Predicting Edema Resolution After Descemet Membrane Endothelial Keratoplasty for Fuchs Dystrophy Using Scheimpflug Tomography | Cornea | JAMA Ophthalmology | JAMA Network
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Figure 1.  Tomographic Features of Low and High Corneal Edema Resolution After Descemet Membrane Endothelial Keratoplasty (DMEK)
Tomographic Features of Low and High Corneal Edema Resolution After Descemet Membrane Endothelial Keratoplasty (DMEK)

Corneal thickness and posterior elevation before and after DMEK in left eyes (OS) with less than 50 μm (A) or more than 100 μm (B) of corneal edema. The cornea with 17-μm edema resolution had no tomographic features of edema before or after DMEK. In contrast, the cornea with 202-μm edema resolution had focal posterior depression with nonparallel isopachs (white arrows) before DMEK and no tomographic features of edema thereafter.

Figure 2.  Performance and Calibration of the Model Predicting Edema Resolution After Descemet Membrane Endothelial Keratoplasty
Performance and Calibration of the Model Predicting Edema Resolution After Descemet Membrane Endothelial Keratoplasty

The scatterplots show overall performance for observed vs predicted edema (orange lines, smoothed 90% prediction intervals). The Bland-Altman plots show 95% limits of agreement between predicted and observed edema (orange lines). Mean differences between predicted and observed edema (blue line) were close to 0. A, In the derivation cohort of predicted vs observed edema, the slope was 1.00 and R2 was 0.56 (95% CI, 0.43-0.69). B, In the validation cohort of predicted vs observed edema, the slope was 1.08 and R2 was 0.49 (95% CI, 0.37-0.62).

Table 1.  Baseline Characteristics by Decrease in Corneal Edema After DMEK
Baseline Characteristics by Decrease in Corneal Edema After DMEK
Table 2.  Model to Predict Corneal Edema Resolution After DMEKa
Model to Predict Corneal Edema Resolution After DMEKa
Table 3.  Summary of the Developed and Validated Prediction Model for Edema Resolution in Patients With Fuchs Dystrophya
Summary of the Developed and Validated Prediction Model for Edema Resolution in Patients With Fuchs Dystrophya
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    Original Investigation
    February 18, 2021

    Predicting Edema Resolution After Descemet Membrane Endothelial Keratoplasty for Fuchs Dystrophy Using Scheimpflug Tomography

    Author Affiliations
    • 1Eye Center, Faculty of Medicine, University of Freiburg, Freiburg, Germany
    JAMA Ophthalmol. 2021;139(4):423-430. doi:10.1001/jamaophthalmol.2020.6994
    Key Points

    Question  Can preoperative Scheimpflug imaging predict corneal edema resolution after Descemet membrane endothelial keratoplasty?

    Findings  In a prognostic study including 88 patients, based on a post hoc analysis of 2 cohort studies of participants with advanced Fuchs dystrophy, a prediction model was derived (derivation cohort, 100 eyes) and validated in a separate cohort (32 eyes). To precisely predict the amount of edema resolution after Descemet membrane endothelial keratoplasty, 5 factors were required: 2 features were visible on tomography maps and 3 were indicators of corneal profile and structure.

    Meaning  The results of this study suggest that preoperative Scheimpflug imaging can help predict corneal edema resolution after Descemet membrane endothelial keratoplasty.

    Abstract

    Importance  Predicting the extent of corneal edema resolution after Descemet membrane endothelial keratoplasty (DMEK) may help in preoperative decision-making by identifying patients who may benefit from restoring endothelial function.

    Objective  To develop and validate a predictive model for edema resolution after DMEK using Scheimpflug tomographic imaging.

    Design, Setting, and Participants  Two prospective studies recruited participants with advanced Fuchs dystrophy at a university-based tertiary referral center between July 1, 2017, and August 31, 2019. Analyses were designed in November 2019 and completed on June 30, 2020. Development of a predictive model using linear least absolute shrinkage and selection operator regression was conducted in a derivation cohort (100 eyes). Overall performance, discrimination, and calibration were tested in the separate validation cohort (32 eyes).

    Exposures  Preoperative Scheimpflug parameters and patient-reported visual disability were considered as potential predictors of edema resolution: (1) tomographic features (irregularity of lines of equal corneal thickness, displacement of the thinnest point of corneal thickness from the inferior-temporal quadrant, and absolute amount of focal posterior corneal depression), (2) standardized anterior and posterior corneal backscatter, (3) preoperative central corneal thickness, and (4) Fuchs dystrophy–specific visual disability.

    Main Outcomes and Measures  Decrease in central corneal thickness after DMEK indicative of edema resolution.

    Results  Of the 88 patients included in the analysis, 54 were women (61%); median age was 68 years (interquartile range [IQR], 59-76 years). A median of 13 months after DMEK (IQR, 9-16 months), median corneal thickness was 77 μm lower (IQR, 51-94 μm) in the derivation cohort and 75 μm lower in the validation cohort (IQR, 54-96 μm) than before surgery. Per 10-μm edema resolution, eyes gained 0.66 Early Treatment Diabetic Retinopathy Study letters (95% CI, 0.09-1.23) in best-corrected visual acuity. Three tomographic features were present in 68 of 100 eyes (68%) in the derivation cohort and in 18 of 32 eyes (56%) in the validation cohort before DMEK and in only 1 of 132 eyes (1%) after DMEK. To predict edema resolution after DMEK based on preoperative assessment, 5 variables were selected by the statistical learning algorithm: nonparallel isopachs, focal posterior depression, anterior and posterior corneal backscatter, and central corneal thickness. In the separate validation cohort, the model showed high overall performance, discrimination, and calibration.

    Conclusions and Relevance  These post hoc analyses of prospective cohorts support a model for use in the prediction of edema resolution after DMEK using Scheimpflug measurement to identify patients benefitting most from DMEK.

    Introduction

    Descemet membrane endothelial keratoplasty (DMEK) has good clinical and patient-relevant outcomes, which results in a tendency to operate earlier in the course of the disease to try to maximize visual rehabilitation.1-3 To identify appropriate timing for intervention in patients with Fuchs endothelial corneal dystrophy, it is generally accepted that a comprehensive evaluation of optics, morphologic factors, and vision-related disability is needed.4 Corneal imaging helps recognize morphologic changes in the entire cornea, even before corneal specialists can detect changes on slitlamp examination.5,6 Once morphologic changes have manifested, they can persist in the cornea even after otherwise successful replacement of the Descemet-endothelium complex and limit complete visual rehabilitation.7-9

    Single measurements of central corneal thickness and slitlamp examinations are not ideal for assessing corneal edema because of high between-individual variation in healthy eyes.10-12 Tomographic Scheimpflug features may help identify corneal edema early in the course of Fuchs dystrophy, using characteristic patterns in pachymetry and posterior elevation maps.6 These patterns were present in corneas with a range of Fuchs dystrophy severity but not in control eyes.6 Patel and colleagues13,14 identified these tomographic features as markers that potentially indicate clinical progression of disease severity. To demonstrate that these tomographic features are truly specific for corneal edema, an interventional study design is needed in which investigators induce edema or help resolve it.

    In this study, we assessed the tomographic features and parameters of corneal shape and structure before and after intervention restoring endothelial function in eyes with advanced Fuchs dystrophy. Using a robust statistical learning technique, we developed a model to predict edema resolution after DMEK based on preoperative features and validated the model in a separate cohort.

    Methods
    Participants

    Participants in the derivation and validation cohorts were derived from 2 separate prospective studies: the Visual Function and Corneal Health Status study (derivation cohort)15 and a diurnal variation study (validation cohort) at the Eye Center Freiburg (recruitment, July 1, 2017, to August 31, 2019).11 The study was designed in November 2019; analysis and interpretation were completed on June 30, 2020. The studies and analyses were approved by the University of Freiburg ethics committee and adhered to the tenets of the Declaration of Helsinki.16 Informed written consent was obtained from all participants. Participants received no compensation other than parking vouchers. This study followed the Transparent Reporting of a Multivariable Prediction Model for Individual Prognosis or Diagnosis (TRIPOD) reporting guideline for cohort studies.17

    Both studies used the same inclusion and exclusion criteria and the same set of tests at baseline. All participants were scheduled for DMEK with or without phacoemulsification and posterior chamber intraocular lens implantation as described previously.3 Participants with corneal comorbidities other than Fuchs dystrophy and previous ocular surgery other than uncomplicated cataract surgery or YAG-laser capsulotomy were not included in the studies. In this analysis, only participants with a minimum stable follow-up of at least 2 months after DMEK and high-quality Scheimpflug imaging before and after surgery were included.

    Best-corrected visual acuity was assessed using Early Treatment Diabetic Retinopathy Study charts18 after standardized subjective refraction. Participants completed the validated German version of the patient-reported visual disability V-FUCHS instrument.15,19 The 2 independent scores—glare factor and visual acuity factor—were calculated using ordered polytomous Rasch-based partial credit models.19 Lower scores indicate less visual disability.

    Data Acquisition and Image Scoring

    Scheimpflug imaging was performed according to manufacturer instructions (Pentacam HR; Oculus). If needed, up to 3 attempts were made to obtain a high-quality image without data acquisition errors.

    To measure corneal shape, structure, and thickness, raw data were exported from the instrument (software versions 1.21r33 and 1.22r03). Corneal backscatter values of the anterior 120 μm and the posterior 60 μm were acquired over a 2-mm-diameter area centered on the corneal apex. Backscatter was standardized for instrument variation using a custom-made, titanium-embedded rigid contact lens as a scatter source and converted to scatter units (SU).20 Corneal edema resolution was calculated as the absolute difference between central corneal thickness before and after DMEK. To study the association between edema resolution and patient-relevant outcomes after DMEK, we assessed the gain of best-corrected visual acuity in eyes with complete preoperative and postoperative acuity tests using linear mixed models accounting for correlation of fellow eyes and adjusting for lenticular status (binary, phakic vs pseudophakic).

    To allow for standardized and masked grading of Scheimpflug patterns of corneal edema, the corneal pachymetry map and posterior elevation map were exported from the 4-map refractive display.6 To mask graders, all images were shuffled in a random order and identifiers were omitted.6 Three independent, board-certified ophthalmologists specialized in cornea (T.L., P.C.M., and K.W.) individually evaluated tomographic features: (1) irregularity of lines of equal corneal thickness (isopachs), (2) displacement of the thinnest point of corneal thickness from its location in the inferior temporal quadrant, and (3) the absolute amount of focal posterior corneal depression (in micrometers) (Figure 1). To assess the consistency of agreement between raters, 2-way random effects intraclass correlation coefficients were calculated for rating of displacement of the thinnest point and nonparallel isopachs. Higher intraclass correlation coefficient values indicate that more of the variance is explained by between-patient differences rather than by between-observer differences. In case of disagreement, the observers reviewed the images together to achieve a consensus. To acknowledge that predictions of edema resolution in the clinic setting will be based on a single ophthalmologist’s rating, the validation cohort was rated by only 1 ophthalmologist (K.W.).

    Model Development

    We developed a predictive model for corneal edema resolution as a continuous outcome in the derivation cohort. The following Scheimpflug parameters were considered as potential predictors of edema resolution based on subject matter knowledge and previous studies: (1) tomographic features of nonparallel isopachs (binary), displacement of the thinnest point (binary), and focal posterior corneal depression (continuous); (2) preoperative central corneal thickness (continuous); and (3) standardized anterior and posterior corneal backscatter (continuous).15,19 In addition to the tomographic features, demographic features (age at DMEK and sex) were considered for selection. In an exploratory analysis, we also evaluated preoperative V-FUCHS Glare Factor and Acuity Factor scores (continuous) and first-order interaction terms of all potential predictors. In addition, continuous variables were modeled as restricted cubic splines with 3 knots to address potential nonlinear associations.21

    To select among these numerous features, the best-performing model was identified using linear least absolute shrinkage and selection operator regression.22 The model with the lowest mean square error was selected after 10-fold cross-validation. The coefficients of the selected variables were estimated using a linear regression model.

    Model Assessment and Validation

    To externally validate the prediction model, the final regression model was then applied to a different group of eyes with advanced Fuchs dystrophy (validation cohort) that was not used during model development. The performance of the prediction model was evaluated in 3 respects.23 First, the overall performance was assessed as R2. Second, discrimination (ie, the ability to distinguish between patients with a certain amount of edema and those without edema) was assessed using C statistics by binarizing the amount of edema resolution. The arbitrary cutoff level selected was 50 μm, which was the lower 25th percentile of edema resolution in this study. The area under the receiver operating characteristic curve was calculated accounting for correlation of fellow eyes with bias-corrected bootstrapped 95% CIs with 1000 repeats. Third, calibration was assessed, indicating the agreement between observed outcomes and predictions. To this end, the mean difference between observed edema and predicted edema with 95% limits of agreement was calculated.24

    For future studies on implementations as a clinical decision support tool, the prediction model was presented as a regression formula.25 Confidence intervals for predictions (90% prediction intervals) were calculated to indicate the uncertainty around the estimated prediction of an individual eye

    Image description not available.

    where ŷ is the predicted value, zα/2 is the critical value of the gaussian distribution, σ̂ is the root mean square error of the model, x′ is the transposed vector of predictors (x1x6), and (X′X)−1 is the variance-covariance matrix of the prediction model.25

    Results
    Baseline Characteristics Before DMEK

    The derivation cohort consisted of 100 eyes and the validation cohort consisted of 32 eyes after excluding eyes with poor imaging quality before (n = 10) and after (n = 3) DMEK. Of the 88 patients included in the analysis, 54 were women (61%) and 34 were men (39%); median age was 68 years (interquartile range [IQR], 59-76 years). Participants in both studies had comparable baseline characteristics (Table 1). Before DMEK, eyes had a median corneal thickness of 586 μm (IQR, 555-611 μm) in the derivation cohort and 603 μm (IQR, 579-625 μm) in the validation cohort. Nonparallel isopachs were present in 77 eyes (77%) in the derivation cohort and 19 eyes (59%) in the validation cohort. In the derivation cohort, focal posterior depression was present in 73 eyes (73%) with a median absolute depression of 18 μm (IQR, 0-30 μm). In the validation cohort, focal posterior depression was present in 21 eyes (66%) with a median absolute depression of 13 μm (IQR, 0-24 μm). Before DMEK, all 3 tomographic features were present in 68 eyes (68%) in the derivation cohort and 18 eyes (56%) in the validation cohort. No tomographic features were present in 23 eyes (23%) in the derivation cohort and 9 eyes (28%) in the validation cohort.

    The consistency of agreement between the 3 raters in the derivation cohort was high for displacement of the thinnest point (intraclass correlation coefficient, 0.82; 95% CI, 0.78-0.85) and for parallelism of isopachs (intraclass correlation coefficient, 0.94; 95% CI, 0.93-0.96).

    Edema Resolution and Outcomes After DMEK

    Median time between the preoperative and postoperative Scheimpflug image was 12 months (IQR, 9-16 months) in the derivation cohort and 14 months (IQR, 10-18 months) in the validation cohort; the overall median time was 13 months (IQR, 9-16 months). After DMEK, the median corneal thickness was 77 μm (IQR, 51-94 μm) thinner than before DMEK in the derivation cohort and 75 μm (IQR, 54-96 μm) thinner in the validation cohort. In eyes with no tomographic features before DMEK, the median edema resolution was 42 μm (IQR, 28-60 μm) in the derivation cohort and 59 μm (IQR, 42-89 μm) in the validation cohort, resulting in a mean difference of 29 μm (95% CI, 17-41 μm) less edema resolution compared with eyes with tomographic features before DMEK. Postoperatively, only 1 eye (1%) in the derivation cohort and none of the eyes in the validation cohort had all 3 tomographic features; 87 eyes (87%) in the derivation cohort and 30 eyes (94%) in the validation cohort had no tomographic edema features after DMEK.

    Gain in best-corrected visual acuity after DMEK was higher in eyes with more edema resolution (n = 80) (mean gain in Early Treatment Diabetic Retinopathy Study letters per 10-μm edema resolution, 0.66 letters; 95% CI, 0.09-1.23 letters).

    Development of Predictive Model in the Derivation Cohort

    In the derivation cohort, the model with the lowest mean square error (473) to predict corneal edema selected the presence of parallel isopachs, focal posterior corneal depression, central corneal thickness, and anterior and posterior corneal backscatter.

    Adding first-order interaction terms and spline transformation of potential predictors selected combinations of previously identified predictors with the addition of displacement of the thinnest point (mean square error, 439). Interpretation of such a model would have been significantly more complicated; thus, the model without interaction and transformations was selected as the final model (Table 2).25

    Assessment and Validation of the Predictive Model

    To internally validate the developed model, goodness-of-fit statistics were calculated in the derivation cohort. In the derivation cohort, the overall performance of the model was high (R2 = 0.56; 95% CI, 0.43-0.69) (Figure 2). The area under the curve was 0.84 (95% CI, 0.73-0.92) to distinguish between patients with greater than 50 μm of edema and those with less edema, indicating high discrimination (eFigure in the Supplement).

    To externally validate the prediction model, the final model was applied to predict edema resolution in a separate cohort not included in the model development process (validation cohort). In the validation cohort, the overall performance of the model was high (R2 = 0.49, 95% CI, 0.37-0.62) (Figure 2). The mean difference between predicted and observed edema was 3.3 μm (95% CI, −41.4 to 48.0 μm), indicating good calibration without clear overestimation or underestimation (Figure 2). The area under the curve was 0.97 (95% CI, 0.86-1.00) to distinguish between patients with greater than 50 μm and those with less edema resolution, indicating high discrimination (eFigure in the Supplement).

    Predictions of edema resolution were illustrated in a patient example with low and high edema resolution. For example, a patient’s eye with Scheimpflug imaging features of clinically mild to moderate disease severity5,6 with anterior corneal backscatter of 1480 SU, posterior corneal backscatter of 800 SU, central corneal thickness of 560 μm, parallel isopachs, and no posterior depression would be predicted an edema resolution of 44 μm (90% prediction interval, 6-81 μm) after DMEK. In contrast, a patient with Scheimpflug imaging features of clinically advanced disease severity5,6 with anterior corneal backscatter of 1700 SU, posterior corneal backscatter of 1100 SU, central corneal thickness of 723 μm, pronounced focal posterior depression of 48 μm, and nonparallel isopachs would be predicted to have an edema resolution of 122 μm (90% prediction interval, 82-163 μm).

    Using nonstandardized measurements of corneal backscatter (corneal densitometry), the same predictors would have been selected (eTable 2 in the Supplement), with similar model performance in the validation cohort (R2 = 0.57; 95% CI, 0.34-0.80; area under the curve, 0.97; 95% CI, 0.87-1.00; mean difference between predicted and observed edema, 3.7 μm; 95% CI, −41.6 to 48.9 μm) as when using standardized predictors. In both patient examples, with low and high predicted edema resolution, edema resolution would not have been predicted to be significantly different, with 44 μm (90% prediction interval, 3-84 μm) and 119 μm (90% prediction interval, 72-166 μm), when using nonstandardized corneal optical densitometry compared with standardized backscatter.

    Discussion

    In this study, we developed and validated a model to help predict corneal edema resolution after DMEK based on a single Scheimpflug tomographic imaging examination in eyes with Fuchs dystrophy. To predict the presence of edema in these eyes, 5 factors are required. Two features were visible on tomography maps and 3 were indicators of corneal profile and structure (Table 3). The developed model performed well in the external validation in a separate cohort not used for model development. The predictive model’s overall performance, discrimination, and calibration were high in patients being assessed for DMEK.

    Quantifying disease severity is required to identify ideal candidates for endothelial keratoplasty and estimate their outcomes. Clinical grading of disease severity based on slitlamp examination alone has been shown to be insufficient to detect edema and subsequent corneal remodeling early in the course of the disease.5,6,26 Tomographic imaging may overcome such limitations. Edematous changes explain focal and diffuse posterior corneal depression and surface irregularities, as indicated by nonparallel isopachs and displacement of the thinnest point of corneal thickness (Figure 1).6,26-29 Herein, we showed that these tomographic features were truly specific for corneal edema by demonstrating their normalization after restoring endothelial function and corneal thickness by DMEK. Eyes without tomographic features of edema before DMEK experienced significantly less edema resolution after DMEK than eyes with any tomographic features. Eyes without tomographic features of edema are predicted to have a small, clinically irrelevant decrease in corneal thickness as well, as one would expect when stripping off a Descemet membrane that is 2-fold to 4-fold thicker in Fuchs dystrophy than in healthy corneas.30,31 Eyes with more edema resolution gained more letters in best-corrected visual acuity after DMEK, independent of previous cataract surgery.

    Prospectively recorded predictors and outcome allowed for post hoc development of a predictive model of edema resolution in eyes with Fuchs dystrophy. All 5 predictors are a plausible selection of the statistical learning algorithm. Anterior corneal backscatter is an indicator of corneal hydration control and a biomarker of early and persistent fibrotic remodeling.5,8,9,13 Posterior corneal backscatter is also known to be associated with early morphologic changes associated with patient-reported visual disability in Fuchs dystrophy.4,5 Although single measurements of central corneal thickness are not useful to detect corneal edema,6 in conjunction with backscatter and tomographic features, central corneal thickness added to the predictive model.

    The predictive model can be applied in future studies by scoring regularity of lines of equal thickness on the pachymetry map and assessing the amount of focal posterior depression, anterior and posterior corneal backscatter, and central corneal thickness. With these numbers on hand, edema resolution can be predicted manually using coefficients provided in Table 2 and the variance-covariance matrix (eTable 1 in the Supplement). Since standardization of corneal backscatter5,20 is not performed routinely in many practices, we provided the coefficients for nonstandardized corneal optical densitometry (eTable 2 in the Supplement).

    The predictive model has been carefully designed and validated (Table 3). Participants presented with tomographic features, morphologic changes, and optical disease stage in line with previous reports.1,8,12,32,33 Nevertheless, the model is predictive and not necessarily a reflection of causally and symptomatically important features of Fuchs dystrophy pathogenesis. Instead, the model uses variables that, in the form they were measured, allow for prediction—nothing more and nothing less. The predictive nature may explain why patient-reported visual disability scores were not selected to predict edema resolution. In contrast to CIs of the mean, prediction intervals for individual patients remained of substantial size, reflecting the uncertainty of the prediction process and natural variability in the population of interest.25

    Limitations

    Limitations of the study include its reliance on data from a single academic center and the use of an intermediate end point: edema resolution. Future studies will have to show whether implementing the model for clinical use results in improved decision-making and better long-term outcomes, such as less visual disability (Table 3).34 Whether the model also predicts disease progression in patients with clinically nonadvanced Fuchs dystrophy is unknown.

    Conclusions

    The developed and validated model described herein appears to predict edema resolution after DMEK in eyes with Fuchs dystrophy. Applying this model in clinical practice and in research settings in conjunction with subjective, morphologic, and optical parameters of disease severity4,19 may allow for more precise and personalized counseling on outcomes and may help set realistic expectations for clinicians, patients, and their relatives after DMEK, which is an elective surgery.

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    Article Information

    Accepted for Publication: December 18, 2020.

    Published Online: February 18, 2021. doi:10.1001/jamaophthalmol.2020.6994

    Corresponding Author: Katrin Wacker, MD, Eye Center, Faculty of Medicine, University of Freiburg, Killianstr. 5, 79106 Freiburg, Germany (katrin.wacker@uniklinik-freiburg.de).

    Author Contributions: Mr Zander and Dr Wacker had full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.

    Concept and design: Zander, Wacker.

    Acquisition, analysis, or interpretation of data: All authors.

    Drafting of the manuscript: Zander, Wacker.

    Critical revision of the manuscript for important intellectual content: All authors.

    Statistical analysis: Zander, Wacker.

    Obtained funding: Zander, Wacker.

    Administrative, technical, or material support: Zander, Grewing, Glatz, Lapp, Wacker.

    Supervision: Maier, Reinhard, Wacker.

    Conflict of Interest Disclosures: Dr Wacker reported being a consultant for ProQR Therapeutics, Leiden, the Netherlands, for projects unrelated to this work. No other disclosures were reported.

    Funding/Support: Mr Zander is supported by the Deutsche Ophthalmologische Gesellschaft (German Ophthalmological Society) with a thesis scholarship. Dr Wacker is supported by the Berta Ottenstein Program, Faculty of Medicine, University of Freiburg, Germany and the Deutsche Forschungsgemeinschaft (German Research Foundation, number 440526480).

    Role of the Funder/Sponsor: The funding organizations had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

    Meeting Presentation: This work was available virtually in part during the annual meeting of the German Ophthalmological Society 2020; October 9-11, 2020; virtual meeting.

    Additional Information: An interactive spreadsheet with the calculator is available freely to researchers from Dr Wacker.

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