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From Moorfields Eye Hospital, London, United Kingdom.
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Abstract |
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METHODS. The approach (1) analyzed 30° sectors of rim area by (2) a novel and reproducible experimental reference plane, (3) estimated and accounted for measurement variability in each sector, and (4) required that any change exceeding variability in a single (positive) test should be confirmed as repeatable by a criterion requiring two of three consecutive tests to be positive. The sensitivity and false-positive rate of a single positive test and the two-of-three criterion were assessed in image series of one eye each of 20 ocular hypertension patients who converted to glaucoma (referred to as converters) who had unambiguous disease progression, and in one eye each of 20 normal control subjects.
RESULTS. Eighteen of 20 (90% sensitivity) converters and 7 of 20 (35% false-positive responses) control subjects had single positive test results, but with confirmation by the two-of-three criterion, the false-positive rate improved to 5% (1/20) whereas sensitivity was relatively preserved at 85% (17/20).
CONCLUSIONS. Estimates of rim area variability in each sector of each nerve allowed change consistent with disease progression to be distinguished from measurement variability. Confirming that change is repeatable by the criterion used in the study resulted in considerably fewer false-positive responses than did testing without confirmation, but with sensitivity not significantly compromised in the former. By this approach, eyes with progressive glaucoma could be distinguished from unchanging normal control eyes.
Although scanning laser tomography appears to be reproducible, analyzing and interpreting the vast information in each image is complex, and consensus remains to be reached on how best to approach these data. This difficulty is evident, for example, in the variety of reference planes proposed to describe anatomic parameters such as the neuroretinal rim and cup in the nerve’s three-dimensional architecture.9 10 11 12 13 14 15 Identifying change requires topography to be assessed in the extra dimension of time. To do this, some advocate directly analyzing surface height for change,16 17 whereas others have analyzed summary parameters such as rim area.9 18 19 Paramount to such assessment is the need to rule out measurement variability as a confounder before glaucomatous change can be judged to truly have occurred.
The parameter rim area has been suggested to be useful as a marker of progression in disc photographs20 21 22 23 and tomograph images9 19 (Heidelberg Retina Tomograph; Heidelberg Engineering GmbH, Heidelberg, Germany). In tomographic image analysis, we have found that rim area is reproducible compared with other parameters.24 Relating rim area loss to disease behavior is also a familiar task to clinicians. We have previously described a novel experimental reference plane that allows the parameter of rim area to be analyzed more reproducibly than reference planes conventionally used in tomographic analysis.25 Herein, we describe an approach that incorporates the experimental reference plane in evaluating progressive rim area loss. We describe how measurement variability can be estimated and accounted for in small regions of the neuroretinal rim in a way that is individualized to each ONH. The approach requires that any detected change be confirmed as repeatable before being attributed to disease progression. We show that this scheme is useful in distinguishing eyes with progressive glaucoma from the unchanging eyes of normal control subjects. Finally, we demonstrate how the technique may be applied clinically.
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Methods |
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Experimental Reference Plane.
This reference plane25 is customized to the morphology of each ONH. The position of the reference plane (REFpos) relative to each ONH is kept constant in any image series and is defined as
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Analysis of Rim Area.
Thirty-degree rim area sectors were evaluated for change. The parameter of rim area was calculated within a longitudinal image series, using the experimental reference plane to define the inner edge of the rim. The outer extent of the rim coincided with the contour line marking the inner margin of the scleral ring of Elschnig, outlined by the same observer (JCHT) in each subject’s baseline mean-topography image. Contour lines were exported to other mean and single-topography images in each series. Mean-topography images were derived from triplets of single-topography images using the software provided by the manufacturer (HRT ver. 2.01; Heidelberg Engineering, GmbH). Only images with a mean pixel standard deviation of less than 50 µm were used. Grainy images having a honeycombed appearance were excluded. Data from the mean-topography image of a test visit were used as the point estimate of rim area for that visit. Single-topography images from within a visit provided the data with which to derive mean-topography images by the tomograph software, as instructed by the manufacturer,10 and to estimate variability (described later). Topographical height was measured by the reference ring, the tomograph’s default referencing region in the image periphery used to establish zero in the z-axis.10 The reference plane differs from the reference ring in that it defines a level in topography by which parameters are defined and measured.
Estimating and Accounting for Sector Rim Area Variability.
Intra-Visit Difference Estimates for Calculating Limits of Variability.
Measurement variability in each sector of an image series was estimated and accounted for by way of limits of variability. Limits were modeled from intravisit difference estimates (denoted 
), calculated as the area difference in each rim sector between a pair of same-visit single-topography images. By this method, three single-topography images per visit yielded three per sector, but the more images acquired per visit, the greater the number of . Hence, four intravisit images yielded six per visit, five images per visit yielded 10 , six images per visit yielded 15 , and so on. The possible number of per visit can be calculated by
 | (2) |
for the visit, with r the number of images used in each combination (in this case, r = 2). The number of in any image series equates the total of all from all visits; all are used to calculate limits of variability. The is taken to be free from glaucomatous change, being derived from data from within a visit, not between visits. Using experimental reference plane analysis, we did not expect to be appreciably affected by glaucoma or testing involving different operators and visits.25
Limits of Variability to Account for Sector Variability in an Image Series.
Limits of variability were the confidence limits for each sector’s range of , calculated by multiplying the standard deviation of by the appropriate point of the t-distribution for n - 1 df. This allowed for better estimates of the limits of variability when dealing with relatively small samples (say, of <60).26 ONH can fluctuate considerably and affect its relationship with the reference plane. In keeping the z-axis distance between the ONH and reference plane constant in each eye’s image series, limits of variability can be considered a measure of agreement between repeated measures of the same sector and can be derived as described by Altman26 and Bland and Altman.27 In this study, the limits of variability define the extent to which measurements vary when compared with baseline rim area.
For an image series, limits of variability for each sector (VARLIM) can be expressed as
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is the sector rim area difference between pairs of intravisit single-topography images, i is the ith value of , X is the mean of observations of , and n is the number of observations of . Y is the t-statistic for degrees of freedom for , corresponding to a chosen two-tailed probability such as P = 0.05. The distribution of in sectors was examined on computer with histograms, normal plots, and Shapiro-Wilk significance testing (SPSS ver. 9 for Windows; SPSS, Inc, Chicago, IL) and found to approximate normality in more than 95% of sectors tested. It is expected that the distribution of differences would tend to be normal,26 but any departures from normality were log transformed. After transformation where needed, more than 99% of all tested sectors had normal distributions. Limits of variability can be expected to narrow with increasing degrees of freedom for . For this study, limits of variability were defined by P = 0.05, compatible with a 95% confidence limit.
Criterion for Confirming Change.
The limits of variability defined the smallest amount of change we could expect to detect above test variability. In addition, we wanted to establish criteria to help ensure that identified change is consistent with glaucomatous progression and not variability. Our criterion took the form of a system of duplicate testing, as espoused by Schulzer1 and Schulzer et al.28 for assessing visual fields in the Collaborative Normal Tension Glaucoma Study. Sequential rim area data for each sector were assessed for change exceeding limits of variability wherein a single observation of change was not accepted as disease progression but only regarded as tentative. To be attributed to progression, tentative change had to be verified as repeatable in at least two of three consecutive tests. After an initially positive result, there are three possible outcomes: (1) the subsequent second test result is positive (confirmed), (2) the second result is negative but the third is positive (confirmed), and (3) both subsequent test results are negative (not confirmed).
We empirically assessed the two-of-three criterion’s sensitivity and false-positive rate for identifying change in a reference data set. The data set comprised longitudinal image series of (1) eyes with progressive glaucoma—that is, eyes with ocular hypertension that convert to glaucoma (referred to as converters) and that had reproducible visual field defects—and (2) unchanging eyes of normal control subjects. These results were compared with other plausible criteria for confirming change: two-of-two, requiring two consecutive positive test results; three-of-three, requiring three consecutive positive results; two adjacent sectors on a single test; and two adjacent sectors on two consecutive tests.
Clinical Application of Approach.
Identifying and Confirming Progression.
Sequential rim area data were plotted as rim area profiles. Spatial and temporal information could thus be integrated simply. Profiles were plots of rim area by angular location round the ONH (0–360°, with 0° temporal, 90° superior, 180° nasal, and 270° inferior) from the same image series. This represented rim area at different points in time in a common graph. Limits of variability for each sector were plotted in relation to the baseline profile, with the region beneath the lower limits termed the zone of change. Rim area in a sector that diminished, exceeded its lower limit of variability, and entered the zone of change was taken to have changed more than measurement variability alone. A single positive result occurred if at least one sector exceeded its limit of variability on a single test. The repeated exceeding of a limit of variability to meet a chosen criterion meant that change was no longer regarded as tentative but to represent disease.
Evaluation in Progressive and Unchanging Eyes.
The approach for detecting progressive rim area loss was tested in the longitudinal image series of 40 eyes of 40 subjects: 20 normal control subjects and 20 age-matched ocular hypertension converters. In each subject only one eye was analyzed: a randomly selected eye in control subjects and the eye that had converted to glaucoma in the converters. Converters and control subjects regularly attended the Ocular Hypertension and Early Glaucoma Research Clinic at Moorfields Eye Hospital and had received imaging on at least six separate occasions over a minimum of 3 years. This study adhered to the tenets of the Declaration of Helsinki, having received appropriate institutional review board approval and the subjects’ informed consent.
Eyes of normal control subjects were taken to be unchanging. Normal subjects were volunteers comprising spouses or friends of hospital patients, hospital staff, or members of external nonmedical social organizations. They had (1) intraocular pressure (IOP) repeatedly less than 22 mm Hg, (2) serially normal and reliable visual fields (program 24-2; Humphrey Instruments, Inc., Palo Alto, CA) with Advanced Glaucoma Intervention Study3 (AGIS) visual field scores of 0, (3) no concurrent ocular disease or previous intraocular surgery, (4) no family history of glaucoma, (5) refractive errors less than ±6 D, and (6) age of more than 40 years. ONH appearance was not taken into account for entry into the study.
Converters were assumed to have progressive glaucoma in the eye that converted. They initially had a diagnosis of ocular hypertension with (1) IOP consistently 22 mm Hg or more in one or both eyes without IOP-lowering treatment, (2) open angles on gonioscopy, (3) initially normal visual fields (program 24-2; Humphrey Instruments) with AGIS scores of 0, determined after a learning period of three consecutive tests, (4) refractive errors ±6 D, (5) no concurrent ocular disease or previous intraocular surgery, (6) were aged more than 40 years, and (7) had development of visual field abnormality during the course of monitoring, according to AGIS criteria (score >0) that was reproducible on three consecutive tests. A glaucoma expert independently confirmed this. Other possible causes of visual field defects were excluded. Those on topical IOP-lowering treatment did not receive intervention that altered IOP during the period of monitoring reported in this study. ONH appearance was not part of the criteria for inclusion.
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Discussion |
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Burgoyne et al.9 reported a method for detecting change in ONH parameters defined by a reference plane fixed 150 µm below zero of the z-axis. Parameters were analyzed singly and in groups by univariate and multivariate analysis of variance, respectively, to tell whether change had occurred between baseline and follow-up visits. Analysis was based on six single-topography images per visit. The method was tested in image series of 12 monkey eyes. Using a criterion requiring two positive test results in a row, multivariate analysis showed confirmed change in 11 eyes having experimental glaucoma but also in four contralateral normal eyes. The method has been reported to be at least as good as expert subjective assessment of stereoscopic disc photographs.18
The approach we have described tests discrete rim area sectors for change and allows the discerning of patterns of loss. A new experimental reference plane was used that facilitates reproducible analysis of rim area. Variability is accounted for in each sector of each ONH by way of limits of variability. This is calculated from intravisit image data from across all test visits. Mean-topography images, each from one visit in time, provide the point estimates of rim area. In judging progression, data from any number of visits can be simultaneously assessed and weighed against variability. Only change repeatedly exceeding variability in two of three tests is attributed to progression. By this approach we found that eyes having unambiguous glaucoma progression could be distinguished from unchanging normal control eyes.
Measurement variability had to be rigorously accounted for, and we dealt with it in several ways. First, we introduced a novel reference plane that allows rim area to be analyzed reproducibly. By this, variability is expected to be significantly less and not appreciably affected by glaucoma or testing involving different operators and visits, compared with other conventional HRT (Heidelberg Engineering, GmbH) reference planes.25 Variability was thus simpler to account for. Second, we did not presume that variability is uniform across the ONH and so estimated variability in each sector separately. Third, estimation of variability was unique to each eye—necessary because, apart from ONH morphology, individual factors, such as media opacity32 and ability to maintain fixation,33 may affect variability differently in each eye. Fourth, only change that was repeatable in two of three tests was attributed to disease progression. This confirmation test strategy had fewer false-positive results than the single-test strategy, and sensitivity in confirming change was not significantly compromised. Hence, confirming change by this criterion resulted in fewer eyes being misidentified as having progressive glaucoma. The two-of-three criterion also had a favorable balance between sensitivity and the false-positive rate compared with other tested criteria. Fifth, variability was estimated using all image data from each series, with limits of variability updateable to factor in data from subsequently acquired images. This is desirable because the estimation of variability can be expected to improve with more values. Higher degrees of freedom of would result in narrower limits of variability, with the t-statistic decreasing as degrees of freedom increase (equation 3) . Sixth, although obtaining three single topographies per visit is advised, more images could be acquired per visit if the number of has to be increased quickly. This is possible because the number of increases exponentially according to mCr (equation 2) . For example, three images per visit yield 3 , but six images yield 15 (a 5-fold increase) and nine images yield 36 (a 12-fold increase). Thus, robust estimates of variability can be obtained rapidly, giving flexibility in clinical situations where indicated. However, fatigue of the patient and its consequences on variability must be considered when many images are acquired at a single sitting.
To verify progression, we constructed a rigorously defined reference data set based on converters with unambiguous visual field progression and normal control subjects. Ascertaining progression in converters—defined as the development of persistent defects in previously normal fields—is simpler than doing so in established glaucomatous fields. The latter can be an uncertain measure for external validation, because perimetric variability1 2 3 34 and inconsistency in interpreting change35 36 make ascertaining true change difficult. Also, perimetric variability in ocular hypertension is expected to be less than in glaucomatous fields.37 We assessed visual field conversion by a rational and accepted visual field template (AGIS), required that defects be repeatable in exactly the same locations in three consecutive tests, and sought expert independent verification. It was reasonable to assume that eyes in which disease progressed to field conversion had coexisting morphologic change.20 21 22 23 Age-matched normal eyes with similar follow-up acted as the controls.
We have described an analytical approach for identifying rim area loss in sequential scanning laser tomography images. We arbitrarily defined measurement variability by 95% confidence limits, tested the approach in two suitable groups of subjects, and found that the approach could distinguish eyes with progressive glaucoma from the unchanging eyes of normal control subjects. In a future study, we will further investigate the clinical significance and accuracy of various limits of variability and criteria for confirming glaucoma-induced change in a larger group of subjects.
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Footnotes |
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Submitted for publication August 20, 2002; revised December 3, 2002; accepted January 1, 2003.
Disclosure: J.C.H. Tan, None; R.A. Hitchings, None
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C. 
1734 solely to indicate this fact.
Corresponding author: Roger A. Hitchings, Research & Development, Moorfields Eye Hospital, City Road, London EC1V 2PD, UK; roger.hitchings{at}moorfields.nhs.uk
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