Astigmatic Vector Analysis of Posterior Corneal Surface: A Comparison Among Healthy, Forme Fruste, and Overt Keratoconic Corneas

Accepted Manuscript Astigmatic Vector Analysis of Posterior Corneal Surface – a Comparison among Healthy, Forme Fruste and Overt Keratoconus Corneas Giuliano de Oliveira Freitas, Renato Ambrósio, Jr., Isaac Ramos, Bernardo Lopes, Bruno de Freitas Valbon, Cristiane Botteon, Milton Ruiz Alve PII:

S0002-9394(16)30178-7

DOI:

10.1016/j.ajo.2016.04.008

Reference:

AJOPHT 9716

To appear in:

American Journal of Ophthalmology

Received Date: 15 December 2015 Revised Date:

1 April 2016

Accepted Date: 13 April 2016

Please cite this article as: de Oliveira Freitas G, Ambrósio Jr R, Ramos I, Lopes B, de Freitas Valbon B, Botteon C, Alve MR, Astigmatic Vector Analysis of Posterior Corneal Surface – a Comparison among Healthy, Forme Fruste and Overt Keratoconus Corneas, American Journal of Ophthalmology (2016), doi: 10.1016/j.ajo.2016.04.008. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Purpose: To determine novel diagnostic parameters for keratoconus, and to assess the correlation between anterior and posterior corneal surfaces based on vectorial astigmatism analyses. Design: Retrospective case-control study. Methods: Six hundred and ninety-eight eyes of 698 patients were enrolled in the study. Healthy corneas, or controls (C, n=264), were compared to keratoconic corneas, further categorized as forme fruste (FFKc, n=212) and overt keratoconus (Kc, n=222). Corneal measurements were obtained from an Scheimpflug-based tomographer. Vectorial analyses were conducted in accordance with the method proposed by Thibos. Results: Posterior corneal astigmatic power vector (APV) >0.23 diopters (D) yielded a test for overt Kc with sensitivity and specificity rates of respectively 81% and 77%; indicating a positive likelihood ratio (LR+) of 3.5 and a negative likelihood ratio (LR-) of 0.25. Posterior corneal overall blur vector (Blur) >6.45 D yielded a test slightly less sensitive and specific, with rates of 75% and 72%, respectively; associated to LR+ of 2.7 and LR- of 0.35. The highest (Spearman’s ρ) correlation coefficients between anterior and posterior corneal astigmatisms were associated with Blur; being 0.93 for Kc, 0.87 for C, and 0.81 for FFKc. The astigmatism vectors along the 45-degree (J45), 0-dregree meridians (J0) and APV most often presented higher coefficient values for Kc and FFKc than for C (P=.01). Conclusions: Posterior corneal vectors APV and Blur constitute objective supplemental parameters for the diagnosis of Kc. Anterior and posterior corneal surfaces correlate in all groups, although it was not possible to accurately predict posterior astigmatism from anterior astigmatism.

ACCEPTED MANUSCRIPT TITLE: Astigmatic Vector Analysis of Posterior Corneal Surface – a Comparison among Healthy, Forme Fruste and Overt Keratoconus Corneas

SHORT-TITLE: Defining novel diagnostic parameters for keratoconus

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AUTHORS: Giuliano de Oliveira Freitas1; Renato Ambrósio Jr2,4;Isaac Ramos2; Bernardo Lopes2; Bruno de Freitas Valbon1,2; Cristiane Botteon3; Milton Ruiz Alves1. 1

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Department of Ophthalmology and Otorhinolaryngology, University of São Paulo (USP), São Paulo – Brazil 2 Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro – Brazil 3 Department of Ophthalmology, Federal University of Minas Gerais (UFMG), Belo Horizonte – Brazil 4 Department of Ophthalmology, Federal University of São Paulo (Unifesp), São Paulo – Brazil

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Correspondence: Giuliano de Oliveira Freitas, Clínica Oftalmológica do Hospital de Clínicas FMUSP, Av. Dr. Enéas Carvalho de Aguiar 255, São Paulo – Brazil. Telephone: +55 (11) 2661-7871. E-mail: [email protected]

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ACCEPTED MANUSCRIPT INTRODUCTION

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Keratoconus (Kc) is a clinical term used to describe an ectatic condition in which the cornea assumes a conical shape as a result of non-inflammatory thinning and protrusion (1). Such corneal thinning typically induces irregular astigmatism and myopia, often leading to a marked deterioration of visual acuity (2, 3). Although both eyes are affected, Kc typically is manifested asymmetrically (4, 5), usually at puberty and progressing into the fourth decade of life (6). The estimated prevalence of Kc is approximately 50 to 230 per 100,000 in the general population. Severe forms of Kc are major reasons for corneal transplantation (1). Undiagnosed preoperative mild forms of Kc have been reported to be a principal reason for iatrogenic corneal ectasia following keratorefractive surgery (7-10). At present, corneal topography of anterior surface, based on Placido’s disk, remains the predominant method for detecting Kc. However, topography-screening methods have inherent shortcomings (9, 11-13). Moderate to severe Kc cases can easily be identified using typical clinical findings and topographic screening. But subclinical forms of the condition, that may later develop ectatic changes, still represent a diagnostic challenge (14, 15). Recently corneal tomography has increased the ability of ophthalmologists to identify corneal ectasia at a much earlier stage (5, 16). Newer techniques, such as Scheimpflug-based tomography, have been developed to obtain a complete analysis of corneal geometry, permitting characterization of the anterior and posterior surfaces and pachymetric mapping (10, 13, 17). As Kc-associated changes apparently first arise on the posterior corneal surface, it has been suggested that corneal Scheimpflug tomography may readily detect topographically normal Kc cases (7, 10, 14). Recent studies, based on Scheimpflug tomography, have found that the shapes of anterior and posterior corneal surfaces correlate in a predictable way in the normal healthy eye (18, 19), although conflicting observations have been reported (20). Astigmatism is a vectorial variable: in addition to its magnitude, astigmatism has an orientation defined by its axis. A precise and complete analysis of corneal astigmatism must take this vectorial character into account (21). The aims of our study were (I) to characterize the astigmatism of posterior corneal surface, based on vector analysis, for healthy corneas, or normal controls (C), in comparison to keratoconic corneas, further categorized as forme fruste (FFKc) and overt Kc. Whether such characteristics could be useful as novel diagnostic parameters was also assessed. In parallel to this analysis, (II) we sought to evaluate any correlations between vectors of anterior and posterior corneal surfaces. All analyses were conducted within each group, followed by comparisons between groups.

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ACCEPTED MANUSCRIPT PATIENTS AND METHODS

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The research protocol of this retrospective case-control study was approved by the Ethics Committee of University of São Paulo (São Paulo, Brazil). Our study is registered at http://www.clinicaltrials.gov (identifier NCT02698709). The tenets of the Declaration of Helsinki were followed throughout the study. The study included 698 eyes of 698 patients. Two databases of patients were examined at the Instituto de Olhos Renato Ambrósio (Rio de Janeiro, Brazil), between July 2004 and October 2013. One of the databases contained the information of normal candidates to refractive surgery who did not develop any sign of corneal ectasia after laser in situ keratomileusis during a two year follow-up period, labeled as C (n = 264). The second database included information concerning keratoconic corneas, categorized as overt Kc (n = 222), if both eyes manifested classic Kc-suggestive topographic features, such as corneal steepness higher than 47.20 diopters (D), superior-inferior asymmetry higher than 1.40 D and thinnest pachymetric reading lower than 500 micrometers (10); or FFKc (n = 212), if only one eye exhibited such features (22). For C and overt Kc groups, only one eye was randomly selected per patient, in order to avoid any eventual correlation existing between the eyes of a single patient (18, 19). For FFKc group, only the unaffected eyes were enrolled in the study (22).

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Contact lens wear was discontinued at least 3 weeks for rigid contact lens and 1 week for soft contact lens before the assessment. All corneal astigmatism measurements were obtained from a rotating Scheimpflug corneal tomographer (Pentacam, Oculus Optikgeräte GmbH, Wetzlar, Germany). The patient’s chin was placed on the chin rest, and the forehead was placed against the forehead strap. After blinking a few times, the patient was asked to open both eyes and stare at the fixation target. Proper alignment was obtained using a joystick, and then the automatic release mode started the scan using 25 single Scheimpflug images captured within 2 seconds for each eye. By “inclusion criterion”, it was meant that only patients with good-quality Scheimpflug scans (labeled ‘‘OK’’ by the device in the ‘‘Examination Quality Specification’’) were selected. The exclusion criteria were previous eye surgery or trauma and any sort of corneal scarring that might interfere with keratometric data acquisition. For each group (C, overt Kc and FFKc), corneal astigmatism values were obtained as follows: I) Anterior astigmatism was calculated from simulated keratometric readings of central three millimeter optical zone (both steepest and flattest ones), multiplied by (1.376 - 1.0)/(1.3375 - 1.0), assuming that the refractive index of the air is 1.0, the refractive index of the cornea is 1.376, and the standardized corneal refractive index is 1.3375; II) Posterior astigmatism was calculated by ray tracing from Snell’s Law of refraction, taking into account the parallel incidence of light beams over the anterior corneal surface, the corneal width, the indices of refraction of the cornea (1.376) and the aqueous humor (1.336);

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ACCEPTED MANUSCRIPT III) For both anterior and posterior surfaces, astigmatism alignment () coincides with the steepest meridian of that surface. Vector astigmatism analyses were conducted using the method proposed by Thibos (23, 24) for both anterior and posterior surfaces according to the following equations:

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I) Average keratometric reading (M) = (Ksteep + Kflat)/2; II) Vector along the 0-degree meridian (J0) = [-(Ksteep - Kflat)/2] x cos2;

III) Vector along the 45-degree meridian (J45) = [-(Ksteep - Kflat)/2] x sen2; IV) Astigmatic power vector (APV) = (J02 + J452)1/2;

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V) Overall blur vector (Blur) = (M2 + J02 + J452)1/2.

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The above-mentioned calculations were performed using Microsoft Excel (version 14.4.7), and statistical analysis was performed using IBM SPSS (version 23.0) for MacIntosh. Descriptive evaluation of data was performed using the mean and median, interquartile range (IQR), and 95% confidence interval (95% CI). Normality of all data samples was checked by the Shapiro-Wilk test. Since normal sample distribution was seldom found among our data, non-parametric tests were chosen. The Mann-Whitney U test was used for comparisons between groups. Spearman’s correlation coefficient () was used to assess the strength of the correlations between pairs of variables. A P value of less than .05 was considered statistically significant. Receiver operating characteristic (ROC) curves were used to determine the overall predictive accuracy of test parameters, as described by the area under the curve (AUC), to calculate the sensitivity and specificity rates and, hence, positive and negative likelihood ratios of such parameters.

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ACCEPTED MANUSCRIPT RESULTS The mean age of the patients was 36.7 years. The median age was 32.4 years, with an IQR of 20.8 years. The subgroups of patients and their respective demographic data are summarized in Table 1.

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Table 2 compares vector parameters of posterior corneal surfaces between groups. The majority of parameters assessed exhibited statistically significant differences between groups (P value < 0.05). Exceptions were (I) the orientation of the steepest meridian between FFKc and overt Kc; (II) the toricity (defined as the difference between the steepest and the flattest corneal keratometric readings) of group C compared to that of FFKc; (III) the astigmatic component J45 that exhibited no difference among all groups and (III) the astigmatic power vector (APV) that exhibited no difference between C and FFKc groups.

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The AUC of the ROC curve, plotted for posterior corneal APV between C and overt Kc, reached 0.855, the highest value found in our study. A cut-off value of 0.50 D yielded a test for overt Kc with sensitivity and specificity rates, respectively, of 27% and 100%. This cut-off value corresponds to the highest value found for C. An alternative cut-off value of 0.23 D yielded a sensitivity of 81%, with a specificity of 77%. Consequently, a positive likelihood ratio (LR+) of 3.5 and a negative likelihood ratio (LR-) of 0.25 were calculated.

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The AUC of the ROC curve, plotted for posterior corneal Blur between C and overt Kc, reached 0.790. A cut-off value of 7.11 D yielded a test for overt Kc with sensitivity and specificity rates of 38% and 100% respectively. Such a cut-off value, arbitrarily chosen, corresponds to the highest value found for C. An alternative cut-off value of 6.45 D yielded a test with a sensitivity of 75%, with a specificity of 72%. Hence an LR+ of 2.68 and an LRof 0.35 were calculated.

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The cut-off values of 0.23 D and 6.45 D, mentioned above, correspond to the lower limit values of a 95% CI of their respective ROC curves. The AUC for all other parameters tested were < 0.790, hence considered irrelevant. Non-parametric correlation analysis between the astigmatism of anterior and posterior corneal surfaces was calculated within each group. The values of the correlation coefficients are shown in Table 3.

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Correlation coefficient values were consistently higher for the overt Kc group in comparison to the other two groups. The parameters J45 and Blur scored respectively - 0.910 and 0.934. Normal healthy corneas exhibited lower values of correlation coefficients, the lowest being equal to .571.

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Vector analysis of anterior corneal astigmatism was performed for each group, to permit the assessment of any eventual correlation with the astigmatism of posterior corneal surfaces (data are presented in the Appendix).

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ACCEPTED MANUSCRIPT DISCUSSION

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Topographic analysis of the anterior corneal surface has traditionally been the principal tool for characterizing Kc. Taking into account geometric and optical properties of the anterior corneal surface, several indices, algorithms and even neural networks have been developed to improve detection of Kc (9, 11-13) . However, clinically relevant posterior corneal astigmatism, as postulated by Javal back in 1890 (20), cannot be assessed by conventional topography (10, 13, 17). Astigmatism associated with the posterior corneal surface is gaining interest, due not only to its influence in overall eye astigmatism (20, 25, 26), but also to the alterations that seem to have taken place on the posterior surface at an earlier stage among keratoconic corneas (14). Newer techniques, such as Scheimpflug tomography, are able to measure both anterior and posterior corneal surfaces, generating corneal thickness and curvature maps (27). It is also possible to measure the amount of backscattered light in the different regions of the cornea (28). These additional data have permitted the computation of several secondary parameters, and have improved sensitivity and specificity in the detection of Kc (27). Power vectors were conceived as a way of transforming conventional refractive error, or keratometric data, into mutually independent, orthogonal components, better suited to statistical analysis (23). Vector analysis permits a complete description of astigmatism characteristics (21). Our study analyzed astigmatism of posterior corneal surface employing vector analysis in the comparison between C, FFKc and overt Kc. The same method was applied to investigate the correlation between anterior and posterior astigmatism within each group, assessing whether anterior and posterior corneal astigmatisms correlate in a predictable manner. Both FFKc and overt Kc groups were statistically younger than C (P value < 0.001), as shown in Table 1. We believe that this difference was due to the fact that C comprised candidates for refractive surgery, so that none of them was younger then 19.2 years old at the time of examination. Overt Kcand FFKc-patients, on the other hand, necessarily presented suggestive signs of Kc at their routine ophthalmologic examination. Neither the patients’ genders, nor eyes (left or right) enrolled in the study, presented statistically significant differences between groups. Considering any given parameter, a regular pattern became evident in Table 2: overlap of measurements was present among all groups; mean, median and IQR values found for overt Kc were usually greater than those found for FFKc and C (P values close to zero); FFKc and C presented similar values for mean and median (P values often close to the significance level of 0.05); a trend for C mean and median values to be slightly greater than those for FFKc; IQR values for FFKc often exhibited a wider range, in comparison to the C group. For example: the vector component J0, despite some overlap in its values among all groups, presented the greatest mean, median and IQR values for overt Kc; J0 mean and median values for C were greater than for FFKc, and IQR value for FFKc was greater than that for C. Our results suggest that C and FFKc groups shared similarities onto the posterior surface, to an extent that made any distinction impossible on a vectorial basis. However, differences between C and overt Kc were sufficiently marked to

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permit a clear distinction between them, based on posterior M, APV and Blur analyses. Each of these parameters was further analyzed using a ROC curve and the resulting AUC. Posterior APV and Blur ROC curves exhibited significant AUC: 0.855 and 0.790, respectively. The ROC curve exhibited an AUC of 0.652, hence considered insignificant. Selecting a cut-off value is always a compromise between sensitivity, the test’s ability to determine true positive cases correctly, and specificity, the test’s ability to determine true negative cases correctly (29). There is generally a trade-off between the two: as one measure increases, the other decreases (30). According to our data, any cornea might virtually be considered as keratoconic, if its posterior APV measured equal to, or greater than 0.50 D due to the test’s specificity rate of 100%. Even though, test’s overall sensibility would be minimal at this scenario. If an alternative cut-off value of 0.23 D were applied, sensitivity and specificity would be of 81% and of 77%, respectively. Such rates would result in a positive likelihood ratio (LR+) of 3.5 and a negative likelihood ratio (LR-) of 0.25; thus increasing the probability of Kc to 25% for a positive test, and decreasing the probability of Kc roughly by the same rate, for a negative test. Although they are seldom used, likelihood ratios have been reported to constitute one of the best ways to measure and express diagnostic accuracy (31). Likelihood ratios do not depend on the prevalence of the disease and can be used at the individual patient level. Their interpretation is intuitive: the larger the LR+, the greater the likelihood of disease; the smaller the LR-, the lesser the likelihood of disease (32). A posterior Blur cut-off measurement of 7.11 D also defines a cornea as keratoconic (rates of 100% and 38% for specificity and sensitivity, respectively). Compared to an APV cut-off value of 0.23 D, a Blur cut-off value of 6.45 D yielded a slightly less powerful differentiating approach. This result was with 75% and 72% sensitivity and specificity rates, respectively. The resulting LR+ of 2.7 increased to 20% the probability of Kc for a positive test. The LR- of 0.35 decreased it by the same rate for a negative test. It is well known that inter- and intra-observer evaluation of curvature maps is subjected to considerable variation (12). In such a subjective clinical context, the assessment of corneal posterior APV and Blur measurements may constitute an objective, and supplementary, friendly approach for the ophthalmologist in order to differentiate C from overt Kc. According to our findings, any posterior APV value above 0.23 D or Blur above 6.45 D might raise the ophthalmologist’s suspicion towards a likely diagnosis of a keratoconic eye. Values above 0.50 D or 7.11 D for posterior APV and Blur, respectively, could virtually ratify such diagnosis. Anterior and posterior corneal surfaces are thought to correlate (19). Our data are in accordance with literature, as shown in Table 3. Acorrelation is generally considered weak, if the Spearman’s correlation coefficient () is  ≤ 0.4, moderate if 0.4 <  < 0.8, and strong if  ≥ 0.8 (33). Overall blur vector presented the highest correlation coefficient values among all groups: 0.93 for Kc, 0.87 for C, and 0.81 for FFKc (P value = 0.01). The analysis of corneal power vectors APV, J0 and J45 revealed the presence of a statistically significant correlation between all anterior and posterior vectors’ magnitudes, especially among overt keratoconic corneas. Correlation coefficients found for FFKc group, most often, presented slightly higher values than those found for the C group. Prior to the analysis of our data, we hypothesized the correlation 8

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between anterior and posterior corneal astigmatism vectors would be stronger for C, somewhat weaker for FFKc and even weaker for overt Kc. This was based on the assumption that irregular astigmatisms, associated to keratoconic corneas, might induce less predictable, and hence, weaker correlations. However, the overt Kc group presented the highest correlation coefficients, both positive and negative, among all groups. A definitive explanation for such finding cannot be inferred based on our data, solely. However, a hypothetical explanation we formulated is that the evolving posterior astigmatism, present among keratoconic corneas, exerts gradual influence over anterior astigmatism, in a coupled manner; so their correlation becomes evident. Since the posterior astigmatism of normal corneas is usually not progressive in nature, its influence over anterior astigmatism tends to be much smaller. Regression analysis is commonly used to assess the relationship between the dependent (or observed) variable and one or more independent (or explanatory) variables, predicting the value of the dependent variable from a given value of independent variables. Regression analysis is based on a number of underlying assumptions, one of which is that variables involved must be linearly independent from one another (33). Inasmuch there is evidence that anterior and posterior corneal astigmatisms correlate (19), that assumption invalidates regression analysis for such cases. Therefore, our findings suggest that any attempt to predict posterior astigmatism vector parameters from anterior data might lead to unreliable results, in accordance with other study conducted by different methods (20). Our study certainly had limitations. The most significant one was the assessment of corneal surfaces limited to the central three millimeters optical zone. It is possible that eccentric keratoconus apices situated beyond such area have not been appropriately analyzed. If this assumption is correct, it might account, at least in part, for the inability to distinguish FFKc from C, or to further highlight the relation between the anterior and posterior surfaces. The assessment of corneal thickness, not performed in our study, and its possible relations to posterior astigmatism, may contribute to refine the diagnostic potential of posterior astigmatism analysis. In summary, we propose the vector analysis of posterior APV and Blur as a simple, objective, supplementary and friendly approach in the differentiation of C from overt Kc, complementing the traditional, and largely subjective, interpretation of maps. We also found the astigmatisms of anterior and posterior corneal surfaces to be correlated, particularly among keratoconic corneas. Despite any attempts to mathematically predict posterior astigmatism as a function of anterior astigmatism, a consistent equation could not be formulated. We believe it is possible that future refinements in data acquisition from posterior corneal surface could lead to further improvements in the analysis of posterior astigmatism.

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ACCEPTED MANUSCRIPT REFERENCES 1. Li X, Yang H, Rabinowitz YS. Keratoconus: Classification scheme based on video keratography and clinical signs. J Cataract Refract Surg 2009;35(9):1597–1603.

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2. Goebels S, Eppig T, Wagenpfeil S, Cayless A, Seitz B, Langenbucher A. Staging of keratoconus indices regarding tomography, topography, and biomechanical measurements. Am J Ophthalmol 2015;159(4):733-738.

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3. Moreira LB, Bardal RAC, Crisigiovanni LR. Contact lenses fitting after intracorneal ring segments implantation in keratoconus. Arq Bras Oftalmol 2013;76(4):215-217.

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4. Raiskup F, Theuring A, Pillunat LE, Spoerl E. Corneal collagen crosslinking with riboflavin and ultraviolet light in progressive keratoconus: ten-year results. J Cataract Refract Surg 2015;41(1):41-46. 5. Gomes JAP, Tan D, Rapuano CJ, et al. Global consensus on keratoconus and ectatic diseases. Cornea 2015;34(4):359-369. 6. Luz A, Fontes BM, Lopes B, et al. Best waveform score for diagnosing keratoconus. Rev Bras Oftalmol 2013;72(4):361-365.

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7. Muftuoglu O, Ayar O, Ozulken K, Ozyol E, Akinci A. Posterior corneal elevation and back difference corneal elevation in diagnosing forme fruste keratoconus in the fellow eyes of unilateral keratoconus patients. J Cataract Refract Surg 2013;39(9):1348-1357.

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8. Smadja D, Santhiago MR, Mello GR, Krueger RR, Colin J, Touboul D. Influence of the reference surface shape for discriminating between normal corneas, subclinical keratoconus, and keratoconus. J Refract Surg 2013;29(4):274-281.

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9. Torricelli AAM, Bechara SJ, Wilson SE. Screening of refractive surgery candidates for LASIK and PRK. Cornea 2014;33(10):1051-1055. 10. mbr sio-Jr R, Faria-Correia F, Ramos I, et al. Enhanced screening for ectasia susceptibility among refractive candidates: the role of corneal tomography and biomechanics. Curr Ophthalmol Rep 2013;1(1):28-38. 11. Randleman JB, Akhtar J, Lynn MJ, et al. Comparison of objective and subjective refractive surgery screening parameters between regular and highresolution Scheimpflug imaging devices. J Cataract Refract Surg 2015;41(2):286-294. 12. Ramos IC, Correa R, Guerra FP, et al. Variability of subjective classifications of corneal topography maps from LASIK candidates. J Refract Surg 2013;29(11):770-775.

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ACCEPTED MANUSCRIPT 13. Qin B, Chen S, Brass R, et al. Keratoconus diagnosis with optical coherence tomography–based pachymetric scoring system. J Cataract Refract Surg 2015;39(12):1864-1871.

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14. Ruiseñor-Vázquez PR, Galletti JD, Minguez N, et al. Pentacam Scheimpflug tomography findings in topographically normal patients and subclinical keratoconus cases. Am J Ophthalmol 2014;158(1):32-40. 15. Bühren J, Schäffeler T, Kohnen T. Validation of metrics for the detection of subclinical keratoconus in a new patient collective. J Cataract Refract Surg 2014;40(2):259-68.

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16. Galletti JD, Ruiseñor-Vasquez PR, Minguez N, et al. Corneal asymmetry analysis by Pentacam Scheimpflug tomography for keratoconus diagnosis. J Refract Surg 2015;31(2):116-123.

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17. Ambrósio-Jr R, Valbon BF, Faria-Correia F, Ramos I, Luz A. Scheimpflug imaging for laser refractive surgery. Curr Opin Ophthalmol 2013;24(4):310-320. 18. Montalbán R, Piñero DP, Javaloy J, Alió JL. Scheimpflug photography– based clinical characterization of the correlation of the corneal shape between the anterior and posterior corneal surfaces in the normal human eye. J Cataract Refract Surg 2012;38(11):1925–1933.

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19. Montalbán R, Piñero DP, Javaloy J, Alió JL. Correlation of the corneal toricity between anterior and posterior corneal surfaces in the normal human eye. Cornea 2013;32(6):791–798.

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20. Koch DD, Ali SF, Weikert MP, Shirayama M, Jenkins R, Wang L. Contribution of posterior corneal astigmatism to total corneal astigmatism. J Cataract Refract Surg 2012;38(12):2080-2087.

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21. Piñero DP, Alió JL, Tomás J, Maldonado MJ, Teus MA, Barraquer RI. Vector analysis of evolutive corneal astigmatic changes in keratoconus. Invest Ophthalmol Vis Sci 2011;52(7):4054-4062. 22. Saad A, Gatinel D. Topographic and tomographic properties of forme fruste keratoconus corneas. Invest Ophthalmol Vis Sci 2010;51(11):55465555. 23. Thibos LN, Horner D. Power vector analysis of the optical outcome of refractive surgery. J Cataract Refract Surg 2001;27:80-85. 24. Read SA, Collins MJ. Diurnal variation of corneal shape and thickness. Optom Vis Sci 2009;86(3):170-180.

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ACCEPTED MANUSCRIPT 25. Eom Y, Rhim JW, Kang SY, Kim SW, Song JS, Kim HM. Toric intraocular lens calculations using ratio of anterior to posterior corneal cylinder power. Am J Ophthalmol 2015;160(4):717-724. 26. Alpins N, Ong JK, Stamatelatos G. Corneal topographic astigmatism (CorT) to quantify total corneal astigmatism. J Refract Surg 2015;31(3):182186.

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27. Gilani F, Cortese M, Ambrósio RR Jr, et al. Comprehensive anterior segment normal values generated by rotating Scheimpflug tomography. J Cataract Refract Surg 2013;11(39):1707-1712.

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28. Lopes B, Ramos I, Ambrósio-Jr R. Corneal densitometry in keratoconus. Cornea 2014;33(12):1282-1286.

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29. Baratloo A, Hosseini M, Negida A, El-Ashal G. Part 1: Simple definition and calculation of accuracy, sensitivity and specificity. Emergency 2015;3(2):48-49. 30. Saunders L , hu , Bunce , or , reemantle N, rabb P. Ophthalmic statistics note 5: diagnostic tests - sensitivity and specificity. Br J Ophthalmol 2015;99(9):1168-1170. 31. MacGee S. Simplifying likelihood ratios. J Gen Intern Med 2002;17(8):647-650.

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32. Attia J. Moving beyond sensitivity and specificity: using likelihood ratios to help interpret diagnostic tests. Aust Prescr 2003;26(5):111-113.

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33. Shi R, Conrad S. Correlation and regression analysis. Ann Allergy Asthma Immunol 2009;103(Suppl):S35-S42.

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ACCEPTED MANUSCRIPT FIGURES’ CAPTIONS Figure 1. Receiver operating characteristic (ROC) curve for posterior corneal astigmatic power vector (APV) between healthy controls (C) and overt keratoconic corneas (Kc).

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Figure 2. Receiver operating characteristic (ROC) curve for posterior overall blur (Blur) between healthy controls (C) and overt keratoconic corneas (Kc).

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ACCEPTED MANUSCRIPT ACKNOWLEDGEMENTS/DISCLOSURE

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A) FUNDING/SUPPORT: No funding, nor grant support. B) FINANCIAL DISCLOSURES: Renato Ambrósio Jr works as a clinical consultant and lecturer for Oculus Optikgeräte (GmbH, Wetzlar, Germany). The following authors have no financial disclosures: Giuliano de Oliveira Freitas, Isaac Ramos, Bernardo Lopes, Bruno de Freitas Valbon, Cristiane Botteon and Milton Ruiz Alves. C) The authors thank Professor Rogério Melo Costa Pinto, PhD, (Head of Biostatistics at Federal University of Uberlândia, Minas Gerais, Brazil) for his contributions to statistical analysis and interpretation.

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TABLE 1. Demographic Data of the Patient Collective - a Comparison among Healthy, Forme Fruste and Overt Keratoconus Corneas C FFKc Kc Eyes (n) 264 212 222 R/L (n) 130/134 104/108 112/110 f/m (n) 138/126 85/127 91/131 Age (years) Mean 44.0 30.8 33.7 Median 44.6 31.1 27.8 IQR 19.6 14.7 13.8 C= control healthy corneas; f = females; FFKc = forme fruste keratoconus; IQR = interquartile range; Kc = keratocous; L = left eye; m = males; n = number; R = right eye.

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TABLE 2. Vector Parameters of Posterior Corneal Surface - a Comparison among Healthy, Forme Fruste and Overt Keratoconus Corneas P value a C C FFKc vs vs vs C FFKc Kc FFKc Kc Kc K steep (D) Mean -6.49 -6.40 -7.48 .030 .000 .000 Median -6.50 -6.40 -7.20 IQR 0.30 0.40 1.18 o α steep ( ) Mean 82.0 90.8 88.4 .006 .038 .916 Median 89.0 92.5 89.6 IQR 19.0 32.8 62.1 ∆K (D) Mean 0.33 0.35 0.83 .300 .000 .000 Median -0.30 0.30 0.70 IQR 0.20 0.20 0.60 M (D) Mean -6.32 -6.23 -7.60 .001 .000 .000 Median -6.30 -6.20 -6.85 IQR 0.30 0.35 1.00 J0 (D) Mean -0.15 -0.12 -0.14 .004 .299 .541 Median -0.14 -0.12 -0.12 IQR 0.11 0.15 0.37 J45 (D) Mean 0.00 0.00 -0.03 .360 .758 .806 Median 0.01 -0.01 0.00 IQR 0.09 0.15 0.47 APV (D) Mean 0.17 0.17 0.41 .403 .000 .000 Median 0.15 0.15 0.35 IQR 0.10 0.10 0.30 Blur (D) Mean 6.32 6.23 7.08 .000 .000 .000 Median 6.30 6.20 6.85 IQR 0.30 0.35 1.01 APV = Astigmatic power vector; Blur = overall blur vector; C= control healthy corneas; D = diopters; FFKc = forme fruste keratoconus; IQR = interquartile range; J0 = posterior corneal astigmatism vector along the 0-degree meridian; J45 = posterior corneal astigmatism vector along the 45-degree meridian; K steep = steepest keratometric reading; ∆K = toricity; Kc = keratoconus; M = average keratometric reading; α = meridian of steepest keratometric reading; o = degree sign; vs = versus; (a) Mann-Whitney U test.

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TABLE 3. Non-parametric correlations between anterior and posterior astigmatic vectors a - a Comparison among Healthy, Forme Fruste and Overt Keratoconus Corneas C FFKc Kc b b J0 (D) -0.78 -0.73 -0.85 b b b J45 (D) -0.59 -0.78 -0.91 b APV (D) 0.57 b 0.64 b 0.83 b b b Blur (D) 0.87 0.81 0.93 b APV = Astigmatic power vector; Blur = overall blur vector; C= control healthy corneas; D = diopters; FFKc = forme fruste keratoconus; J0 = posterior corneal astigmatism along the 0-degree meridian; J45 = posterior corneal astigmatism along the 45-degree meridian; Kc = keratoconus; (a) Spearman’s ρ correlation coefficient; (b) significant correlation (P value = .01).

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