The present study shows that the Fourier analysis of the RNFL thickness measurements obtained with SLP using variable corneal compensation improves the discrimination of glaucomatous from normal eyes, compared with the parameters provided by the GDx software. The area under the ROC curve for the LDF combining Fourier measures (LDF Fourier) was greater than the ROC area of any of the GDx software–provided parameters investigated. In this study, we also calculated sensitivities at high (≥90%) and moderate (≥80%) specificities. Depending on the patient population and diagnostic criteria, each of these conditions may be more desirable. At a fixed specificity of at least 90%, the LDF Fourier had a sensitivity of 84% to detect glaucoma, whereas the GDx parameters had sensitivities ranging from 24% to 69%. At a fixed specificity of at least 80%, the sensitivities of GDx parameters ranged from 40% to 82%, whereas the LDF Fourier had sensitivity of 93%.
Previous reports have also shown that GDx software–provided parameters have a limited ability to discriminate between normal and glaucomatous eyes.
6 7 8 9 10 11 The lower diagnostic ability of the GDx parameters may be related to the wide variability of absolute RNFL thickness measurements in healthy subjects. The RNFL thickness has been found to vary widely in the normal population.
4 14 This may limit the identification of glaucomatous eyes with loss of nerve fibers, but with absolute RNFL thickness still within normal limits. Rather than emphasizing absolute thickness itself, the Fourier analysis of RNFL thickness measurements provides a global measure that takes into account the whole shape of thickness distribution around the optic disc, emphasizing relative differences between local areas. In addition, by comparing relative differences in the shape of RNFL thickness distribution curve, the Fourier method may better identify patients with glaucoma with localized RNFL defects compared with the GDx parameters, which are usually calculated based on RNFL thicknesses averaged over a large region.
Although different methods of analyzing thickness measurements from SLP may result in an improved detection of eyes with glaucomatous RNFL loss compared with the GDx parameters, a persistent source of error may be related to the erroneous compensation for anterior segment birefringence.
17 18 19 20 The erroneous compensation for anterior segment birefringence produces a wider range of retardation measurements in normal eyes, which may complicate the identification of abnormalities. The effects of the axis and magnitude of corneal birefringence on RNFL retardation measurements have been described,
18 23 24 25 and algorithms designed to correct for this have been reported.
19 20 26 Garway-Heath et al.
20 proposed a correction of RNFL retardation measurements obtained using the GDx with fixed corneal compensation using perifoveal or peripapillary temporal retardation values. This method resulted in a narrower normal range of retardation measurements and improvement in the discrimination between normal and glaucomatous eyes. In another approach, Greenfield et al.
19 showed that the incorporation of CPMs improved the discriminatory ability of some GDx parameters. We used SLP data obtained using variable corneal compensation according to the method described by Zhou and Weinreb.
26 This method of anterior segment polarization compensation has been incorporated into the new commercially available scanning laser polarimeter (GDx VCC; Laser Diagnostic Technologies, Inc.) and is based on the determination of the magnitude and axis of anterior segment birefringence by polarimetry imaging of the Henle fiber layer. Individualized anterior segment compensation can be achieved with this method so that the measured retardation largely reflects the RNFL retardance. In a recent work, Weinreb et al.
27 showed that the diagnostic ability of several GDx parameters to classify eyes as glaucomatous or normal is improved considerably with SLP, using variable corneal compensation compared with SLP using fixed corneal compensation. This improvement was stronger for thickness parameters than for ratio–modulation parameters, probably because the latter may already compensate for some of the changes in retardation measurements caused by an inadequate corneal compensation in some patients. In our study, the areas under the ROC curve for the thickness parameters were generally greater than the ROC areas for the ratio/modulation parameters. The three summary parameters—superior average, ellipse average and inferior average—performed comparably. However, the area under the ROC curve for the best GDx parameter, superior average, was still significantly inferior to the area under the ROC curve for the LDF Fourier.
The GDx parameters evaluated in our study were the ones shown in the standard GDx printout and previously identified as having the best performance to discriminate glaucomatous from normal eyes. Thus, it is not surprising that the means of all GDx parameters (except symmetry) showed significant differences between glaucomatous and normal eyes. In contrast, among all the Fourier components, just a few seem to be important for discriminating glaucomatous from normal eyes. This is also not a surprising result, because the RNFL thickness profile has certain characteristics (like its double-hump shape) which are better described by some Fourier components than by others. When the Fourier components are combined, as in the LDF developed in our study, they become a powerful tool for analysis of polarimetry data, showing higher sensitivity and specificity than GDx parameters. In the present study, we did not examine the diagnostic ability of the GDx parameter, the number, because this parameter has been developed as a best means to interpret data obtained from SLP, using fixed corneal compensation. This parameter is calculated with a neural network approach and has been reported to be the best of the GDx software–provided parameters in the discrimination of glaucomatous from normal eyes.
9 10 11 42 43 44 It is possible that a new neural network based parameter using SLP-VCC data will have better diagnostic precision than the GDx parameters reported in our study, and the comparison of this method to the Fourier analysis of RNFL measurements should be investigated.
The application of Fourier analysis to the RNFL polarimetry data was initially reported by Essock et al.
16 Using SLP with fixed corneal compensation, they found a sensitivity and specificity of 96% and 90%, respectively, in the differentiation of glaucomatous from normal eyes. In our study, for a similar level of specificity, we found a lower level of sensitivity (84%). Different methods to evaluate the Fourier measurements and different population characteristics may be related to the different results. In the study by Essock et al., the average visual field MD of patients with glaucoma was −8.9 dB, considerably higher than the average MD of the patients included in our study (−5.9dB). Therefore, one of the reasons for the discrepancies in the results of the two studies may be related to different severity of glaucoma in the patient population. In another study using RNFL data obtained from SLP with fixed corneal compensation, Sinai et al. (Sinai MJ, Bowd C, Essock EA, Zangwill LM, Weinreb RN, ARVO Abstract 717, 2001) found an area under the ROC curve of 0.928 for discrimination between glaucoma and healthy eyes, using a Fourier-based LDF. Although this LDF significantly outperformed GDx parameters in that study, the overall unbiased assessment of its performance by split-half analysis resulted in a sensitivity of 73% with specificity of 73%. Fourier measures included in their LDF were the amplitudes of the 2nd, 12th, and 13th components, and also the phases of the 12th and 14th components. In the present study, we found an area under the ROC curve of 0.949 for the LDF, using RNFL data obtained from SLP using variable corneal compensation. The bootstrap estimate of bias of the area under the ROC curve was small and the application of a standard split-half analysis as an internal validation procedure for our LDF resulted in a sensitivity and specificity of 86% and 89%, respectively. This is an improvement over the previously reported Fourier-based LDF obtained with fixed corneal compensation data. Furthermore, the internal validation analysis of our LDF indicates that its robustness seems to be superior to the discriminant function developed using SLP with fixed corneal compensation data. The lower degree of robustness of the Fourier LDF developed with SLP FCC may be related to the wider variability of RNFL retardance measurements introduced by the erroneous compensation of anterior segment birefringence.
In our LDF, the second Fourier component was the most important (in terms of discriminative power) in the LDF equation. Both the amplitude and phase of this component were entered in the LDF after stepwise discriminant analysis. This is an expected result, because the second component has two humps and hence contributes the most to the shape of the RNFL double-hump curve. The other components serve to shape the pattern provided by the second component, so that the composite curve matches the original RNFL pattern. It is likely that the incorporation of higher-frequency components in the LDF may also be involved in the identification of glaucomatous eyes with localized RNFL defects, although our study did not directly address this question. Also, the pattern of the RNFL thickness profile of normal and glaucomatous eyes shows an apparent indentation of the superior hump
(Fig. 1) . This indentation may be related to the split of nerve fiber layer bundles, as described by Colen and Lemij.
45 Higher-frequency Fourier components may be also necessary to better describe this characteristic of the RNFL thickness profile. The mean overall RNFL thickness, or DC component, was also incorporated in our LDF obtained from SLP-VCC data, as opposed to the previously reported LDF obtained from SLP-FCC data. In that the absolute thickness parameters have improved diagnostic precision with the VCC compared with the FCC,
27 this is not a surprising finding.
One limitation of our study was that we did not test our discriminant function on another cohort of subjects to estimate its sensitivity and specificity independently. However, the provided bootstrap estimate of bias under the area of the ROC curve was relatively small, resulting in a reduction of the area under the ROC curve of 1.7%. Therefore, we expect that our results of sensitivity and specificity may be overstated by approximately the same amount. A recent analysis of our LDF with an independent sample resulted in an area under the ROC curve of 0.941 with sensitivity of 80% and specificity of 90% to discriminate glaucomatous from normal eyes (Michael Sinai, Ph.D., Laser Diagnostic Technologies, unpublished data, September 2002).
In conclusion, we showed that the combination of Fourier RNFL measures in an LDF obtained using SLP with variable corneal compensation improved the ability to differentiate between healthy eyes and eyes with glaucomatous visual field loss, compared with the GDx software–provided parameters. Further studies using larger samples and different populations are needed to develop and validate standard Fourier-based measures to be incorporated and tested in clinical practice.
The authors thank Michael Sinai, Ph.D., for valuable suggestions provided during a critical review of the manuscript.