wang/Koch/Maloney vs Barrett True-K0.57996170.3226680.85928210.3397657−0.27932040.41162330.497

Node-splitting analysis of inconsistency in mean absolute error

NameDirect estimate (95% Cl)Indirect estimate (95% Cl)Overall (95% Cl)P-value



CoefficientSECoefficientSECoefficientSE
SToP (SRK/T) vs Shammas-PL0.1899990.19926850.21163160.202537−0.02163260.20253790.915
SToP (SRK/T) vs Barrett True-K0.07999850.18700840.05836170.213910.02163680.20253870.915
SToP (Holladay 1) vs Shammas-PL0.130.19926880.15163260.2025379−0.02163260.20253790.915
SToP (Holladay 1) vs Barrett True-K0.02000010.1870087−0.00163670.2139110.02163680.20253870.915
Haigis-L vs Shammas-PL0.0338250.05478510.01219210.20064750.02163290.20253970.915
Haigis-L vs Barrett True-K−0.09780880.0727115−0.07617410.1948677−0.02163460.20253860.915
Shammas-PL vs OCT−0.1898830.1515766−0.19283390.21485650.00295090.25615430.991
Shammas-PL vs Barrett True-K−0.13262140.0759552−0.10144120.1750405−0.03118020.18327930.865
Wang/Koch/Maloney vs Barrett True-K−0.09840540.145714−0.14309950.10506550.04469410.15535710.774

Meta-analysis results in subgroup analysis

Direct-comparison meta-analysis
Barrett True-K0.5 D: 0.554 (0.31,0.99)0.5 D: NA0.5 D: 0.622 (0.452,0.857)0.5 D: 0.776 (0.563,1.071)
1.0 D: 0.498 (0.275,0.899)1.0 D: 1.277 (0.483,3.375)1.0 D: 0.588 (0.385,0.897)1.0 D: 0.897 (0.544,1.479)
MAE: 0.28 (0.025,0.535)MAE: NAMAE: 0.164 (0.048,0.28)MAE: 0.048 (−0.091,0.187)

0.5 D: 1.70 (1.23,2.35)Wang/Koch/Maloney0.5 D: NA0.5 D: 1.109 (0.836,1.47)0.5 D: 1.267 (0.857,1.872)
1.0 D: 2.05 (1.24,3.38)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: NAMAE: 0.04 (−0.062,0.143)MAE: −0.08 (−0.392,0.224)

0.5 D: NA0.5 D: NAOCT0.5 D: NA0.5 D: NA
1.0 D: 0.96 (0.47,1.97)1.0 D: 0.47 (0.23,0.95)1.0 D: 0.654 (0.31,1.378)1.0 D: 0.612 (0.316,1.186)
MAE: NAMAE: NAMAE: NAMAE: NA

0.5 D: 1.50 (1.14,1.97)0.5 D: 0.88 (0.68,1.14)0.5 D: NAShammas-PL0.5 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: NAMAE: −0.027 (−0.13,0.079)

0.5 D: 1.41 (1.07,1.87)0.5 D: 0.83 (0.64,1.08)0.5 D: NA0.5 D: 0.95 (0.78,1.14)Haigis-L
1.0 D: 1.69 (1.10,2.60)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: NAMAE: 0.03 (−0.07,0.14)
Network meta-analysis

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

NameSUCRA value (%)PrBest (%)
Barrett True-K99.598.7
Haigis-L541.1
Shammas-PL37.50.2
Wang/Koch/Maloney90

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

NameSUCRA value (%)PrBest (%)
OCT85.254.9
Barrett True-K85.144.6
Shammas-PL46.60.4
Haigis-L26.30.1
Wang/Koch/Maloney6.80

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

NameSUCRA value (%)PrWorst (%)
Barrett True-K6.884.9
Haigis-L49.75.7
Wang/Koch/Maloney70.67
Shammas-PL72.82.4

Node-splitting analysis of inconsistency in subgroup analysis

NameOutcomeDirect estimate (95% Cl)Indirect estimate (95% Cl)Overall (95% Cl)P-value



CoefficientSECoefficientSECoefficientSE
Haigis-L vs Shammas-PL±0.50 D−0.06241740.09750580.10084450.3692068−0.163260.3709250.66
Haigis-L vs Barrett True-K±0.50 D0.36868690.14931190.20542480.35146410.1632620.3709250.66
Shammas-PL vs Barrett True-K±0.50 D0.40822510.14576970.35696230.40166740.0512630.4180370.902
Wang/Koch/Maloney vs Barrett True-K±0.50 D0.45526680.20304350.62367130.2218308−0.16840.2638610.523
Haigis-L vs Shammas-PL±1.00 D0.1508020.1520639−0.50235160.53211010.65315360.5327440.22
Haigis-L vs Barrett True-K±1.00 D0.42316420.23491611.0763180.500621−0.65315340.5327440.22
Shammas-PL vs OCT±1.00 D0.4469210.36636930.40198530.78767630.04493570.8550380.958
Shammas-PL vs Barrett True-K±1.00 D0.35548420.22214650.94266240.6908429−0.58717820.7132690.41
OCT vs Wang/Koch/Maloney±1.00 D−0.66100510.4709804−0.80201790.40050510.14101270.458620.758
OCT vs Barrett True-K±1.00 D−0.32481790.48947860.10062590.3976941−0.42544380.4793570.375
Wang/Koch/Maloney vs Barrett True-K±1.00 D0.57901560.32482480.87244290.3425536−0.29342730.4147730.479
Haigis-L vs Shammas-PLMAE0.03439880.05645120.01200960.20421390.0223890.2061640.914
Haigis-L vs Barrett True-KMAE−0.09799040.0745031−0.07560120.1983416−0.022390.2061640.914
Shammas-PL vs Barrett True-KMAE−0.13323820.0777479−0.10191180.1789881−0.031330.1873680.867
Wang/Koch/Maloney vs Barrett True-KMAE−0.10113110.1489445−0.14359840.10781040.0424670.1589150.789
Authors

From School of Ophthalmology and Optometry and Eye Hospital of Wenzhou Medical University, Wenzhou, Zhejiang, People's Republic of China (DW, JY, ZZ, LH, KF, YW, BS, SC, RN, YJ, QW, AY, JH); Key Laboratory of Vision Science, Ministry of Health People's Republic of China, Wenzhou, Zhejiang, People's Republic of China (ZZ, LH, SC, QW, AY, JH); Quanzhou Aier Eye Hospital, Quanzhou, Fujian, People's Republic of China (DW); and the Department of Ophthalmology, Singleton Hospital, Swansea Bay University Health Board, Swansea, United Kingdom (CM).

Supported in part by the Foundation of Wenzhou City Science & Technology Bureau (Grant No. Y20180174); Medical and Health Science and Technology Program of Zhejiang Province (Grant No. 2019KY111); Zhejiang Provincial Key Research and Development Program (Grant No. 2018C03012); Zhejiang Provincial High-level Talents Program (Grant No. 2017-102); and Wenzhou Key Team of Scientific and Technological Innovation (Grant No. C20170002).

The authors have no financial or proprietary interest in the materials presented herein.

Drs. Wen, JYu, and Zeng contributed equally to this work and should be considered as equal first authors.

AUTHOR CONTRIBUTIONS

Study concept and design (DW, JY, ZZ, QW, AY, JH); data collection (JY, KF, YW, RN, YJ); analysis and interpretation of data (CM, LH, BS, SC); writing the manuscript (JY, RN, YJ, AY, JH); critical revision of the manuscript (DW, JY, ZZ, CM, LH, KF, YW, BS, SC, RN, YJ, QW, AY, JH); statistical expertise (DW); administrative, technical, or material support (JH); supervision (DW, JY, ZZ, LH, QW, AY, JH)

Correspondence: A-Yong Yu, MD, PhD ( yaybetter@hotmail.com), and Jinhai Huang, MD, PhD ( vip999vip@163.com), Eye Hospital of Wenzhou Medical University, 270 West Xueyuan Road, Wenzhou, Zhejiang 325027, People's Republic of China.

This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (https://creativecommons.org/licenses/by-nc/4.0). This license allows users to copy and distribute, to remix, transform, and build upon the article non-commercially, provided the author is attributed and the new work is non-commercial.
Received: February 22, 2020
Accepted: May 19, 2020

10.3928/1081597X-20200519-04

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