Investigative Ophthalmology & Visual Science, Vol. 33, No. 1, January 1992
Copyright © Association for Research in Vision and Ophthalmology
Discrimination Between Normal
and Glaucomatous Eyes
Joseph Caprioli
Discriminant analysis of quantifiable optic nerve, nerve fiber layer, and visual field measurements were
used to assign eyes to normal or glaucomatous groups. A database of 185 glaucoma patients with early
visual field loss and 54 normal controls was used to develop and test the discriminant function. Parameters that discriminated best between normal and glaucoma were relative nerve fiber layer height and
visual field mean defect. Cup-disc ratio, an estimate of optic nerve structure most commonly used by
practitioners, was the weakest of the structural parameters to discriminate between normal and glaucoma. The combination of structural and functional measurements performed better than structural or
functional measurements alone. When the discriminant function was applied to a group of 124 agematched ocular hypertensives, 20% were assigned to the glaucoma group. Discriminant analysis of
structural and functional measurements increases precision in identification of early glaucomatous
damage, provides a probability that glaucomatous damage is present, and may help identify those
ocular hypertensives who actually may have early damage. Invest Ophthalmol Vis Sci 33:153159,1992
Measurements of intraocular pressure have limited
value in diagnosing glaucoma. This realization has
placed greater emphasis on the evaluation of the early
structural and functional abnormalities caused by
glaucoma. The contemporary care of glaucoma patients requires careful, sequential examinations of the
optic nerve head and measurements of the visual
field. Despite advances in the technology used to perform perimetry and to record and measure the appearance of the optic nerve head and nerve fiber layer,
considerable uncertainty exists about making diagnoses of early structural and functional abnormalities. Treatment is not usually initiated in individuals
with mildly or moderately elevated intraocular pressure unless there is evidence of glaucomatous damage
because of the small proportion of such patients who
actually develop damage and because of the potential
morbidity of treatment.1 Reliable measures of early
glaucomatous damage are needed to identify those
who would most likely benefit from treatment and to
accurately assess whether the damage is stable or advancing in those being treated.
We have developed a database of quantitative visual field, optic nerve, and nerve fiber layer measurements in age-matched normals, ocular hypertensives,
and patients with early glaucoma. This study was performed to evaluate the relative abilities of structural
and functional measurements to discriminate between normal and early glaucoma, to test the discriminating power of combined structural and functional
measurements, and to explore the usefulness of discriminant analysis for identifying ocular hypertensives who may have early damage.
Materials and Methods
Subjects
Normal subjects had no history of eye disease and
were recruited from hospital staff and spouses or
friends of patients. None had presented for medical
evaluation. Those older than 40 years with a normal
eye history and examination, with normal visual
fields tested with automated threshold perimetry (Octopus programs 32 or Gl; Humphrey programs 30-2
or 24-2), and with no family history of glaucoma were
included. The eye examination consisted of slit lamp
biomicroscopy, tonometry, gonioscopy, dilated indirect ophthalmoscopy, stereoscopic optic disc photography, and computerized image analysis of the optic
nerve head.
All glaucoma patients over 40 years of age who had
automated threshold perimetry (Octopus programs
32 or Gl; Humphrey programs 30-2 or 24-2), stereoscopic optic disc photographs, and computerized
From the Glaucoma Service, Yale University School of Medicine, Department of Ophthalmology and Visual Science, New Haven, Connecticut.
Presented in part at the annual meeting of the Association for
Research in Vision and Ophthalmology, May, 1990.
This study was supported in part by grants from The National
Institutes of Health, Bethesda, Maryland (EY-07353), The Robert
Leet and Clara Guthrie Patterson Trust, Stamford, Connecticut,
Research to Prevent Blindness, Inc., New York, New York, and the
Connecticut Lions Eye Research Foundation, Inc., New Haven,
Connecticut.
Submitted for publication: December 12,1990; accepted July 22,
1991.
Reprint requests: Joseph Caprioli, Glaucoma Service, Yale University School of Medicine, Department of Ophthalmology and Visual Science, 330 Cedar Street, New Haven, CT 06510.
153
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INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / January 1992
image analysis were included. Computerized image
analysis was performed in patients with reasonably
clear media (20/50 or better) who could be dilated to 5
mm or more. Patients were considered glaucomatous
if they had elevated intraocular pressure (or a history
of elevated intraocular pressure before treatment) and
typical, early glaucomatous visual field defects as determined by the clinical criteria given below. Ocular
hypertensives met the same criteria as glaucoma patients, except that the visualfieldswere clinically normal. Nearly all ocular hypertensives and glaucoma
patients had previous experience with automated perimetry. A reliable visualfieldwas defined as one with
fewer than 15% false positive responses, fewer than
15% false negative responses, and patient performance judged by the perimetrist to be "good" or "excellent" (on a scale of "unreliable," "poor," "fair,"
"good," or "excellent"). Typical glaucomatous visual
field defects were defined, in a reliably performed visual field test, as at least:
1. two or more contiguous points with a 10 decibel
loss or greater in the superior or inferior Bjerrum's
areas, compared with perimeter-defined agematched controls;
2. three or more contiguous points with a 5 dB loss
or greater in the superior or inferior Bjerrum's
areas; or
3. a 10 dB difference across the nasal horizontal midline in two or more adjacent locations.
The most superior and inferior rows of threshold
measurements from the 30° programs were excluded
from these criteria to avoid including rim artifacts.
Visual field indices mean defect, corrected loss variance, and short-term fluctuation as described by
Hammer and coworkers were calculated for each visual field.2 These visual field parameters were not
used to define a glaucomatous defect. Pupils were dilated for perimetry in eyes with a pupil size of <2.0
mm. One eye of each patient was used in the study; it
was chosen randomly if both eyes were eligible. Informed consent was obtained from each subject after
the nature of the procedure was fully explained.
Image Analysis
A system for computerized image analysis (Rodenstock Instruments, Munich, FRG) was used to acquire fundus images and perform the preliminary topographic analyses. Measurements of disc area, cupdisc ratio, disc rim area, and cup volume were made
with the software supplied by the manufacturer. The
methodology and reproducibility of these measurements have been reported.34 The method used to
measure the relative height of the nerve fiber layer
Vol. 33
(NFL) at the edge of the optic disc has been previously
described with the reproducibility of the technique.5'6
Measurements of the height of the NFL surface relative to a standardized retinal reference plane were
made 100 microns outside the disc edge at 64 separate
locations around the disc. These measurements were
corrected for the optical magnification of the eye and
are in microns. Correction to absolute measurements
were made with ultrasonic measurements of axial
length (in most cases) or with refractive and keratometric measurements.7 The set of 64 individual measurements of relative NFL height are summarized by
the following parameters.
1. NFL height: The average of all 64 individual relative NFL height measurements.
2. Superior polar NFL height: The average of 8 individual relative NFL height measurements included in a 45° sector at the superior pole of the
disc, centered at the vertical axis.
3. Inferior polar NFL height: The average of 8 individual relative NFL height measurements included in a 45° sector at the inferior pole of the
disc, centered at the vertical axis.
4. Polar NFL height: The average of all relative NFL
height measurements within the two polar sectors
defined in 2 and 3.
Statistics
Probability plots were used to evaluate the normality of the data. For data that were normally distributed, Student's t-test was used for hypothesis testing
of the means. For data that were not normally distributed, the Mann-Whitney U-test was used for hypothesis testing. The level of statistical significance used
was P < 0.05. When multiple simultaneous comparisons were made, the critical significance level was adjusted downward with the Bonferroni correction.
A statistical software package (SYSTAT; Systat
Inc., Evanston, IL) was used to estimate the linear
model coefficients of the multivariate data set. The
discriminant function has the general form
a(X,) + b(X2) + c(X3) + • • • = k + diagnosis code
where a, b, c, • • • are the dependent variable coefficients, Xl5 X2, X3, • • • are the measured dependent
variables, and k is a constant. In this instance, the
diagnosis code is set to 1 for normal and 2 for glaucoma.8 Eight measured variables were used in the
model; stepwise regressions were not performed.
Two-thirds of the normal and glaucoma cases were
randomly chosen and used to calculate the discriminant function. The remaining one-third of cases were
classified with the discriminant function. This random selection process was repeated five times. The
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No. 1
DISCRIMINATION BETWEEN NORMAL AND GLAUCOMATOUS EYES / Coprioli
reported values are the average of the five passes, and
the standard deviation is reported where appropriate.
The probability of an eye being either glaucomatous
or normal was calculated. The discriminant score for
each of the normal cases was plotted in two-dimensional discriminant space to identify "normal" space.
Discriminant scores for the glaucoma and ocular hypertensive populations also were plotted with reference to the normal space. The discriminant function
was used to estimate the probabilities of ocular hypertensive cases being classified as either normal or glaucomatous.
Visual field mean defect was not used to identify
"true" glaucomatous cases, but it is likely to be correlated with the presence of visual field abnormalities
used here to establish glaucoma cases. Its effect on the
analysis was determined by calculating a separate discriminant function with mean defect omitted and
comparing it to the original function. Separate discriminant functions also were calculated for the structural parameters alone and for functional parameters
alone to test the relative abilities of structure and
function to discriminate between normal and glaucoma.
Results
Summary data for age, refractive error, visual field
indices, and structural parameters of the optic nerve
head are given in Table 1. The groups did not differ
significantly for age. There were statistically significant differences in refractive error between the groups
(P < 0.003). The visual field indices did not differ
significantly between the normals and the ocular hypertensives. The values in the glaucoma group re-
155
flected the clinical selection criteria for visual field
loss—most patients had early field loss (mean defect
4.5 ± 4.4 dB [mean ± standard deviation]). The visual
field indices in the glaucoma group were significantly
greater than those in the normal or ocular hypertensive groups (P = 0.000). There were no significant
differences among the groups for disc area. The cupdisc ratio and cup volume were significantly larger (P
= 0.000) and disc rim area was significantly smaller (P
= 0.000) in glaucoma patients compared to normal
controls. Values for ocular hypertensives were intermediate between those of glaucoma patients and normal controls.
A discriminant function was calculated from a randomly chosen sample made up of two-thirds of the
normal and glaucomatous cases in the database. The
dependent variable group classification coefficients
and constants are given in Table 2. These are used to
assign each case to the group with the largest function
value for that case. Table 3 contains the results of the
univariate F-tests and probabilities, and demonstrates
the relative strengths of all parameters to discriminate
between normal and glaucoma by listing F-values
standardized against the value for relative nerve fiber
layer height, the variable with the highest F-value.
The remaining one-third of randomly chosen cases
was used to test the classification scheme based on the
previously calculated discriminant function. The
mean (±SD) proportion of correct assignments in the
test sample (classification precision) was 87 ± 3%, the
mean sensitivity was 90 ± 5%, and the specificity was
76 ± 5%.
Discriminant analysis was repeated with the single
parameter mean defect omitted. Mean (±SD) classification precision was 85 ± 3%, sensitivity was 91 ± 4%,
Table 1. Descriptive statistics for age, refractive error, visual field, and optic nerve head*
Age (years)
Refractive error
(spherical equiv., diopters)
Visual field
Mean defect (dB)
Corrected loss variance (dB2)
Short-term fluctuation (dB)
Optice nerve head
Disc area (mm2)
Cup-disc ratio
Rim area (mm2)
Cup volume (mm3)
Nerve fiber layer
Relative nerve fiber layer
Height (microns)
Relative polar nerve fiber
Layer height (microns)
Normal
(n = 54)
Ocular hypertensive
(n = 124)
Glaucoma
(n = 185)
60.6 ± 11.0
57.1 ± 12.2
60.6 ± 10.8
-0.46 ± 2.66
-0.75 ± 2.72
0.2 ± 2.2
5.0 ± 14.4
1.7 ± 1.1
4.5 ± 4.4
30.4 ±35.4
2.9 ± 4.1
0.83 ± 1.83
-0.5 ± 1.5
2.6 ± 4.4
1.5 ± 0.7
1.67 ±
0.52 ±
1.08 ±
0.35 ±
0.29
0.15
0.22
0.15
1.79 ±
0.57 ±
1.03 ±
0.51 ±
0.44
0.22
0.33
0.33
1.72 ±
0.63 ±
0.84 ±
0.60 ±
0.41
0.14
0.27
0.27
-56
± 51
-82
± 66
-120
±68
34
± 51
8
± 78
-53
±92
' All data are presented as mean ± standard deviation.
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INVESTIGATIVE OPHTHALMOLOGY G VISUAL SCIENCE / January 1992
Table 2. Dependent variable group classification,
coefficients and constants
Normal
Vol. 33
10 -|
Normal
Glaucoma
a
W
Coefficients*
Visual field
Mean defect (dB)
Corrected loss variance (dB2)
Short-term fluctuation (dB)
Optic nerve head
Cup-disc ratio
Rim area (mm2)
Cup volume (mm3)
Nerve fiber layer
Relative nervefiverlayer
Height (microns)
Relative polar nerve fiber
Layer height (microns)
Constants*
0.596
0.0202
0.333
0.199
0.0442
0.471
81.2
43.0
-21.5
87.6
46.8
-26.3
-0.122
-0.129
0.089
-49.7
0.087
-44.7
6
M
UJ
OC
r\
\J
O
(O
4
2
* The average coefficients and constants of the discriminant functions calculated from five random samplings of the dataset is reported.
4
10
6
SCORE 1
and specificity was 60 ± 2%. The relative strengths of
the remaining parameters in this model to discriminate between normal and glaucoma were identical to
those of the original model.
Discriminant analyses were performed for structural parameters alone and for functional parameters
alone. Classification precision was 76 ± 2% for the
structural discriminant function (sensitivity = 88
± 4%, specificity = 35 ± 12%), and 77 ± 3% for the
functional discriminant function (sensitivity = 99
± 1%, specificity = 6 ± 6%). The relative strengths of
individual parameters in each of these models were
identical to those of the original model.
The ability of discriminant analysis to separate normal from glaucoma can be visualized in two dimensional discriminant space. Discriminant scores for
each normal case are plotted in Figure 1, and a Gaussian ellipse has been drawn that contains within its
1.0-
0.80.7O.60.5 0.40.3O.20.1 -
B
0.0
O.2
0.4
0.6
0.8
1.0
PROBABILITY OF BEING NORMAL
Table 3. Relative strengths of parameters to
discriminate between normal and glaucoma
1) Relative nerve fiber
layer height
2) Relative polar nerve
fiber layer height
3) Mean defect
4) Rim area
5) Cup volume
6) Correctd loss variance
7) Cup-disc ratio
8) Short-term fluctuation
Normal
0.9-
Univariate
F value
P
Standardized*
F value
25.0
0.000
1.00
25.0
24.5
23.7
23.2
22.0
13.4
6.2
0.000
0.000
0.000
0.000
0.000
0.001
0.010
1.00
0.98
0.95
0.93
0.88
0.54
0.25
• These values are standardized to the value for the relative nerve fiber
layer height, and indicate the relative strengths of individual parameters to
discriminate between normal and glaucoma. The values are the means of five
random samplings of the dataset.
Fig. 1. (A) The discriminant scores for normal eyes are plotted in
two-dimensional discriminant space. The Gaussian ellipse that is
drawn contains within its boundaries 95% of all cases. (B) The distribution of values of the probability of being classified as normal
for the same population.
boundaries 95% of all normal cases. Thus, a normal
discriminant space is identified and the locations of
glaucoma cases can be compared with it (Fig. 2). The
further a case lies away from normal discriminant
space, the less probable that it is normal.
Ocular hypertensives were classified with the combined discriminant function as being either "normal"
or "glaucoma"; 99/124 (80%) were classified as "normal" and 25/124 (20%) were classified as "glau-
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by the desire to recognize the earliest signs of glaucomatous optic nerve damage and to efficiently monitor
the status of advancing disease. The sensitivity and
specificity of measurements of the optic nerve head,9
nerve fiber layer,10 visual field,"'12 and other parameters13 have been evaluated. We have applied the statistical method of discriminant analysis to evaluate the
combined use of quantitative measurements of the
optic nerve, nerve fiber layer, and visual field to dis-
10 -i
Glaucoma
8 -
o a
UJ
K
O
o
CO
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DISCRIMINATION DETWEEN NORMAL AND GLAUCOMATOUS EYES / Coprioli
No. 1
4
10 -i
Ocular Hypertensive
2 8 -
4
10
6
6 UJ
cc
O
U
SCORE 1
2 -
1.0Glaucoma
tz °-9"
=
4 -
0.8-
o
4
5 0.7 H
SCORE 1
Q
6
10
< 0.6tt 0.5-
1.0-1
^0.4H
0.9-
Eocc °-3H
3 0.8
Q
cc
5 0.7 i
o
§ 0.2 H
°- o.H
rQ
0.0
B
0.2
0.4
0.6
0.8
1.0
PROBABILITY OF BEING NORMAL
Fig. 2. (A) The discriminant scores for glaucomatous eyes are
plotted in two-dimensional discriminant space. The 95% Gaussian
ellipse for the normal population is redrawn from Figure I for comparison. (B) The distribution of values of the probability of being
classified as normal for the same population.
coma." Figure 3 shows the locations of the ocular hypertensives with reference to normal discriminant
space.
Discussion
Attempts to quantify the early structural and functional abnormalities caused by glaucoma are driven
<
v>
Ocular Hypertensive
0.6
cc 0.5 H
UJ
CC
O
0.3 H
0.2 H
O.H
0.0
B
0.2
0.4
0.6
0.8
1.0
PROBABILITY OF BEING NORMAL
Fig. 3. (A) The discriminant scores for ocular hypertensive eyes
are plotted in two-dimensional discriminant space. The 95% Gaussian ellipse for the normal population is redrawn from Figure I for
comparison. (B) The distribution of values of the probability of
being classified as normal for the same population.
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158
INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / January 1992
criminate, with a calculable probability, normal from
glaucomatous eyes.
Discriminant analysis, introduced by Fisher in the
1930s, uses a combination of two or more measured
variables to separate a group of objects into two or
more populations. The approach is to determine a
function of the measured variables so that as many
members as possible of one population have high values for the function and as many members as possible
of the other population have low values for the function. Thus, the function can discriminate between the
two populations better than any of the measured variables can singly. The probability that a new object
belongs to either of the populations is calculated, and,
on that basis, the object is assigned to one of the populations. Discriminant and similar multivariate analyses have previously been used to predict visual field
defects from features of the glaucomatous disc,14 to
identify persons with glaucomatous visual field defects,15 and to evaluate multivariate data sets with respect to the identification ofriskfactors for glaucomatous damage.16'17
Discrimination is the process of deriving classification rules from samples of already classified objects.
Classification is the process of applying the rules to
new objects of unknown class. A commonly accepted
approach is to randomly choose two-thirds of the sample to derive the discriminant function and to use the
remaining one-third of the sample to test the classification accuracy. The cross-validation test uses repeated
random selections to evaluate the stability of repeated
passes of discriminant analysis to classify objects accurately. In each case, we calculated five discriminant
functions on separate random samples of % of the
population and tested the function five times on the
remaining '/»of the population. The averages of these
five passes provide a robust estimate of the precision
of classification and of the relative strengths of parameters to discriminate between normal and glaucoma.
The discriminant function that combined structural and functional parameters correctly classified
87% of eyes in this database compared to 76%
correctly classified by the structural discriminant
function and 77% correctly classified by the functional discriminant function. The combination of the
structural and functional parameters thus enhanced
the ability to correctly recognize a case as normal or
glaucomatous. Interestingly, the functional parameters had a high sensitivity (the ability to detect glaucoma cases) but a low specificity (the ability to detect
normal cases). The poor specificity of the functional
discriminant could be explained by several factors: (1)
nonglaucomatous causes for abnormalities of the visualfieldmean defect, especially cataract; (2) the early
nature of the visualfieldloss for which the visual field
Vol. 33
indices were not used as a diagnostic criteria; and (3)
the extensive overlap of the values of the functional
variables between the normals and the glaucoma patients. In comparison, the structural parameters had a
better specificity, but sensitivity was not as good.
Thus, the disc and nerve fiber layer parameters identify "normal" better than the visual field parameters.
The database used in this study was made up of eyes
with early glaucomatous damage to provide a rigorous test of discrimination. Higher proportions of
correctly classified eyes could be obtained if more
advanced glaucoma cases were used. These results
cannot be directly compared with other series of sensitivity or specificity measurements in different populations of glaucoma patients. The functional parameters used here are collected from both Octopus and
Humphrey instruments and represent several different visual field programs. The functional parameters
may have performed better if a more uniform test had
been applied.
The relative strengths of individual variables contained in the discriminant function to separate normal from glaucomatous eyes was approximated by
the relative average values of the univariate F-statistic
(see Table 3). Nerve fiber layer height measurements
and visual field mean defect were the strongest contributors to the discriminant function, followed by
rim area, cup volume, and visual field corrected loss
variance. Cup-disc ratio and visual field short-term
fluctuation contributed relatively little to the discriminant function. Measurements of cup-disc ratio used
here were calculated with image analysis techniques
and are more reproducible than subjective estimates
made from examination of patients or from disc photographs as routinely performed in practice.18"20 Despite this, cup-disc ratio was the weakest of the structural parameters to discriminate between normal and
glaucomatous eyes.
While the visual field index mean defect was not
used to identify "true" glaucomatous cases, it is likely
to be correlated with the presence of visualfieldabnormalities used to establish glaucoma cases. Therefore,
discriminant analysis was repeated with mean defect
omitted. The precision of classification with this
model was 85 ± 3% (SD), and therefore did not detract much from the model. The relative strengths of
the remaining parameters were unchanged compared
to the initial analysis.
The probability that a case is either normal or glaucomatous can be calculated with discriminant analysis and is the basis on which cases are assigned to either group. The same classification rules were applied
to a group of ocular hypertensives, and the probability
of each case being either normal or glaucomatous was
calculated. Twenty percent of ocular hypertensives
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DISCRIMINATION DETWEEN NORMAL AND GLAUCOMATOUS EYES / Coprioli
had a greater than 50% probability of being glaucomatous. These cases are more likely to have early glaucomatous damage and may be at risk for further damage. This approach integrates a large amount of numerical data that would otherwise be difficult to
quantitatively assimilate. It also provides an index
that an individual patient may actually have early
glaucomatous damage. Plots of the discriminant
scores in two-dimensional space with reference to the
boundaries of normal discriminant space is helpful
for graphically assessing the combined degree of structural and functional aberration of an individual patient, whether glaucomatous or ocular hypertensive.
The qualitative integration of numerous bits of
clinical information is done by practitioners every
day. When it is done well, it constitutes the "art" of
medicine. The introduction of large amounts of
quantitative information makes this kind of "cerebral" integration much more difficult. New, quantitative information about the status of visual function
and the structural characteristics of the optic nerve
should increase the precision with which we can make
an early diagnosis of glaucomatous damage. We present a method for integrating this type of quantitative
data to help the practitioner make decisions about
patients. Although optic nerve and nerve fiber layer
measurements are not yet commonplace, this preliminary report should serve as a basis for additional
work. Further progress will depend on the development of more robust quantitative structural parameters, visual field indices that more sensitively reflect
the character of early glaucomatous defects, and prospective evaluation of discriminant analysis for the
long-term follow up of glaucoma patients and ocular
hypertensives.
Key words: glaucoma, image analysis, optic nerve head, visualfield,discriminant analysis
Acknowledgments
The author thanks Maureen Roche and Pamela Ossorio
for their technical contributions to this study, and Karen
Lawhorn for assistance with the manuscript.
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