Detection of Subclinical Keratoconus by Using Corneal Anterior and Posterior Surface Aberrations and Thickness Spatial Profiles

Abstract

Purpose.: To assess the suitability of corneal anterior and posterior surface aberrations and thickness profile data for discrimination between eyes with early keratoconus (KC), fellow eyes of eyes with early KC, and normal eyes.

Methods.: Thirty-two eyes (group 1) of 25 patients were newly diagnosed with KC; 17 eyes of 17 patients (group 2) were asymptomatic fellow eyes without clinical signs of KC. One hundred twenty-three healthy eyes of 69 patients were negative control eyes (group 3). Zernike coefficients from anterior and posterior surfaces, data from corneal thickness spatial profiles, and output values of discriminant functions based on wavefront and pachymetry data were assessed by receiver operating characteristic (ROC) curve analysis for their usefulness in discriminating between KC (groups 1, 2) eyes and control eyes.

Results.: Vertical coma (C₃ ⁻¹) from the anterior surface was the coefficient with the highest ability to discriminate between groups 2 and 3 (area under the ROC curve [A_zROC] = 0.980; cutoff, −0.2 μm). For posterior wavefront coefficients and pachymetry data, A_zROC values were lower. Constructing discriminant functions from Zernike coefficients increased A_zROC values. The function containing first-surface data reached an A_zROC of 0.993; the functions containing posterior surface or pachymetry data had lower A_zROC values (0.932 and 0.903, respectively). The function with anterior, posterior, and pachymetry data reached an A_zROC of 1.0.

Conclusions.: Corneal wavefront and pachymetry data enabled highly accurate distinction of eyes with subclinical keratoconus from normal eyes. Posterior aberrations and thickness spatial profile data did not markedly improve discriminative ability over that of anterior wavefront data alone.

Post-LASIK iatrogenic keratectasia (IK) is a rare but dreaded, serious complication after keratorefractive surgery. ^1–3 It is associated with excess ablation of corneal tissue, thin residual stromal beds, and, most important, corneal refractive surgery in eyes with undetected keratoconus (KC) or, much less frequently, pellucid marginal degeneration. Studies have often revealed abnormal corneal topographic patterns. ^3–7 KC is a noninflammatory, progressive disease with a prevalence of 1 per 2000 in the general population and is characterized by a thinning of the corneal stroma, protrusion of the anterior corneal surface, and an irregular astigmatism. ⁸ Although clinical diagnosis of advanced KC stages is relatively easy to determine with biomicroscopic, keratometric, and retinoscopic signs, it is rather difficult to rule out subclinical KC before surgery. The term subclinical KC describes the very early preclinical stage of KC that can only be detected with diagnostic examinations such as corneal topography. ^9,10 Eyes that show suspicious topographic features that may be indicative of KC without any clinical sign or history are labeled suspected KC. With improving technology for corneal topography, much effort has been made to implement these data for patient screening in refractive surgery. So far, there have been several different approaches to discriminating between a cornea with subclinical KC and a normal cornea by using corneal topography. ^11–19 However, exact diagnosis of subclinical KC is still difficult, as there is a lack of defined threshold criteria. A major reason for that difficulty is that persons with suspected bilateral KC continue in their suspected status until definitive KC develops in one eye. However, because of lack of symptoms in the early stages, patients often present with advanced KC. Studies revealed differences in the corneal topographic pattern between normal eyes and eyes with presumed subclinical KC, as represented by fellow eyes or eyes of family members of KC patients. ²⁰  

We recently showed that data obtained from a Zernike decomposition of the first corneal surface could be used as a highly sensitive and specific diagnostic tool for the detection of subclinical KC, as represented by asymptomatic fellow eyes of eyes with early KC. ²¹ Zernike polynomials can be used for characterization of wavefront aberrations of the human eye and for complex corneal shapes, as found in KC. ^22–24  

Currently, most diagnostic and classification criteria for KC are based on anterior corneal curvature data derived from corneal topography. However, in recent studies, researchers report that early changes in eyes with KC are also present on the posterior corneal surface. ^18,19,25,26 In contrast to other placido disc–based videokeratoscopes, Scheimpflug-based topography technology enables analysis, not only of the anterior, but also of the posterior corneal curvature. Since the results of our previous study were very encouraging, ²¹ the present study was initiated to analyze wavefront data from the posterior corneal surface of KC eyes, subclinical KC eyes represented by asymptomatic fellow eyes of patients with newly diagnosed KC, and normal eyes. In addition, as it is known that keratoconic corneas display a more abrupt increase in corneal thickness from the thinnest point toward the periphery, ²⁷ the corneal thickness spatial profile was also analyzed. A major goal was to assess further improvement of sensitivity and specificity of discriminant analysis by adding input data from the posterior corneal surface and the thickness profile to better identify eyes with subclinical KC and to aid in the development of an automated KC detection system. 

Methods

Patients

Forty-two KC patients were enrolled between 2002 and 2008 at the Department of Ophthalmology of the Johann Wolfgang Goethe-University (Frankfurt am Main, Germany). Most of the data were collected for a prospective study published earlier. ²¹ For the present study, the dataset was enlarged by adding 14 eyes of seven patients, retrospectively. The eyes were assigned to two groups. The inclusion criteria for group 1 (early or moderate KC) were mild or moderate KC with no or only minor clinical symptoms (e.g., image distortion) and no clinical signs (e.g., Vogt striae, Fleischer ring, stromal scarring), no contact lens (CL) wear for at least 4 weeks (rigid CL) or 2 weeks (soft CL), and no history of eye disease or eye surgery. Diagnosis of KC was made if corneal topography (Orbscan IIz; Bausch & Lomb, Rochester, NY) displayed an asymmetric bowtie pattern, with or without skewed axes, as described elsewhere, ⁸ and a paracentral inferior–superior dioptric difference (PISD, ²¹ ) of >1.4 D. The inclusion criteria for group 2 (fellow eyes of early KC) were a diagnosis of KC in the contralateral eye (group 1); a PISD of <1.4 D; no clinical signs or symptoms, such as blurred or distorted vision, with best correction or subjective perception of comet-like asymmetric starbursts; no previous CL wear, as described earlier; and no history of eye disease or eye surgery. A set of 123 normal eyes of 69 patients served as the control group (group 3). All group 3 patients presented to the Refractive Surgery Unit of the University of Frankfurt and underwent a comprehensive ophthalmic examination to rule out contraindications for LASIK, as described elsewhere. ²⁸ Topography was considered normal if no irregular bowtie, no skewed axes, no “moustache” or “crab claw” sign, and no scar-related irregularities were present. Patients were excluded if they had a history of connective tissue disease, eye disease, or previous eye surgeries, or if corneal topography showed any suspect anomaly that might indicate KC or pellucid marginal degeneration. All patients underwent uncomplicated LASIK for myopia (81 eyes) or hyperopia (42 eyes) and had a regular 12-month follow-up without signs of ectasia. 

Informed consent was obtained from all patients after the purpose and characteristics of the study were explained. At the time the study was initiated, a review by the local ethics committee was not required. All study procedures adhered to the tenets of the Declaration of Helsinki. 

Corneal Topography

Corneal topographic examinations were performed (Orbscan IIz topographic system; Bausch & Lomb). Topographic examinations with movement artifacts and irregularities (e.g., due to tear film break-up or misalignment) were not included. For assessment and clinical classification, axial keratometric maps were used. The color scale of the software was set to 70 colors at 0.25-D increments, resulting in a range from 33.4 to 50.7 D. The PISD was calculated from axial keratometric data, as described before. ²¹  

Wavefront Aberrations of the Anterior and Posterior Corneal Surface

Anterior corneal surface aberrations were calculated from axial-keratometric data (Visual Optics Laboratory [VOL] Pro 7.14; Sarver and Associates, Carbondale, IL) by applying a least-squares fit over a pupil radius of 5 mm (linear sampling, dx, dy = 0.1 mm, wavefront Zernike modes). For analysis of posterior elevation data (best-sphere fit over a pupil radius of 5 mm), a custom program (written in MATLAB; The MathWorks, Inc., Natick, MA) was used. A Zernike approximation was performed for a corneal diameter of 6 mm up to the seventh order according to the VSIA (Vision Science and Its Application) standards for reporting aberration data of the eye.²⁹ Enantiomorphism was neutralized by inverting the sign of the mirror-symmetric coefficients of the left eyes,^30,31 as shown in equations 1 and 2.  

 

 

 

 

Corneal Thickness Spatial Profiles

Corneal thickness spatial profiles according to Ambrósio et al. ²⁷ were created by using pachymetry data (Orbscan; Bausch & Lomb, Inc.) corrected for inherent thickness overestimate with an acoustic factor of 0.92. ³² Data were exported in polar format (dθ = 24°, dr = 210 μm, centered to the thinnest point) and were processed with custom software (MATLAB). On each ring of data, the radius r (range, 0–4400 μm) yielded 15 data points according to the 15 meridians. The following metrics were generated from the data of each ring: (1) median (ME), minimum (MI), and maximum (MA) of absolute pachymetry data (A); (2) median, minimum, and maximum of percentage of thickness increase relative to the thinnest point (R); and (3) median, minimum, and maximum of the slope of the pachymetry profile (D). Slope data were obtained by computing the first derivative of a fourth-order polynomial fitted to the data of each meridian. 

Outcome Variables and Statistical Analysis

Differences between KC and Normal Eyes.

In the first step, normal distribution of the values of total higher order aberration (HOA) root mean square (RMS), coma RMS (RMS of all C _n ^±1), spherical aberration RMS (SA RMS and RMS of all HOA C _n ⁰), residual HOA RMS (RMS of all HOA C _n ^{> ±2}), first- to seventh-order RMS, and individual Zernike coefficients was checked by using a one-way Kolmogorov-Smirnov-Lillefors test. Differences between the KC groups (group 1 or 2) and the control group (group 3) were compared by Student's t-test or, in the case of non-normal distribution, with a paired Wilcoxon test. A global level of P < 0.05 for multiple tests was attained with the Bonferroni correction. Intergroup differences between groups 1 and 2 were not explored in the study and were not checked accordingly. For parametric testing, the sample size was adequate for the present analysis (β error <0.001 for P < 0.05). 

Discriminant Analysis.

Linear stepwise discriminant analysis was applied by using a two-group approach, to build metrics with input from data obtained from the anterior and posterior surfaces and from pachymetry. The stepwise method was applied to find the lowest possible number of independent variables necessary for correct classification. The following discriminant functions were generated:

•  
  DA (Zernike coefficients of the anterior corneal surface)
•  
  DP (Zernike coefficients of the posterior corneal surface)
•  
  DT (pachymetry metrics)
•  
  DAP (Zernike coefficients of the anterior and posterior corneal surfaces)
•  
  DAT (Zernike coefficients of the anterior corneal surface and pachymetry metrics)
•  
  DPT (Zernike coefficients of the posterior corneal surface and pachymetry metrics)
•  
  DAPT (Zernike coefficients of the anterior and posterior corneal surfaces and pachymetry metrics)

Each function was generated both with input data from groups 1 and 3 and from groups 2 and 3 (indicated by the subscript numbers, e.g., DA₁₃). Independents with the smallest Wilk's λ (the quotient from the intragroup square sum of values and the sum of intra- and intergroup square sum of values) and an F > 3.84 returned from an intergroup ANOVA were included in the function. The output values of the discriminant functions represent filtered and weighted wavefront errors and were used as a metric to discriminate between KC and normal eyes (groups 1 and 3) and between subclinical KC and normal eyes (groups 2 and 3).

ROC Analysis: Analysis of Sensitivity and Specificity.

ROC curves were plotted to obtain critical values (cutoff values) that allow classification with maximum accuracy. For each variable tested, the area under the ROC curve (A_zROC); sensitivity [true positive/(true positive+false negative)]; specificity [true negative/(true negative+false positive)]; and accuracy [(true positive+true negative)/total number of cases] and the cutoff value that corresponded to the maximum A_zROC were calculated. To reduce the amount of data, only parameters that yielded a correct classification rate of 80% and higher are reported. 

For ROC analysis a custom-written program was used (MATLAB). Another program was used for all other statistical tests (SPSS, ver. 11.0; SPSS Inc. Chicago, IL). 

Results

Demographics

Demographic data are shown in Table 1. Thirty-two eyes of 25 patients were classified in group 1 and 17 fellow eyes of 17 patients in group 2. The control group (group 3) consisted of 123 eyes of 69 patients. 

Table 1.

 

Demographic Data of the Patient Collective

	Group 1: Early KC	Group 2: Fellow Eyes	Group 3: Normal Eyes
Mean age in years ± SD	34 ± 10	33 ± 10	42 ± 10
(Range)	(18 to 55)	(19 to 55)	(19 to 63)
Eyes, n	32	17	123
SE, D
Mean	−2.38 ± 2.61	−1.60 ± 1.81	−2.33 ± 4.04
(Range)	(−9.63 to +1.00)	(−5.13 to 0)	(−9.25 to +5.0)
Sphere, D
Mean	−1.46 ± 2.71	−1.23 ± 1.65	−2.18 ± 3.78
(Range)	(−8.75 to +2.75)	(−4.50 to +0.50)	(−8.67 to +5.0)
Cylinder, D
Mean	−1.84 ± 1.42	−0.70 ± 0.57	−0.38 ± 1.31
(Range)	(−5.25 to 0)	(−2.00 to 0)	(−4.75 to 0)
BSCVA, logMAR
Mean	0.17 ± 0.2	0.02 ± 0.17	0 ± 0.08
(Range)	(−0.1 to +0.7)	(−0.1 to +0.3)	(−0.2 to +0.2)

Intergroup Differences: Wavefront Parameters

Among the wavefront data derived from the anterior corneal surface, statistically significant differences between groups 1 (KC) and 3 (normal control eyes; all P < 0.001 after Bonferroni correction, except those indicated below) were found for all RMS values of each order (first- to seventh-order RMS) for total HOA RMS; residual HOA RMS; coma RMS (P < 0.01), SA RMS; and the coefficients C₁ ⁻¹, C₂ ⁻², C₃ ⁻³, C₃ ⁻¹, and C₄ ⁻² (P < 0.01), C₄ ⁰, C₅ ⁻³, C₅ ⁻¹, and C₆ ⁴ (P < 0.01), and C₆ ⁶ (P < 0.01). There were fewer posterior surface wavefront parameters with significant differences between groups 1 and 3 (P < 0.001 unless otherwise indicated): total HOA RMS, residual HOA RMS, third- to sixth-order RMS, and C₃ ⁻¹, C₅ ⁻¹, and C₆ ² (P < 0.01) and C₇ ⁻¹ (P < 0.01). 

Statistically significant intergroup differences between group 2 (fellow eyes) and 3 were found for first-order RMS, coma RMS, and C₁ ⁻¹ and C₃ ⁻¹ from the anterior surface (all P < 0.001; Table 2). C₃ ⁻¹ was the only posterior-surface parameter with a significant difference between groups 2 and 3 (P < 0.05). 

Table 2.

 

Wavefront Parameters with Statistically Significant Differences between Groups 2 and 3

	Group 1: Early KC	Group 2: Fellow Eyes	Group 3: Normal Eyes
Anterior
First-order RMS	4.472 ± 2.419 (1.051 to 12.726)*	1.079 ± 0.349 (0.33 to 1.617)*	0.520 ± 0.373 (0.019 to 2.134)
Coma RMS	1.725 ± 0.995 (0.225 to 3.775)*	0.609 ± 0.300 (0.118 to 1.215)*	1.027 ± 0.732 (0.056 to 3.561)
C1 −1	−2.465 ± 3.881 (−8.203 to 8.335)*	−0.918 ± 0.361 (−1.577 to 0.292)*	0.127 ±0.475 (−1.233 to 1.611)
C3 −1	−1.320 ± 0.648 (−2.903 to 0.327)*	−0.322 ± 0.111 (−0.539 to 0.099)*	0.030 ± 0.174 (−0.330 to 0.891)
Posterior
C3 −1	0.432 ± 0.256 (−0.066 to 1.024)*	0.114 ± 0.110 (−0.038 to 0.306)†	−0.013 ± 0.072 (−0.178 to 0.242)

 Data are expressed as mean micrometers ± SD (range).

 Difference compared with group 3:

*   P < 0.001;

†   P < 0.05; (t-test or Wilcoxon test with Bonferroni correction).

Intergroup Differences: Pachymetry Data

All absolute thicknesses at the thinnest point and surrounding midperiphery were significantly smaller (P < 0.001) in KC (group 1) than in normal eyes (Fig. 1A, Table 3). Among median and minimum values, the outermost significant data points were those obtained 3150 μm from the thinnest point, whereas maximum data points beyond a distance of 2520 μm were not significantly different in both groups. Percentage thickness increases in groups 1 and 3 were significantly higher (P < 0.001) in KC eyes (group 1), regardless of the distance to the thinnest point (Fig. 1B, Table 4). Also profile slope values showed highly significant (P < 0.001) intergroup differences with higher slopes in group 1 eyes except for those data points obtained at the corneal periphery beyond 2730 μm from the thinnest point (Fig. 1C, Table 5). 

Figure 1.

 

Corneal thickness spatial profiles. (A) Absolute thickness. (B) Percentage thickness increase relative to the thinnest point. (C) Slope of the thickness profile. Data are the mean and standard deviation of the median obtained from each ring around the thinnest point.

Table 3.

 

Absolute Thickness

Absolute Corneal Thickness	Group 1: Early KC	Group 2: Fellow Eyes	Group 3: Normal Eyes
Median
0 mm	501 ± 41* (393–561)	522 ± 36* (456–583)	561 ± 29 (439–617)
2.10 mm	575 ± 36* (516–637)	576 ± 28* (524–625)	609 ± 26 (510–669)
4.41 mm	683 ± 38 (598–775)	687 ± 28 (644–730)	699 ± 34 (597–807)
Minimum
2.10 mm	554 ± 36* (477–629)	558 ± 30* (484–596)	592 ± 28 (469–654)
4.41 mm	775 ± 38* (598–683)	649 ± 63* (478–713)	671 ± 48 (510–778)
Maximum
2.10 mm	596 ± 36† (535–662)	598 ± 29† (537–644)	627 ± 27 (536–706)
4.41 mm	738 ± 44 (643–852)	728 ± 38 (649–813)	729 ± 38 (626–832)

 Data are expressed as mean micrometers ± SD (range). For clarity, only data for the 0-, 2.1-, and 4.2-mm radii are reported.

 Difference compared with group 3:

*   P < 0.001;

†   P < 0.01; (t-test or Wilcoxon test with Bonferroni correction).

Table 4.

 

Increase in Thickness

Thickness Increase	Group 1: Early KC	Group 2: Fellow Eyes	Group 3: Normal Eyes
Median
2.10 mm	15.2 ± 6.2* (6.7–33.3)	10.65 ± 4.61 (4.41–23.94)	8.69 ± 2.06 (4.7–16.4)
4.41 mm	37.2 ± 11.2† (17.5–66.3)	32.24 ± 9.64‡ (17.68–57.62)	24.84 ± 6.09 (8.51–41.98)
Minimum
2.10 mm	11 ± 5.8‡ (3.5–27.4)	7.04 ± 4.44 (2.12–20.95)	5.61 ± 1.98 (1.33–11.89)
4.41 mm	26.2 ± 23.8* (−72.6–60.7)	24.87 ± 14.51 (−11.39–51.35)	14.21 ± 19.48 (−70.02–40)
Maximum
2.10 mm	19.4 ± 7.5* (8.9–41.1)	14.77 ± 5.4 (9.67–27.7)	11.82 ± 3.01 (5.59–26.7)
4.4.1 mm	48.4 ± 13.8* (26.3–89.4)	40.12 ± 11.88† (20.32–75.41)	30.08 ± 6.52 (13.86–50.93)

 Data are expressed as the mean percentage ± SD (range). For clarity, only data for the 2.1- and 4.2-mm radii are reported.

 Difference compared with group 3:

*   P < 0.001;

†   P < 0.01;

‡   P < 0.05; (t-test or Wilcoxon test with Bonferroni correction).

Table 5.

 

Thickness Profile Slopes

Slope of Thickness Profile	Group 1: Early KC	Group 2: Fellow Eyes	Group 3: Normal Eyes
Median
2.10 mm	0.05 ± 0.014* (0.03 to 0.082)	0.042 ± 0.014 (0.018 to 0.081)	0.036 ± 0.009 (0.015 to 0.068)
4.41 mm	0.051 ± 0.026 (−0.059 to 0.085)	0.057 ± 0.015 (0.034 to 0.088)	0.041 ± 0.03 (−0.159 to 0.093)
Minimum
2.10 mm	0.042 ± 0.016† (0.017 to 0.076)	0.032 ± 0.014 (0.011 to 0.073)	0.028 ± 0.01 (−0.012 to 0.068)
4.41 mm	−0.039 ± 0.196 (−0.895 to 0.07)	−0.005 ± 0.104 (−0.31 to 0.065)	−0.066 ± 0.205 (−1.01 to 0.085)
Maximum
2.10 mm	0.066 ± 0.016† (0.042 to 0.102)	0.054 ± 0.013 (0.04 to 0.096)	0.049 ± 0.013 (0.024 to 0.103)
4.41 mm	0.09 ± 0.03 (0.007 to 0.144)	0.098 ± 0.023 (0.058 to 0.144)	0.074 ± 0.05 (−0.159 to 0.489)

 Data are expressed as the mean slope values ± SD (range). For clarity, only data for the 2.1- and 4.2-mm radii are reported.

 Difference compared with group 3:

*   P < 0.01;

†   P < 0.001 (t-test or Wilcoxon test with Bonferroni correction).

Also, when groups 2 (fellow eyes) and 3 (control eyes) were compared, absolute pachymetry profiles obtained from the same range across the cornea were significantly smaller in group 2 (P < 0.001; Fig. 1A); however, differences were not as pronounced as between groups 1 and 3. Among the percentage thickness increases, there were only a few data points at the peripheral cornea with higher median values in group 2 at 3570 and 4441 μm (P < 0.05; Fig. 1B) and higher maximum values from 3360 μm (P < 0.01). Significant differences in profile slope data were found only at the corneal periphery (median and maximum from 3360 μm, P < 0.05). 

Linear Stepwise Discriminant Analysis

The formulas of all discriminant functions are shown in 1. All output values for group 1 or 2 eyes were significantly different from group 3 normal control eyes (all P < 0.001; Table 6). The kind and the number of Zernike coefficients, as well as the magnitude of the discriminant coefficients, were dependent on the input data groups. The function DA₁₃, which was derived from the anterior surface Zernike coefficients of groups 1 and 3, consisted of the three Zernike coefficients C₃ ⁻³, C₃ ⁻¹, and C₄ ⁰, where C₃ ⁻¹ had the highest discriminant coefficient (0.87). The corresponding function DA₂₃, with input from group 2 and 3 data, needed eight coefficients (C₁ ⁻¹, C₂ ², C₃ ³, C₄ ⁰, C₅ ⁻³, C₅ ¹, C₆ ⁴, and C₆ ⁶) for optimum discrimination with C₁ ⁻¹, having the highest impact in the discriminant function (0.98). Functions with data from the posterior surface (DP₁₃ and DP₂₃) both contained C₃ ⁻¹ as the dominant Zernike coefficient. The input data for the pachymetry data–based discriminant functions (DT₁₃ and DT₂₃) were entirely different for the function based on data from groups 1 and 3, compared with that containing data from groups 2 and 3. DT₁₃ contained chiefly absolute maximum data, whereas DT₂₃ consisted of one of each value from minimum absolute, minimum relative, and maximum relative data. Slope data were not included in the function. Coefficients of further functions are shown in 1. Generally, the coefficients and pachymetry metrics of discriminant functions with combined input (e.g., DAP₁₃ and DAP₂₃ with input from both the anterior and posterior surfaces) were mostly identical with those included in functions with input from only anterior or posterior surface data. 

Table 6.

 

The Discriminant Function Output Values

	Group 1: Early KC	Group 2: Fellow Eyes	Group 3: Normal Eyes
DA13	−4.07 ± 2.05 (−8.88 to −0.06)	−0.23 ± 0.72 (−2.16 to 0.64)	1.1 ± 0.5 (0.01 to 2.25)
DA23	−7.74 ± 8.08 (−22.31 to 9.88)	−3 ± 1.21 (−5.23 to 0.97)	0.42 ± 0.97 (−2.02 to 3.13)
DP13	2.86 ± 1.98 (−1.59 to 7.39)	0.64 ± 0.96 (−1.09 to 2.01)	−0.84 ± 0.52 (−2 to 0.98)
DP23	5.23 ± 3.15 (−1.87 to 13.05)	2.54 ± 1.83 (−0.77 to 7.05)	−0.35 ± 0.83 (−2.15 to 1.75)
DT13	1.99 ± 1.7 (−0.54 to 6.58)	0.64 ± 1.13 (−0.55 to 3.4)	−0.63 ± 0.68 (−2.31 to 1.34)
DT23	−2.31 ± 1.75 (−6.48 to 0.86)	−1.82 ± 1.41 (−5.16 to 0.47)	0.22 ± 0.96 (−2.54 to 2.3)
DAP13	−4.29 ± 1.95 (−9.05 to 0.15)	−0.66 ± 0.76* (−2.29 to 0.19)	1.22 ± 0.58 (−0.24 to 3.1)
DAP23	7.14 ± 7.13 (−13.88 to 19.74)	3.26 ± 1.43 (0.94 to 6.2)	−0.45 ± 0.93 (−2.82 to 1.44)
DAT13	−4.12 ± 1.99 (−8.94 to 0.16)	−0.49 ± 0.86 (−2.44 to 0.55)	1.17 ± 0.52 (−0.28 to 2.4)
DAT23	−5.27 ± 6.32 (−16.58 to 10.75)	−3.15 ± 1.47 (−5.17 to 0.65)	0.41 ± 0.96 (to 2.06 to 3.18)
DPT13	3.09 ± 1.86 (−0.6 to 7.1)	0.82 ± 0.96 (−0.48 to 2.43)	−0.95 ± 0.62 (−2.58 to 0.45)
DPT23	−5.9 ± 3.45 (−14.68 to 0.88)	−3.4 ± 1.79 (−6.91 to 0.65)	0.48 ± 0.84 (−1.48 to 2.44)
DAPT13	−4.25 ± 1.93 (−9 to 0.02)	−0.72 ± 0.85 (−2.69 to 0.28)	1.23 ± 0.57 (−0.41 to 2.99)
DAPT23	−8.48 ± 7.47 (−24.8 to 5.63)	−4.3 ± 1.54 (−7.09 to 2.24)	0.61 ± 0.9 (−1.77 to 2.67)

 Data are expressed as the mean ± SD (range).

 Difference compared with group 3:

*   P < 0.01; for all others, significance at P < 0.001 (t-test with Bonferroni correction) was obtained.

ROC Analysis

In Figure 2, the discriminative ability (A_zROC) of individual Zernike coefficients from the anterior and posterior corneal surfaces is displayed graphically. Only anterior surface wavefront parameters discriminated between groups 2 and 3, with an accuracy of ≥80% (Table 7). Primary vertical coma (C₃ ⁻¹) had the highest discriminative ability (A_zROC 0.98, sensitivity 94.1%, and specificity 96.7%), followed by tilt (C₁ ⁻¹; A_zROC 0.968, sensitivity 100%, and specificity 85.4%) and first-order RMS (A_zROC 0.870, sensitivity 94.1%, and specificity 71.5%). 

Figure 2.

 

A_zROC values of each corneal Zernike coefficient. (A) First-surface aberrations, group 1 (early keratoconus) versus group 3 (normal eyes). (B) First-surface aberrations, group 2 (inconspicuous fellow eyes of group 1 eyes) versus group 3 (normal eyes). (C) Posterior surface aberrations, group 1 (early keratoconus) versus group 3 (normal eyes). (D) Posterior surface aberrations, group 2 (inconspicuous fellow eyes of group 1 eyes) versus group 3 (normal eyes). A higher A_zROC value (dark shading) signifies a better discriminative ability.

Table 7.

 

Results of ROC Analysis of Parameters to Discriminate between Normal and Keratoconus Eyes

	Cutoff Value		AzROC		Sensitivity (%)		Specificity (%)		Accuracy (%)
	1 vs. 3	2 vs. 3	1 vs. 3	2 vs. 3	1 vs. 3	2 vs. 3	1 vs. 3	2 vs. 3	1 vs. 3	2 vs. 3
First-order RMS anterior	≥1.412 μm	≥0.592 μm	0.996	0.870	96.9	94.1	97.6	71.5	97.2	82.8
C1 −1 anterior	≤−1.039 μm	≤−0.289 μm	0.814	0.968	81.3	100.0	99.2	85.4	90.2	92.7
C3 −1 anterior	≤0.276 μm	≤ −0.200 μm	1.000	0.980	100	94.1	99.2	96.7	99.6	95.4
MEA210	≤539 μm	≤549 μm	0.931	0.842	87.5	82.4	87.7	77.9	87.6	80.1
MEA840	≤546 μm	≤556 μm	0.918	0.844	84.4	82.4	90.2	77.9	87.3	80.1
MEA1050	≤553 μm	≤559 μm	0.908	0.843	84.4	82.4	87.7	77.9	86.0	80.1
MEA1260	≤558 μm	≤565 μm	0.892	0.846	81.3	82.4	87.7	78.7	84.5	80.5
MEA1470	≤571 μm	≤572 μm	0.872	0.844	84.4	82.4	79.5	78.7	81.9	80.5
MAA210	≤539 μm	≤549 μm	0.931	0.841	87.5	82.4	87.7	77.9	87.6	80.1
MAR4410	≥42.0 %	≥33.3 %	0.913	0.820	75.0	88.2	97.5	74.6	86.3	81.4
MED3570	≥0.053	≥0.052	0.714	0.819	56.3	82.4	80.8	80.0	68.5	81.2
MED3780	≥0.049	≥0.054	0.683	0.827	68.8	82.4	61.7	85.8	65.2	84.1

 Only those parameters are shown that discriminated between groups 2 and 3 with an accuracy of ≥80%. MEA, median of absolute thickness; MAA, maximum of absolute thickness; MAR, maximum of percentage increase; MED, median of slope of pachymetry profile.

Figure 3 graphically summarizes the A_zROC of the different pachymetry metrics. The single value with the highest discriminative ability was the median of the pachymetry profile slope 3780 μm from the thinnest point (MED3780; A_zROC 0.827, sensitivity 82.4%, and specificity 85.8%). Absolute thickness (MEA and MAA) reached maximum A_zROC values of ∼0.84 (Table 7). The only percentage increase that discriminated between groups 2 and 3 with an accuracy of ≥80% was the maximum at 4410 μm (MAR4410; A_zROC 0.820, sensitivity 88.2%, and specificity 74.6%). 

Figure 3.

 

A_zROC values of corneal thickness profile metrics. (A) Group 1 (early keratoconus) versus group 3 (normal eyes). (B) Group 2 (inconspicuous fellow eyes of group 1 eyes) versus group 3 (normal eyes). A higher A_zROC value (dark shading) signifies a better discriminative ability.

For the distinction between groups 1 and 3, output values of the discriminant functions showed high discriminative abilities, ranging between 84.4% (DT₂₃) and 100% (DA₁₃; Table 8). Also group 2 (KC fellow) eyes were distinguished from normal eyes (group 3) with high accuracy. The function DA₂₃, based on anterior Zernike coefficients from groups 2 and 3, discriminated with an accuracy of 96.7% (A_zROC 0.993, sensitivity 100%, and specificity 93.4%). Adding posterior surface and pachymetry data to the function (DAPT₂₃) improved performance to 100% accuracy (Table 8). However, functions based on posterior surface data (DP₂₃) or pachymetry data (DT₂₃) alone or on anterior and posterior surface data (DAP₂₃) had a lower discriminative ability (Table 8). 

Table 8.

 

Results of ROC Analysis of Discriminant Functions to Discriminate between Normal and Keratoconus Eyes

Discriminant Function	Cutoff Value		AzROC		Sensitivity (%)		Specificity (%)		Accuracy (%)
	1 vs. 3	2 vs. 3	1 vs. 3	2 vs. 3	1 vs. 3	2 vs. 3	1 vs. 3	2 vs. 3	1 vs. 3	2 vs. 3
DA13	≤ −0.025	≤0.417	1.000	0.970	100	94.1	100	91.0	100	92.6
DA23	≤ −2.122	≤ −0.966	0.815	0.993	81.3	100	100	93.4	90.6	96.7
DP13	≥0.219	≥ −0.375	0.965	0.919	93.8	88.2	97.5	85.2	95.6	86.7
DP23	≥1.261	≥0.934	0.963	0.932	93.8	88.2	95.9	94.3	94.8	91.2
DT13	≥0.291	≥ −0.458	0.951	0.861	84.4	94.1	90.2	65.6	87.3	79.8
DT23	≤ −0.544	≤ −0.372	0.913	0.903	84.4	94.1	84.4	78.7	84.4	86.4
DAP13	≤ −0.269	≤0.228	0.999	0.992	96.9	100	100	96.7	98.4	98.4
DAP23	≥2.135	≥0.924	0.825	0.992	81.3	100	100	92.6	90.6	96.3
DAT13	≤ −0.099	≤0.556	1.000	0.976	100	100	99.2	88.3	99.6	94.2
DAT23	≤ −2.253	≤ −0.627	0.828	0.986	78.1	100	100	88.5	89.1	94.3
DPT13	≥0.452	≥ −0.269	0.989	0.959	93.8	94.1	100	87.7	96.9	90.9
DPT23	≥ −1.566	≥ −1.099	0.971	0.990	93.8	94.1	100	96.7	96.9	95.4
DAPT13	≤0.041	≤0.286	0.999	0.991	100	100	97.5	96.7	98.8	98.3
DAPT23	≤ −2.004	≤ −2.004	0.860	1.000	78.1	100	100	100	89.1	100

 DA, wavefront data from the anterior corneal surface; DP, wavefront data from the posterior corneal surface; DT, pachymetry data; DAP, wavefront data from the anterior and posterior corneal surfaces; DAT, wavefront data from the anterior surface and pachymetry data; DPT, wavefront data from the posterior surface and pachymetry data; DAPT, wavefront data from the anterior and posterior surfaces and pachymetry data.

Discussion

By application of linear discriminant analysis, metrics were constructed that differentiated, with maximum sensitivity and specificity (100%), between normal eyes and fellow eyes of eyes with early KC, which represents the subclinical stage of KC. ²¹  

The present study is an extension of our previous investigation, ²¹ including wavefront data from the posterior corneal surface and corneal thickness spatial profile data. ²⁷ The discriminative ability of first-surface wavefront data and corresponding discriminant functions (Tables 7, 8, Fig. 2) was consistent with results in our previous study. ²¹ As expected, the discriminant function with input from group 2 and 3 eyes (DA₂₃) distinguished better between the two groups than did DA₁₃, and vice versa. This result is reflected in the different types and number of Zernike coefficients that showed significant intergroup differences and that were included in the discriminant functions. Figures 2A and 2B comprehensively demonstrate these differences. Coefficients on the cosine side of the Zernike pyramid that represent vertical asymmetry, such as primary and secondary coma (C₃ ⁻¹, C₅ ⁻¹), were the individual coefficients with the highest discriminative ability, as represented by the area under the ROC curve (A_zROC). For the discrimination of group 2 and 3 eyes, a similar pattern was found, with lower discriminative ability of nonprism, noncoma terms. However, not all coefficients that were included in the discriminant function DA₂₃ had reached high A_zROC values, as single coefficients for differentiation between groups 2 and 3. In general, posterior-surface wavefront data did not discriminate as high as first-surface data. There was no single posterior-surface coefficient or RMS value that classified correctly ≥80% of the group 2 and 3 eyes. In addition, the output values of the discriminant functions DP₁₃ and DP₂₃ did not separate as well as the output values from corresponding first-surface data functions (Table 8). This result strongly suggests that posterior surface data alone are not sufficient for the diagnosis of subclinical KC. This notion has been discussed recently by others. ^19,33 De Sanctis et al. ¹⁹ found that the maximum posterior elevation value (best-fit sphere over 5 mm) was discriminated with a sensitivity of 68% and a specificity of 90.8% between normal eyes and eyes with subclinical KC. ¹⁹ Khachikian and Belin ³³ suggested either fitting a toroid to the corneal back surface or using the elevation value obtained from the thinnest point, to increase sensitivity and specificity. The discriminant function DP₂₃, based on posterior surface Zernike data, reached sensitivity (88.2%) and specificity (94.3%) clearly above the results obtained from posterior elevation data by de Sanctis et al., ¹⁹ probably because Zernike-based discriminant functions contain more complex spatial information than does the posterior elevation maximum value. However, combining Zernike data from the anterior and the posterior corneal surface in one discriminant function increased the discriminative ability only if groups 2 and 3 were analyzed by using the function DAP₁₃ (Table 8). In the other cases, A_zROC and accuracy dropped minimally if posterior surface data were included in the discriminant function. 

Ambrósio et al. ²⁷ introduced the analysis of corneal thickness spatial profiles and found significant differences in absolute thickness and percentage thickness increase as a function of distance from the thinnest point between normal and KC eyes. The authors did not include eyes with subclinical KC and did not perform analysis of sensitivity and specificity, however. Their method, in conjunction with discriminant analysis, when applied to our patient collective, showed good discriminative ability between early KC eyes (group 1) and control eyes (group 3; function DT₁₃ A_zROC 0.951, sensitivity 84.4%, specificity 90.2%). Although A_zROC (0.903) and sensitivity (94.4%) of the function DT₂₃ for the discrimination between subclinical KC eyes (group 2) and control eyes were high, the specificity of 78.7% revealed that there was a considerable false-positive rate, thus putting the usefulness of DT₂₃ as a single metric into question. Table 7 and Figure 3 show that not all corneal regions were equally relevant for the differentiation between KC and normal eyes. The thinnest absolute pachymetry values, which are typically located centrally, provided higher discriminative ability than did the peripheral values. In contrast, percentage thickness increase and slope values obtained in the more peripheral regions (∼3 mm from the thinnest point) performed better than corresponding data from the central cornea. Of note, slope data had a higher specificity for the discrimination between subclinical KC and normal eyes than did absolute pachymetry results. Other combined discriminant functions yielded high accuracy, both for discrimination in group 1 versus 2 and in group 2 versus 3. The discriminant function with input from all three parameter categories (DAPT₂₃) yielded maximum sensitivity and specificity for separation of group 2 from group 3 eyes. Although this result suggests that a multimodal model may be needed for the detection of subclinical KC, it should be noted that the discriminant functions that include only first-surface data already had an excellent accuracy of 100% (DA₁₃ for the discrimination between groups 1 and 3) and 96.7% (DA₂₃ for the discrimination between groups 2 and 3), respectively. With regard to the marginal benefit of the multimodal approach (the functions DAPT₁₃ and DAPT₂₃) over the functions DA₁₃ and DA₂₃, first-surface Zernike coefficients alone may be sufficient for the detection of subclinical KC. 

Although the results from the present study are promising, the usefulness of the Zernike method for clinical practice must still be shown. It is possible that, in a sample drawn a priori, the performance of the discriminant functions that were based on this specific, relatively small patient collective would be poorer. Potential reasons for lower accuracy are higher false-positive rates due to the low prevalence of subclinical KC or other forms of subclinical KC that fail to be detected by the discriminant functions (e.g., superior or central steepening). Also the ceiling effect of a near-perfect classification rate for discriminant functions with different information contents may not be present in an a priori sample, with normal corneas mimicking subclinical KC and vice versa. In this case, the multimodal approach with input from both anterior and posterior surfaces and pachymetry data could be superior. This hypothesis will be tested in a study currently under way. Moreover, the present study method was used on input data generated with one instrument, the Orbscan IIz (Bausch & Lomb, Inc.). This device has certain shortcomings, such as a quadratic placido disc that does not cover the lower and upper corneal regions. Other Scheimpflug or Scheimpflug/placido hybrid systems that have recently become commercially available may also have a better image resolution than that of the Orbscan. Although the method has proved valid only for the Orbscan so far, the results of our studies showed high consistency. ^21,24 Thus, we believe that it can be applied to other devices. 

Summary

In summary, in the present study metrics constructed by discriminant analysis obtained from Zernike coefficients from the corneal first surface detected subclinical KC with excellent accuracy. Adding information from the posterior corneal surface and corneal thickness spatial profiles did not notably increase discriminative ability, most likely because the correct classification rates of anterior corneal surface data were already high (ceiling effect). In contrast, data obtained from the posterior corneal surface and from corneal thickness spatial profiles alone did not show classification rates superior to those from corneal first-surface data. Future studies including a larger sample size drawn a priori will elucidate the benefit of posterior surface and thickness spatial profile data. 

Footnotes

 Disclosure: J. Bühren, None; D. Kook, None; G. Yoon, Bausch & Lomb, Inc. (C); T. Kohnen, Bausch & Lomb, Inc. (C)

Appendix A

Formulas of the Discriminant Functions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

where MA is maximum, ME is median, and MI is minimum; A is absolute thickness, R is percentage increase in thickness, and D is the slope of the pachymetry profile; a is anterior, and p is posterior. The distance from the thinnest point along the radius is denoted (e. g., MAA4410 is the maximum absolute thickness at 4410 [μm]). The discriminant functions are described in the Methods section and in Table 8.