Selective loss of pattern discrimination in early glaucoma
Bruce A. Drum, Matthew Severns, David K. O'Leary, Robert W. Massof, Harry A. Quigley, Michael E.
Breton, and Theodore Krupin
A new perimetric pattern discrimination test was compared with conventional automated perimetry (Hum-phrey program 30-2 or Octopus program 32) in glaucoma patients, glaucoma suspects, and control subjects.The new test is based on the rationale that a greater percentage of retinal ganglion cells should be needed todetect a stimulus by its shape, or pattern, than by its brightness. The pattern discrimination stimulus was apatch of nonrandom dots embedded in a surrounding random dot field of the same average density. Patterndiscrimination thresholds were measured by changing the degree of regularity, or coherence, of the stimulus
dots. The fully coherent target was a static, 1-s duration, 20 X 20-dot checkerboard. Using a criterion-free
relative operating characteristic analysis, we estimated the ability of both the pattern discrimination andconventional tests to distinguish the normal data distribution from the suspect and glaucoma distributions.The pattern discrimination test appeared to produce separations greater than conventional perimetry forglaucoma suspects and separations equivalent to conventional perimetry for glaucoma patients.
1. Introduction
Conventional perimetry is based on detection of aspot of light superposed on a background field of uni-form luminance. Visual field loss measured in thisway has long been considered the definitive clinicaltest for glaucoma. However, it has recently becomeclear that conventional perimetry cannot detect theearliest stages of glaucomatous nerve damage.1 Thislack of sensitivity is not surprising in hindsight. Elec-trophysiological studies2'3 have shown that individualganglion cells can respond to light intensities that areclose to normal psychophysical thresholds. A signifi-cant sensitivity loss therefore may require a nearlycomplete gap in ganglion cell receptive field coverage.Because retinal ganglion cell receptive fields are exten-sively overlapping, 4 many ganglion cells could be lostbefore such a gap in visual field coverage occurs. Moresensitive tests are needed that will detect ganglion celldamage before it reaches such an advanced stage. Onepromising approach is to devise a stimulus that cannot
Bruce Drum, Matthew Severns, David O'Leary, Robert Massofand Harry Quigley are with Johns Hopkins University, School ofMedicine, Wilmer Ophthalmological Institute, Baltimore, MD21205; Matthew Severns is with LKC Technologies, Inc., 2 Profes-sional Drive, Gaithersburg, MD 20879; and Michael Breton andTheodore Krupin are with Presbyterian-University of PennsylvaniaMedical Center, Scheie Eye Institute, Philadelphia, PA 19104.
be detected unless a high percentage of ganglion cellsrespond to it. For example, a pattern stimulus that isvisible only by virtue of its shape would require cooper-ation from a number of neighboring intact ganglioncells. A test using such a pattern stimulus should thusbe more sensitive to glaucomatous damage than a testusing a simple spot of light. Similar theoretical ideashave motivated the recent development of glaucomatests involving pattern stimuli, such as acuity perim-etry5 and high-pass resolution perimetry.6 7
One mechanism that might make the detection ofsome types of pattern stimuli sensitive to early glauco-matous damage involves the retinal coding of spatialposition. The early stages of glaucomatous damagehave been reported to be largly diffuse 8 suggestingthat early ganglion cell loss tends to be distributedevenly over large areas of the retina. Even withinsmall areas of localized damage, the spatial pattern ofloss is likely to be somewhat random. On the assump-tion that the position of each point in the visual field iscoded by the weighted responses of all ganglion cellswhose receptive fields cover that point, we hypothe-sized that early ganglion cell loss might disturb thecoding of relative position in the visual field well beforea sensitivity loss becomes apparent. In other words,random ganglion cell loss might tend to randomize theapparent positions of neighboring points in the field bychanging the spatial center of gravity of the remainingganglion cell responses for each point.
To test the above ideas, we developed a visual fieldtest based on pattern discrimination rather than lightdetection.9 -13 The patient is asked to detect a patch ofnonrandom black and white dots embedded in a sur-
rounding field of random dots. The average dot densi-ties of the target and surrounded fields are equal,eliminating luminance cues to detection. Target visi-bility is controlled by the addition of random noise,and threshold is determined by the amount of addednoise necessary to render the target invisible.
In this paper, we compare glaucomatous visual fieldloss measured with pattern discrimination perimetry(PDP) and conventional automated visual fields(CVF) using the Humphrey and Octopus perimeters.The PDP test appears to distinguish between normalsubjects and glaucoma suspects better than the CVFtests, suggesting that the PDP test may be more sensi-tive to early glaucomatous damage.
II. Apparatus
The pattern discrimination perimeter consists of amicrocomputer, a video display, a video stimulus gen-erator, and equipment to maintain the subject's align-ment and to monitor fixation. The entire stimulusdisplay, including the stimulus patterns, the randomdot background field and a continuously presentedcentral fixation target, is under microcomputer con-trol. In addition, the microcomputer is programmedto provide fully automated testing protocols as well asautomatic data collection and storage. All PDP stud-ies reported in this paper were performed on two iden-tical prototype instruments stationed at the Wilmerand Scheie Eye Institutes. Details of the hardwareconfiguration and calibration procedures for these in-struments are given below.
A. PDP Hardware Configuration
The video display of the pattern discrimination pe-rimeter was a high-resolution 40-in. diagonal rear-pro-jection TV (Mitsubishi model VS-403R), with a videobandwidth of -10 MHz. The luminance and contrastof the images on the screen were set using the appropri-ate TV controls.
The stimulus display was generated with a graphicsboard (Matrox model ALT-512) and a custom hard-ware random dot generator under the control of amicrocomputer (North Star Horizon). The graphicsboard manipulated an array of 256 X 256 pixels, ofwhich 256 horizontal X 238 vertical pixels were visibleon the TV screen. Images were displayed at 60 Hz,with no interface. Each pixel in the video display wascontrolled by 1 bit of display memory, thus each pixelwas either black or white (no gray scale). The graphicsboard contained two memory planes. While onememory plane was being displayed, a new image couldbe created in the other. To display a new image, thedisplay memory planes were interchanged during thevideo display's vertical retrace interval. This avoideddisturbances in the display as the image was updated.
A custom hardware pseudorandom binary sequencegenerator, controlled by the microcomputer, was usedto generate the random dot background stimulus. Togenerate a new image, the microcomputer first createda background of random dots by signaling the randomdot generator to fill the unused memory plane. The
microcomputer then generated the test stimulus byoverwriting a portion of the display memory with thedesired target. A fixation target was also generated inthe center of the screen by setting a 7 X 7 patch ofpixels to black if the fraction of white pixels was >0.5,and to white if the fraction of white pixels was <0.5.The random number generator provided seven whitepixel density options, including 0, 0.125, 0.25, 0.5, 0.75,0.875, and 1.0. The system could generate and displaynew images at adjustable rates of up to 30 times/s.
At the testing distance of 0.67 m from the videodisplay screen, the screen subtended 490 vertically by62.5° horizontally, and each pixel subtended -15 minof arc of visual angle in the direction of fixation. Be-cause the TV display was flat, eccentric pixel dimen-sions were equal to the foveal values times the squareof the cosine of the eccentricity. At 28.50 (the largesteccentricity tested) the pixel size was -11 min of arc.
An adjustable chin and forehead rest maintained thesubject's alignment directly in front of the fixationtarget. Corrective lenses were provided to the subjectas needed to bring the screen into sharp focus. Fixa-tion was monitored with a miniature CCD TV camerathat sent a magnified image of the subject's eye to astandard TV display. A push button connected to acomputer input port was used to automatically recordpatient responses. A warning beep 0.5 s before eachtrial cued the subject to prepare for the next stimuluspresentation.
B. PDP Calibration Procedures
The luminance and contrast of the TV screen wereperiodically calibrated from the patient's vantagepoint with a spot photometer (Spectra Spotmetermodel UBA 1/4). Because of the directionality of therear-projection screen and the short distance from thescreen to the patient's eye, the luminance of the screendecreased substantially with increasing eccentricity.At the smallest eccentricity tested (4.3°), the lumi-nances of the alternating white and black pixels withina checkerboard pattern were 82 and 34 cd/m2 , respec-tively, for a contrast of 0.41. (Contrast is defined asthe difference between the white and black pixel lu-minances divided by the sum of the white and blackpixel luminances.) At the largest eccentricity tested(28.5°), the corresponding luminances were 21 and 14cd/m2 , for a contrast of 0.20. The contrast betweenwhite and black screen areas larger than 1 pixel (e.g.,the clumps of black and white pixels in the random dotsurround) was consistently above 0.9 at all eccentrici-ties. These luminance and contrast variations werenot readily apparent to the patients, but their possibleeffects on the pattern discrimination test results can-not be ruled out (see Sec. III.B).
111. Stimuli
With the microcomputer-controlled PDP, it is possi-ble to generate a wide variety of different types of teststimuli in the dynamic random dot surround. In prep-aration for the present study, we therefore conducted anumber of pilot experiments to identify stimulus pa-
rameters that appeared to have the greatest potentialfor detecting early glaucomatous nerve damage. Webegin this section with a general discussion of specifi-cations and definitions of basic stimulus parameters(A), followed by a brief summary of the pilot studies(B) that led us to the specific stimulus parameters usedin the present study (C). For completeness, we alsobriefly state the stimulus parameters used in the con-ventional visual field tests (D).
A. Specifications and Definitions
A primary requirement of the stimulus patterns wasthat they should not be detectable by luminance dif-ferences alone. All stimuli therefore were constrainedto have the same space-averaged and time-averagedpixel density as the random dot surround. Also, noisepixels in the test stimulus were constrained to have thesame size and refresh rate as pixels in the surround.
Except for the spatial and temporal quantizationimposed by the TV raster, there is no general restric-tion on stimulus position or velocity. Because we in-tended to compare the pattern discrimination tests toconventional static perimetry on the Humphrey andOctopus perimeters, however, we arbitrarily con-strained target position to the test positions in theHumphrey 30-2 and Octopus 32 protocols. These testpositions are illustrated in Fig. 1. Because of thelimited vertical extent of the screen, PDP data werenot obtained for the top and bottom row of positions.Some pilot studies included only a subset of the sixty-eight PDP test positions.
Test stimuli usually were square patches of pixelswith an even number of pixels per side. This configu-ration made it straightforward to maintain an exactmatch of average pixel density between the test stimu-lus and the surround. The requirement for an evennumber of pixels per side was relaxed only for dynamicstimuli whose pixel density altered between valuesequal amounts above and below the surround densityon successive frames, and whose duration was an evennumber of surround frames. The time-average stimu-lus pixel density was thus equal to that of the surroundeven though the stimulus and surround densities dif-fered for each individual frame. This made it possible,for example, to measure size thresholds for counter-phase checkerboard stimuli with a precision of 1 pixelper side and still maintain an average luminancematch between stimulus and surround.
The visibility of a nonrandom stimulus pattern canbe manipulated by varying the degree of regularity, orcoherence, of the stimulus dots. Coherence can bedefined in both the spatial and the temporal domains.We define spatial coherence as the degree to which it ispossible to reconstruct the entire stimulus, knowingonly the state of a single pixel at a single moment oftime. For example, a checkerboard is completely spa-tially coherent because, if the state of any one pixel isknown, the states of all the other pixels in the stimulusare known. Spatial coherence is reduced by randomlyselecting (without replacement) and interchangingpairs of black and white pixels in the image. The
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Fig. 1. Stimulus map for Humphrey program 30-2 and Octopusprogram 32. Positions tested with the pattern discrimination pe-rimeter are enclosed by the large octagonal box. Positions markedby large symbols are tested twice per session. The fixation point isindicated by the central cross. Positions tested during the first halfof the session are within the dashed square, and positions testedduring the second half of the session are outside the dashed square.
Spatial Coherence Series
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Fig. 2. 20 X 20-pixel stimuli decreasing in spatial coherence fromleft to right, embedded in random dot surrounds. The white-blackdot ratio is 1/1 for both stimuli and surrounds. Spatial coherence is
indicated below each stimulus.
percent of interchanged pixel pairs quantitatively de-fines a spatial coherence variable ranging from 100%coherence with no pairs interchanged to 0% coherencewith 50% of the pairs interchanged. If the ratio ofwhite-black pixels is not 1/1, the less frequent polaritydetermines the number of available pixel pairs. It isworth noting that, if all the pairs of a checkerborad areinterchanged, the result is a fully coherent checker-board in counterphase with the original. A series ofimages of decreasing spatial coherence is shown in Fig.2.
We define temporal coherence as the degree towhich it is possible to predict future stimulus patterns,knowing only the pattern of pixels at a given instant intime. A static test stimulus is therefore completelytemporally coherent, as is a test stimulus that is alter-nated in counterphase, rotated, scrolled, or translatedat a constant rate. Temporal coherence is reduced byrandomly interchanging a known percentage of black-white pixel pairs in the test stimulus, just as for thecase of spatial coherence, except that an independentset of pairs must be interchanged for each new frame ofthe surround.
Most stimulus patterns contain elements of bothspatial and temporal coherence. For example, staticand counterphase checkerboards embedded in dynam-ic random dot surrounds are both spatially and tempo-
rally coherent. Pure temporal coherence requires thatthe stimulus contain no spatial information (e.g., apatch of static random dots in a surround of dynamicrandom dots). Conversely, pure spatial coherence re-quires that the stimulus contain no temporal informa-tion. In practice, this means that the surround mustbe static, as in Fig. 2, or that the stimulus must beexposed only for a single surround frame.
B. Pilot Studies
To optimize stimulus parameters for the detectionof early glaucomatous defects, we designed pilot ex-periments to measure thresholds for stimulus size, du-ration, spatial coherence, and temporal coherence.Initially, we conducted studies on normal subjects todetermine the interaction of the size and duration ofthe test stimulus on threshold values. We found thatthe threshold for test stimulus duration became inde-pendent of size when the test stimulus was about 12pixels square at an eccentricity of 12.7°. The spatialand temporal coherence thresholds became indepen-dent of size when the test stimulus was about 20 pixelssquare. Similarly, thresholds for the size and spatialcoherence tests became constant as a function of dura-tion when the test stimulus was presented for morethan 0.6 s. For the temporal coherence tests, however,thresholds did not become constant until the test stim-ulus duration exceeded 1.5 s.
Another pilot study was conducted to determine theoptimal ratio of light to dark pixels and to comparesubject performance for asymmetric ratios with mostlydark pixels vs mostly light pixels. However, the re-sults of this study could not easily be interpreted be-cause limitations in video bandwidth caused the lightpixels to smear, making them effectively larger thanthe dark pixels. For subsequent studies, a 1/1 ratio oflight to dark pixels was selected.
We also examined the effect of changing the rate atwhich the background and stimulus patterns are up-dated on the screen. We found that higher updatefrequencies result in better detection up to at least 30Hz. However, a hardware limitation related to thetime required for the computer to generate the teststimulus display caused noticeable slowing of the fre-quency during stimulus presentation at frequenciesabove 20 Hz. Presentation frequency was thereforelimited to 15 Hz in subsequent studies.
In our first formal studies involving glaucoma pa-tients, we compared thresholds for target size, dura-tion, spatial coherence, and temporal coherence. Thesubject sample included seven glaucoma patients, sixglaucoma suspects, and twenty-three normal controlsubjects. The size, duration, and spatial coherencethresholds in these studies were determined using analternating (counterphase) pattern, and thus did notinclude a measurement of pure spatial coherencethreshold. The results suggested that the temporalcoherence threshold measurement, using a static, spa-tially random stimulus provided the best separation ofglaucoma patients from normal subjects.9 However,normal thresholds were so high for this stimulus thatlittle coherence range remained to estimate the sever-
ity of sensitivity loss. In an attempt to increase theavailable temporal coherence range above threshold,we then tested a dynamic version of the spatially ran-dom stimulus that scrolled through a static window.Although this modification did increase the testingrange, it was poor at detecting glaucomatous field de-fects; e.g., some glaucoma patients with known CVFmean defects of nearly a log unit performed normallyon the scrolling temporal coherence test.1" These re-sults suggested that stimulus motion on the retinamight permit even a depleted ganglion cell layer toextract information about the pattern that could betemporally integrated and interpreted at cortical lev-els. We therefore reasoned that a static spatially co-herent stimulus might provide the desired increase intesting range while minimizing the potential for corti-cal integration of moving retinal image patterns.
Brief pilot studies of the effects of pixel size andluminance contrast were also conducted to assess thepotential benefits of improving the spatial resolutionand contrast capabilities of the instrument. Pixel sizewas varied by placing the subject at various distancesfrom the screen and changing the stimulus position onthe screen to maintain a constant retinal position. Atan eccentricity of 4.3°, coherence threshold increasedonly slightly until the pixel size fell below 5 min of arc.Contrast was varied by combining a uniform veilingluminance with the stimulus screen by positioning In-conel neutral density filters at a 450 angle in front ofthe subject's eye. At 4.3° eccentricity, coherencethreshold for a static checkerboard was completelyunaffected by contrast reductions down to levels nearcontrast threshold. These results suggest the possibil-ity of significant further increases of test sensitivityfrom the optimization of pixel size and contrast.
C. Stimulus Parameters for Present StudyAs a result of the pilot studies outlined above, we
decided for the present study to measure coherencethresholds for static checkerboard stimuli that are co-herent in both space and time. The stimuli weresquares containing 20 X 20 pixels (as in Fig. 2) and were1 s in duration. The random dot surround was re-freshed 15 times/s. The spatial and temporal coher-ence of the target were simultaneously reduced byreversing the contrast of a new independent set ofrandomly selected black-white pairs of dots with eachbackground frame. Coherence was specified in termsof the percentage of black-white dot pairs reversed perstimulus frame, ranging from 100% coherence with nodot pairs reversed to 0% coherence with half of the dotpairs reversed. Since the 20 X 20 dot stimulus con-tained 400 pixels, 100-dot pair reversals were needed tocompletely randomize the stimulus, i.e., coherence wasreduced by 1% for each dot pair reversal.
D. Conventional Perimetry Stimulus ParametersStandard stimulus parameters were used for the
Humphrey 30-2 and Octopus 32 tests. The Humphreybackground field luminance was 10 cd/M2 and thestimuli were size 3 (0.43° diameter) and 0.2 s in dura-tion. The Octopus background luminance was 1.3 cd/
m2 and the test stimuli were 0.43° in diameter and 0.1 sin duration.
IV. Methods
A. Patients
Subjects for the study were recruited from the pa-tient populations of the glaucoma clinics at the Wilmerand Scheie Eye Institutes, referrals from outside oph-thalmologists and optometrists, referrals from otherstudy subjects, and respondents to local advertise-ments. The experimental procedures were explainedand written informed consent was obtained from allsubjects prior to the start of testing.
Open-angle glaucoma patients, glaucoma suspects,and normal control subjects were categorized on thebasis of a complete ophthalmological exam, includingcentral visual fields with either the Humphrey or Octo-pus perimeter. A strict and arbitrary criterion fordetectable visual field loss was adopted. To be consid-ered abnormal, a visual field had to have sensitivitylosses >4 dB for at least three contiguous test positionson the Humphrey 30-2 or Octopus 32 protocol com-pared to the age-corrected normal means suppliedwith the instruments. The four topmost positions andthe position above the blind spot were excluded fromthe criterion because of large normal variability.Glaucoma patients had histories of intraocular pres-sure (IOP) > 21 mm Hg and visual field defects exceed-ing the criterion. Glaucoma suspects had IOP >21mm Hg, but no visual field loss exceeding the criterion.Control subjects had IOP <18 mm Hg, no family histo-ry of glaucoma, and no visual field loss exceeding thecriterion. All patients and control subjects were freeof nonglaucomatous eye disease. Table I shows num-bers and age information for the three subject catego-ries. Approximately two-thirds of the sample in eachpatient category was tested with the Humphrey perim-eter and one-third with the Octopus perimeter.
B. Experimental Procedures
One eye of each subject was tested with the staticcheckerboard coherence test at sixty-eight of the testpositions used for the Humphrey program 30-2 and theOctopus program 32, excluding only the eight positionsin the topmost and bottommost rows as shown in Fig.2. The locations were arranged in a square array with60 of visual angle between nearest neighbors and wereoffset 3° from the horizontal and vertical meridians.
Coherence thresholds were measured with a stair-case procedure, starting at 100% coherence and de-scending in 20% steps, followed by 10% steps after thefirst reversal and 4% steps after the second reversal.The sequence ended after the second negative reversalat the 4% step size, and the coherence threshold wasdefined as the weighted average of the last three rever-sals:
threshold = (C,, + 2Cp + Cn2)/4,
where C,1 and C,,2 are coherences at the two negativereversals and Cp is the coherence at the positive rever-sal. If the subject failed to see two successive stimuli
at 100% coherence, the staircase was terminated andthe coherence threshold was recorded as 100%. Ran-domly interleaved staircases were run simultaneouslyfor pairs of locations symmetrically arranged aroundthe fixation point. This minimized the subject's un-certainty about where the next target would appear14
while still avoiding the tendency to fixate the target.If one of a pair of threshold measurements was finishedbefore the other, dummy stimuli were inserted at thecompleted position to avoid fixation bias. About 10%of all stimulus trials were randomly interspersedblanks, consisting of 0% coherence stimuli, to estimatethe subject's response criterion. A total of eight sub-jects were deleted from the study (and from Table I)because they were judged unreliable, i.e., they eitherresponded to a high percentage of blanks (>20%) orthey required a total number of trials in excess of 2 s.d.above the mean (>1000) to complete the session.
A typical PDP session lasted about an hour, includ-ing rest periods. A 5-min break was scheduled aftertesting was completed for the central thirty-six posi-tions within the dashed square in Fig. 1. Additionalbreaks were taken as needed to minimize fatigue, usu-ally at 6-8-min intervals. Pairs of positions were test-ed in a fixed pseudorandom order within the centralthirty-six positions and within the outer thirty-twopositions. The four diagonal positions marked withlarge squares in Fig. 1 were always tested twice, at thebeginning and at the end of the first half-session. Thefirst and second measurements at these positions wereaveraged for purposes of the ROC analysis, to be de-scribed below.
On the same day as the pattern discrimination pe-rimetry session, we also obtained a conventional visualfield from each subject using either the Humphrey (30-2 protocol) or the Octopus (program 32) perimeter.Since the stimulus conditions are not equivalent forthe two perimeters, we attempted to make the datacomparable by adding to the Octopus data the point-by-point mean differences between Humphrey andOctopus fields from fifteen age-matched pairs of nor-mal subjects from another study. Justification forthis procedure is provided by Asman and Heijl,15 whocompared Humphrey visual field tests at backgroundluminances of 10 and 1 cd/M2 with an ROC analysissimilar to ours and found no differences in the abilityof the two conditions to distinguish between glaucomapatients and normal subjects.
C. Data Analysis
The primary metric used to assess the performanceof the PDP and conventional visual field tests was anestimate of the area under the relative operating char-
acteristic (ROC) curve.12' 1 617 ROC analysis is a meth-od for determining how well two data distributions (anoise distribution and a signal plus noise distribution)can be distinguished from one another. In the presentanalysis, the noise distribution consisted of the visualfield data for the sample of normal control subjects,and the signal plus noise distributions consisted of thevisual field data for the glaucoma suspect and glauco-ma patient samples. Thus, the signal was the differ-ence between the glaucoma (or suspected glaucoma)and the normal data distributions. The ROC curveitself is a plot of the cumulative probability distribu-tion of the signal plus noise data on the ordinateagainst the cumulative probability distribution of thenoise data on the abscissa. The area under the ROCcurve is equivalent to the probability of making acorrect choice (P0 ) in a two-alternative forced-choiceprocedure18 and is a nonparametric, criterion-freemethod of assessing the performance of a diagnostictest that makes no assumptions about the form of thedata distributions.1 6 Since Pc is 0.5 if the two distribu-tions are identical, the probability of detecting thesignal (Pd) is given by Pd = 2(P, - 0.5).
To estimate the area under the ROC curve, we ex-ploited the relationship between it and the Wilcoxonstatistic.1 9 2 0 After preliminary data processing, 2 1 wecompared the value of each patient data point (Dp) tothe values of each of the normal subjects' data points(D) for each test condition. Each comparison wasscored (1 if DP < D, 0 if DP > Dn, 1/2 if D = DJ) andthe scores were averaged over all the comparisons.Note that this is the same as performing all possibletwo-alternative forced-choice procedures and report-ing the average value. The result of this analysis was aprobability of detection of the signal (glaucoma orsuspected glaucoma) for each point in the visual field,both for pattern discrimination perimetry (PDP) andfor the conventional visual fields (CVF). The individ-ual Pd values were plotted in the form of visual fieldmaps and as scatterplots of PDP vs CVF values.
It is also useful to estimate the composite probabili-ty of detecting glaucoma based on the combination ofall the test points in the visual field. If all the points inthe visual field were statistically independent, theoverall probability of detecting a signal would be givenby 1 - II(1 - Pd), where II indicates the product ofindividual position Pd terms. Since many, if not all, ofthe points in the visual field covary, this is likely togrossly overestimate the ability of the test. The co-variance matrix can be computed, but testing the hy-pothesis based on the 2278 covariance terms is notfeasible because of the prohibitive amount of data thatwould be required to obtain acceptable statistical con-fidence.
A more realistic alternative is to collapse the visualfield data in some way that preserves the essentialinformation contained in the individual position Pdvalues and to perform an ROC analysis on the col-lapsed data set. For the present study, we computed aweighted average threshold over all the test positionsfor each patient. The weights for the averages are the
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Fig. 3. Mean sensitivity vs age for normal control subjects. Eachdata symbol is the average sensitivity for all sixty-eight test posi-tions. Circles indicate conventional visual field data and squaresindicate pattern discrimination data. Solid lines are least-squaresregressions. The log luminance sensitivity and coherence sensitiv-ity scales are normalized by equating the mean residual errors from
the regressions.
signal-to-noise ratios of the data, as determined by theZ-score transformations of the individual position PCvalues. Thus, test positions that distinguish well be-tween the patient populations contribute more heavilyto the average than positions that distinguish poorly.The Z-score transformation amplifies the effects of theweighting for PC values close to 1. In the extreme, asingle position that discriminates perfectly betweenthe patient populations will dominate the entireweighted average, whereas a position that does notdiscriminate at all will contribute nothing to theweighted average (as PC ranges from 0.5 to 1, the Z-score ranges from zero to infinity).
The weighted-average method of collapsing the vi-sual field data also can be used to compute a compositePd estimate for any desired subset of test positions.For example, we have computed a composite Pd valuefor all positions at each eccentricity. This techniquealso could be used to streamline clinical protocols byidentifying test positions that could be eliminatedwithout reducing the composite Pd value.
V. Results
A. Normal Data vs Age
The three patient groups in the study have differentage distributions, as shown in Table I. We used Dun-nett's Multiple Range Test to assess the significance ofthese differences, and found that the difference be-tween the normal and glaucoma patient ages is signifi-cant (D = 2.77, a < 0.01), but the difference betweenthe normal and glaucoma suspect ages is not (D = 1.30,a > 0.05). In light of these differences, it was ofinterest to determine how normal sensitivities for theCVF and PDP tests depend on age. Figure 3 showsmean sensitivities, averaged over all the test positionsas a function of age for the twenty-nine control sub-jects in the sample. The CVF and PDP sensitivityscales have been made commensurate by computing a
Fig. 4. Mean coherence sensitivity vs mean log luminance sensitivity for (A) normal control subjects, (B) glaucoma suspects, and (C)
glaucoma patients. Each small data symbol is the average sensitivity over all sixty-eight test positions for one subject. The three large data
symbols indicate group means. The log luminance sensitivity and coherence sensitivity scales are normalized as in Fig. 3. The horizontal and
vertical dashed lines intersect at the group mean sensitivities of the control subject sample.
linear regression for each data set and scaling the axesby the root mean squares of the residual errors. Sensi-tivity decreases with increasing age for both tests, andthe normalized slopes are virtually identical. Sincethe patients are older on average than the normalsubjects and the ROC analysis does not correct for age,the slopes of the sensitivity vs age functions shouldcause overestimates of the differences between thenormal and patient sensitivity distributions. Thisdoes not invalidate the analysis, however, because theoverestimates apply equally to the CVF and PDP tests.
B. Raw Data Comparisons
Figure 4 shows scatterplot comparisons of the meanCVF and PDP data for control subjects, glaucomasuspects, and glaucoma patients. Each data pointindicates the mean sensitivity over the sixty-eight testpositions (see Fig. 1) for one patient. To the extentthat the CVF and PDP data are correlated, the pointswill fall along a positive diagonal line whose slopedefines equivalent sensitivities for the two tests. Sig-nificant correlations are evident for the normal group(R = 0.652, p < 0.01) and the glaucoma group (R =0.613, p < 0.01) but not the suspect group (R = 0.105, p> 0.05). Although the group mean conventional sensi-tivity for glaucoma suspects is lower than the normalmean by nearly 0.1 log unit [see Fig. 4(b)], correctingfor the age differential between the normal and suspectgroups (see Table I and Fig. 3) reduces the sensitivitydifference to 0.06 log unit. The limited testing rangeof the PDP is apparent in the data of the four glaucomapatients with the largest CVF defects. These patientscould not even see the fully coherent checkerboardpatterns at most of the test positions.
C. Discrimination Index for Individual Test Positions
Figure 5 shows summary maps of the point-by-pointdiscriminability results comparing normal and patient
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Fig. 5. Point-by-point discrimination probabilities (Pd) betweenpatient and normal threshold distributions. For each position, thearea of the black square isproportionaltoPd. Left panels show PDPdata and right panels show CVF data. Top panels show compari-sons between glaucoma patients and normal subjects, and the bot-tom panels show comparisons between glaucoma suspects and nor-
mal subjects. Shaded ovals show the blind spot location.
Fig. 6. PDP vs CVF scatterplot of the Pd values in Fig. 5. Opencircles are glaucoma suspect data and filled circles are glaucomapatient data. Points above the diagonal line indicate that the PDPtest discriminated between normal and patient distributions better
than the CVF test.
data. For each test position, the area of the blacksquare is proportional to the discrimination index, Pd,determined from the area under the correspondingROC curves. The most striking feature of the data isthe difference between the test comparisons for glau-coma suspects and glaucoma patients. That is, theCVF and PDP tests distinguish about equally betweennormals and glaucoma patients, but the PDP test ap-pears to outperform the CVF test in distinguishingnormals from glaucoma suspects. These trends areconfirmed by the scatterplots in Fig. 6.
A second noteworthy finding evident in Fig. 5 is thatthree of the four data sets show little systematic varia-tion in Pd across test position. Aside from a slighttendency for better discrimination toward more pe-ripheral locations, all areas of the central visual fieldappear to distinguish patients from normals aboutequally well. The only major exception is the CVFglaucoma suspect data set, which, by design, is indis-tinguishable from normal in that no field may containmore than two contiguous positions with defects ex-ceeding 4 dB. While the Pd values are indeed muchlower on average than those in the other data sets, anarcuate pattern of positions that discriminate glauco-ma suspects from normal is clearly visible, with theupper arcuate band cutting closer to the fovea than thelower band. This pattern is in strikingly good agree-ment with published studies of the locations of theearliest visual field defects in glaucoma.2 2 - 26
D. Composite Discrimination Index
Figure 7 shows the results of an ROC analysis de-rived from averages of the individual position sensitiv-ity measurements weighted by the Z-score transforma-tions of the corresponding Pd values shown in Figs. 5and 6. Confidence intervals are computed as de-scribed by Massof and Emmel16 on the assumptionthat P, is binomially distributed. Since the compositeanalysis emphasizes individual positions with high Pdvalues, it enhances Pd more for the suspect CVF data
1.0
0.81
0.61
0.4
0.21
0.0
-0.2Suspect Glaucoma
Fig. 7. Composite Pd estimates for comparisons of normals andglaucoma suspects (left) and normals and glaucoma patients (right),obtained by averaging sensitivity measurements weighted by indi-vidual position signal-to-noise ratios and performing an ROC analy-sis on the weighted averages. Error bars indicate 95% confidence
intervals, computed assuming a binomial distribution.
xa)-D
C0
. _
E.D
0
0.E00
1.2
1.0
0.8 -
0.61-
0.4 1-
0.2 F
O.CI -0 5 10 15 20
Eccentricity (degrees)
25 30
Fig. 8. Composite Pd estimates for comparisons of normals andglaucoma suspects (open symbols) and normals and glaucoma pa-tients (filled symbols), obtained by averaging sensitivity measure-ments for each eccentricity, weighted by individual position signal-to-noise ratios, and performing an ROC analysis on the weighted
averages.
than for the suspect PDP data, for which the individ-ual position Pd values are more uniformly distributed.Nevertheless, the composite Pd value for glaucomasuspects is twice as large for the PDP test as for theCVF test. A binomial comparison test establishedthat high confidence can be placed in the differencebetween the PDP and CVF data distributions for sus-pects, however, the difference does not achieve statis-tical significance (a = 0.14) due to the small number ofpatients in the sample. A similar test for the differ-ence between the PDP and CVF glaucoma patientdistributions showed a lower level of confidence thanthe tests performed differently (a = 0.37).
Figure 8 shows composite Pd values as functions ofeccentricity. The overall pattern of results confirmsdifferences between conditions that are apparent in
Figs. 5-7. Although the data appear to exhibit someinteresting features, such a slight positive slope witheccentricity for the glaucoma patient data and a sharpdownturn of the CVF Pd at large eccentricities forsuspects, the present patient samples are too small todetermine whether these features are significant.
VI. Discussion
We have presented evidence that the pattern dis-crimination test outperforms conventional automatedperimetry in distinguishing between groups of normalsubjects and patients with suspected glaucoma. Al-though our ROC analysis is not appropriate for diag-nosing individual patients, it nevertheless provides avalid comparison of the relative diagnostic potential ofthe PDP and CVF tests. It has also provided evidence,in the lower right section of Fig. 5, suggesting thatconventional visual fields contain information aboutearly glaucomatous defects in glaucoma suspects thatis not accessible by standard techniques of visual fieldanalysis.2 7 The similarity of this spatial pattern to thepublished locations of the earliest glaucomatous fielddefects further suggests that small unrecognized fielddefects in glaucoma suspects may indicate early glau-comatous damage rather than a benign side effect ofintraocular pressure elevation.
It can be argued that, since the patients were catego-rized on the basis of their CVF results, the PDP testtends, a priori, to discriminate between normals andsuspects better than the CVF test, because subjectswho have abnormal CVF results but normal PDP re-sults have been assigned to the glaucoma patient cate-gory. This is a technically sound argument, but itsimplications are far from clear given that the relation-ship between CVF defects and glaucomatous opticnerve damage is still very poorly understood. What isclear is that the PDP test adds potentially useful diag-nostic information about a group of subjects whoseCVF results appear grossly normal. In addition, theargument is weakened in the present study by ourfinding that, in spite of our rigorous criterion for CVFdefects, the ROC analysis showed that the CVF datafor glaucoma suspects were still discriminable fromnormal. Thus, it would have been possible for theCVF test to discriminate between suspects and nor-mals better than the PDP test.
Most glaucoma suspects never go on to exhibit clearsigns of glaucomatous optic nerve damage such as con-ventional visual field defects and/or atrophy of theoptic disk and nerve fiber layer. Therefore, it is possi-ble that the observed discrimination between the sus-pect and normal subject samples is due primarily tothe subset of suspects who already have early glauco-matous damage. The observed discrimination indicesbetween the normal and glaucoma suspect samplesmay thus underestimate the magnitude of the patterndiscrimination deficit for patients with early glauco-matous damage but normal conventional visual fields.
The differences between the performance of thePDP and CVF tests may be more than a simple differ-ence in sensitivity. Differences in stimulus size and
contrast as well as in the psychophysical task leaveopen the possibility that the two tests may detectdifferent aspects, or even different types, of glaucoma-tous nerve damage.13
The PDP test is still under active development, andwe anticipate that future modifications will furtherimprove its effectiveness in the detection of early glau-comatous field loss. For example, the present versionof the test is limited to a single nominal pixel size andto relatively high stimulus contrast. If our model ofreceptive field damage is correct, it is reasonable toexpect that optimization of pixel size for differenteccentricities should increase the power of the test. Inaddition, a brief pilot study suggests that the coher-ence thresholds for normal subjects may be virtuallyunaffected by reductions of stimulus contrast down tonear-threshold levels. A reduced contrast version ofthe test may therefore provide a major additional ad-vantage in the testing of early glaucoma patients forwhom contrast sensitivity may be marginally reduced.
Regardless of present advantages or future improve-ments, we cannot conclude that the PDP test is moresensitive to early glaucomatous optic nerve damageuntil we have demonstrated directly that the earlyselective defects that we have seen in glaucoma sus-pects either correspond to early nerve fiber damage orpredict future nerve fiber damage. We are currentlyplanning a large-scale prospective study of glaucomasuspects in an effort to answer these questions.
VII. Conclusions
We have developed and tested a new type of visualfield test that assesses pattern discrimination ratherthan light detection. The new test appears to distin-guish between normal subjects and patients with sus-pected glaucoma better than conventional incrementthreshold techniques currently in clinical use. Pro-spective studies are needed to determine whether earlydefects in pattern discrimination are indicative of ear-ly glaucomatous nerve damage.
This work was supported in part by NEI SBIR grantEY05136 to LKC Systems, Inc. (now LKC Technol-ogies, Inc.), and by unrestricted grant funds from Na-tional Glaucoma Research, the American Health As-sistance Foundation, Rockville, MD, and Research toPrevent Blindness, Inc., New York, NY. This paper isbased in part on a talk presented at the fourth OSATopical Meeting on Noninvasive Assessment of theVisual System, Incline Village, NV, 16-18 Feb. 1988.LKC Technologies, Inc. and three of the authors(Drum, Massof and Breton) have a proprietary inter-est in the pattern discrimination perimeter. The pat-tern discrimination perimeter is protected by U.S. Pat.4,634,243.
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