Discriminating analysis formulas for detecting glaucomatous optic discs

DISCRIMINATING ANALYSIS FORMULAS FOR DETECTING GLAUCOMATOUS OPTIC DISCS*

MICHELE IESTER,1 CHRISTIAN Y. MARDIN,2 WIDO M. BUDDE,2

ANSELM G. JÜNEMANN,2 JOCHEN K. HAYLER,2 GIOVANNI CALABRIA1 and JOST B. JONAS2,3

1Department of Neurological Sciences, Ophthalmology, Genetic, Clinica Oculistica, University of Genoa and Division of Ophthalmology, G. Gaslini Institute, Genoa, Italy; 2Department of Ophthalmology and Eye Hospital, Friedrich-Alexander- University Erlangen-Nürnberg, Erlangen, Germany; 3Department of Ophthalmology and Eye Hospital, University of Heidelberg, Heidelberg, Germany

Abstract

Purpose: To evaluate whether discriminant analysis formulas of optic disc variables measured by confocal laser scanning tomography detect glaucomatous visual field defects. Methods: One hundred and sixtyone patients with perimetrically defined glaucomatous optic nerve damage and 194 normal subjects were recruited. All patients underwent confocal laser scanning tomography of the optic disc. The data were analyzed by four linear discriminant analysis formulae (sectorial, Bathija’s, Mikelberg’s, and Mardin’s formulae). The discriminant formulae had been obtained in completely different data sets from those of the present study. Results: The areas under the ROC curves of the three formulas and of the cup shape measure as a single parameter ranged from 0.649-0.81 in the group as a whole, and the results did not change when age-matched eyes were considered (from 0.618-0.812). All three formulas were better than the cup shape measure as the single parameter. Conclusions: In the various chronic open-angle glaucomas, the sectorial formula and Bathija’s formula tended to have higher diagnostic precision than Mikelberg’s formula and the cup shape measure. The scores of the formulae are weak indicators of the amount of glaucomatous visual field loss.

Introduction

Since the introduction of confocal laser scanning tomography,1-6 new quantitative parameters have become available for discriminating between normal and damaged optic discs.7-12 In an effort to increase the predictive value of these variables in differentiating normal eyes from eyes with early glaucomatous damage, mathematical equations combining various morphometric variables have been proposed.

*The details of this study have been published in British Journal of Ophthalmology 2000.

Address for correspondence: Michele Iester, MD, Viale Teano 71/1, 16147 Genoa, Italy. Email: iester@ csita.unige.it

Perimetry Update 2002/2003, pp. 287–292

Proceedings of the XVth International Perimetric Society Meeting, Stratford-upon-Avon, England, June 26–29, 2002

edited by David B. Henson and Michael Wall

© 2004 Kugler Publications, The Hague, The Netherlands

The purpose of the present investigation was to evaluate and compare four of these mathematical models (linear discriminant functions), which have previously been calculated and tested on different study populations in other glaucoma centers, on a new group of glaucoma patients.

Patients and methods

One hundred and ninety-four glaucomatous patients (mean defect, 7.5 dB; range, 1.6– 25.1 dB) and 161 normal subjects were included in the study. Per subject and patient, one randomly selected eye was taken for statistical analysis.

Criteria for the diagnosis of open-angle glaucoma were an open anterior chamber angle and glaucomatous visual field defects. A glaucomatous visual field defect was defined as an Octopus G1 field when the mean defect was greater than 2 dB and the corrected loss variance greater than 4 dB². All patients were perimetrically examined using the Octopus program G1 on the same day that the optic disc was evaluated.

The optic nerve heads were morphometrically evaluated using the Heidelberg Retina Tomograph (HRT, Heidelberg Engineering, Heidelberg; software version 2.01). The details of this technique, including its reproducibility and reliability, have already been described in detail elsewhere.1-12 The optic disc margin, defined as the inner edge of Elschnig’s ring, was outlined by an experienced observer (CYM). In case of doubt, an optic disc photograph, taken on the same day as the HRT image, was projected simultaneously in order to better visualize the border of the optic disc.

The HRT variables were measured for the optic disc as a whole and in four separate disc sectors. The right-angled superotemporal sector and the right-angled inferotemporal sector were tilted 15 degrees temporal to the vertical optic disc axis.13 The temporal horizontal disc sector with 60 degrees and the nasal sector with 120 degrees covered the remaining area. This disc sectioning is different from previous studies in which the optic nerve head was divided into six sectors (superotemporal, superonasal, nasal, inferonasal, inferotemporal and temporal).14

Formulas for early detection of morphological abnormalities:

1.A discriminant analysis formula developed by Mikelberg et al.:7 A = 10.99 * RV – 7.245 * HVC – 13.079 * corCSM – 2.662 (corrected CSM (cor CSM) = CSM + (0.001981 * (50-age))

(Reviewer’s comment: this formula is equivalent to the two formulas originally given. In this way, all four LDFs can be interpreted in the same way, i.e., if negative→ glaucoma).

2.A linear discriminant function developed by Bathija et al.:10

A = [-3.722803 - 5.57 * HVC + 11.78 * RNFLt - 4.37 * CSM + 1.85 * RA]

3.A sector based formula which was adjusted for varying sector size15:

A = [10.068 * ABRI - 7.018 * EAI + 4.181 * MHCN + 3.1 * MHCT - 2.081 * PHCS + 6.094 * CSM - 11.048 * RV – 8.047 * VBST + 1.828]

CA=cup area; corCSM=age-corrected cup shape measure; CSM=cup shape measure; CV=cup volume; EAI=inferior effective area; HVC=height variation of contour line; MHCN=mean height of contour line (nasal); MHCT=mean height of contour line (temporal); PHCS=peak height of contour line (superior); RA=rim area; inferior area below reference; RNFLt=retinal nerve fiber layer thickness; RV=rim volume; VBST=volume below surface (temporal)

4.A linear discriminant function developed by Mardin and colleagues12:

A = [-2.77 + 0.3 * RA + 3.7 * RV + 4.3 * RNFLt - 3.7 * CSM - 3.1 * CV - 0.9 * CA]

The total study group was subdivided into three strata by the size of the optic disc. In the subgroup with small optic discs, disc area was less than 2 mm2. In the subgroup with medium sized optic discs, disc area ranged between 2 and 3 mm2. In the subgroup with large optic nerve heads, disc area was larger than 3 mm2.

Student’s t tests were used to compare the two groups when the distribution of the data was normal, otherwise, Mann-Whitney non-parametric tests were used. p values below 0.05 were considered to be statistically significant. Sensitivity, specificity, and diagnostic precision were calculated for all the methods examined. Kappa statistics were used to assess the agreement between the five methods.19

Table 1. Descriptive analysis

DA: disc area; HRT: Heidelberg Retina Tomograph; CSM: cup shape measure; MIK: Mikelberg et al. formula; BATH: Bathija et al. formula; SECT: sector formula: MARD: Mardin et al. formula

Results

The glaucoma and normal groups, and their respective subgroups, differed significantly for all HRT variables measured (Table 1). Sensitivity and specificity of the four formulas ranged between 50 and 94% in the group as a whole (Table 2).

In terms of agreement, a kappa of 0.57 was found between the five methods with a standard error of 0.01 and a 95% confidence interval between 0.54 and 0.59. Among all five formulas examined, the sector formula had the highest agreement with all the other methods (Table 3).

Table 3. Kappa statistic

Kappa values for agreement ranged from 0.54 (moderate agreement, Mikelberg versus Mardin’s formula) to 0.83 (good agreement, Mardin’s versus sector formula) (Table 3).

In the small optic disc group subgroup, the formulae of Mikelberg et al. and Bathija et al. obtained the best results, while in the subgroups with medium large optic discs, the sector and Bathija formulae obtained the best results.

Discussion

Previous studies evaluated the sensitivity and specificity of these new quantitative optic disc variables for the differentiation of normal eyes and eyes with glaucomatous optic nerve damage. Using ROC curves, Iester et al. showed that the variable cup shape measure was the best single HRT parameter in their study for differentiating normal eyes from eyes with glaucomatous visual field defects.17 Correspondingly, Uchida et al. reported that the variable cup shape measure was the best single parameter for detecting glaucomatous optic nerve damage. In Uchida’s study, cup shape measure was even better than a combination of variables, and was similar to a trained neural network.8 Mikelberg et al. introduced all global parameters measured by the confocal laser scanning system in a discriminant analysis function, and obtained a discriminant formula.7 This formula was tested in a second study group that was different from the study group used to create the formula, and the results were similar.9 In a similar strategy, Bathija et al. used a linear discriminating analysis to dis-

tinguish between ocular hypertensive subjects with normal visual field from ocular hypertensive subjects with visual field defects.10 In addition, Bathija et al.10 tested the formula calculated by Mikelberg et al.,7 and obtained a relatively high diagnostic precision. However, Mikelberg’s formula did not reach the same diagnostic precision as Bathija’s formula, probably because, in contrast to Mikelberg’s formula, Bathija’s formula was created and tested on the same study population.

The differences in the diagnostic precision between the four formulas tested in the present study were not very marked; however, we found that the sector-based formula had the highest diagnostic precision of 82.0%. This in particular held true for the subgroup with the medium large optic discs and the subgroup with large optic nerve heads. The reason for these findings may be that, in the early stages of the disease, glaucomatous optic nerve damage leads to morphological changes, predominantly in the inferior and superior disc regions,18 which will be detected more sensitively in a sector-based strategy than in a strategy examining the entire optic disc area. It agrees with previous computerized ONH analysis and planimetric studies of optic disc photographs, in which the neuroretinal rim area measured separately in the temporal inferior and temporal superior disc sectors achieved higher correlation coefficients than the neuroretinal rim area as a whole, when correlated with the visual field damage.11 Correspondingly, the sector-based formula had a relatively low diagnostic precision in the subgroup of small optic discs (Table 3) in which an optic cup is often not present,22 and a division of the neuroretinal rim into different disc sectors is artificial.

Despite the increase in diagnostic precision obtained by calculating the discriminating formulas, the diagnostic precision of confocal laser scanning tomographic measurements of the optic nerve head were still relatively low for clinical conditions. The main reason for this could be the pronounced inter-individual variability for all optic disc parameters measured in the normal population. In previous studies, similar results were obtained when optic disc parameters were measured by planimetry of stereo optic disc photographs.13 The marked inter-individual variability also being typical of many other biological variables, such as body height and weight, this could be the reason why the normal group and the glaucoma group showed a pronounced overlap in quantitative optic disc variables. At the present time, all five methods have various limitations, and their clinical application can only be used as an indicative result to be added to all the other tests.

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