Threshold Equivalence Between Perimeters

Threshold Equivalence Between Perimeters Douglas R. Anderson, M.D., William J. Feuer, M.S., Wallace 1. M. Alward, M.D., and Gregory 1. Skuta, M.D.

To determine equivalence between perimeters, 49 eyes of 35 subjects underwent static threshold testing of the central 30 degrees twice on each of three automated perimeters and twice by manual kinetic threshold testing with the Goldmann perimeter. The OctopusHumphrey difference was 3.3 dB (2.3 dB in the upper two rows for programs 32 and 30-2). The Dicon-Octopus difference was 3.5 dB and the Dicon-Humphrey, 6.5 dB. The 140 stimulus of the Goldmann perimeter was equivalent to 17.1 dB, 13.6 dB, and 10.8 dB on the Humphrey, Octopus, and Dicon perimeters, respectively. The 11140 stimulus of the Goldmann perimeter, used for visual impairment determination, was roughly equivalent to 7 to 10 dB, 4 to 7 dB, and 0 to 6 dB on the Humphrey, Octopus, and Dicon perimeters, respectively. The prediction when converting from one instrument to another was only 10% less reliable than the ability of a perimeter to predict the values on a second examination with the same perimeter. Validity of the conversion formulas was confirmed by the age-corrected normal values available for the Octopus, Humphrey, and Goldmann perimeters. CERTAIN automated perimeters have become more popular than others, none has become a universal standard. There is therefore a need to determine rough equiva-

ALTHOUGH

Accepted for publication Jan. 24, 1988; revised manuscript received Feb. 13, 1989. From the Bascom Palmer Eye Institute, Anne Bates Leach Eye Hospital, University of Miami, Department of Ophthalmology, Miami, Florida. This study was supported in part by National Glaucoma Research, a program of the American Health Assistance Foundation, Rockville, Maryland; and by United States Public Health Service National Research Service Award T32 EY 07021 and Core Center Grant P30 EY 02180, each awarded by the National Eye Institute, Bethesda, Maryland. Reprint requests to Douglas R. Anderson, M.D., Bascom Palmer Eye Institute, P.O. Box 016880, Miami, FL 33101.

©AMERICAN JOURNAL OF OPHTHALMOLOGY 107:49~505,

lents of the values expressed in the relative decibel units of one perimeter with the units of another, for example, when comparing the results of a patient tested on two occasions on two different instruments, perhaps in two different offices. The same need exists in comparing the results of automated perimetry with manual kinetic perimetry with a Goldmann perimeter.' Conversion formulas are needed because available perimeters are not standardized with respect to the psychophysiologically important features of stimulus size, maximal available stimulus intensity, and background illumination. For example, the background illumination of the Octopus perimeter is 4 apostilbs (asb) (1.27 cd/m") in order to provide a broader dynamic range of testing than would be available with the background of 31.6 asb (10.1 cd/rn") used by other perimeters," Size I stimulus (0.25 mrn" at 30 cm distance) is standard for the Goldmann perimeter, and on this instrument the 1,000-asb (318.3-cd/m 2) stimulus of that size is arbitrarily assigned a value of 0 dB. The Octopus and Humphrey perimeters standardly use a size III stimulus (4 mrn" at 30 em or 11 mm! at 50 ern). The assignment of arbitrary relative units of stimulus intensity also differs. The Octopus assigns 0 dB to a 1,000-asb stimulus intensity. The Humphrey Field Analyzer':' assigns 0 dB to a 10,000-asb (3,183-cd/m2) stimulus intensity and standardly uses size III. The Dicon Autoperimeter uses a light-emitting diode emitting light from 550 to 600 nm (peak, 570 nm; yellow-green") in a 2-mm 2 hole surrounded by white light as a stimulus'" and assigns 0 dB to a 10,000-asb stimulus of that size. Psychophysical formulas exist that might be used to predict a theoretical equivalence between stimuli, but they may not apply universally. The fixed ratio between the threshold stimulus intensity and the surround (Weber's law 9.1O ) applies only when retinal adaptation is photopic (which might not occur with the background intensities used in clinical pertmetry.':" MAY,

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especially with a small pupil), and additionally may not hold when a dim stimulus is presented within a dark hole.P' The relationship between stimulus area and intensity of stimulus is not the same in all retinal areas, and estimates of intensity equivalence when switching from one size stimulus to another is only approximate. 12 Differences in stimulus duration or bowl radius probably do not have much effect on threshold, but some differences between instruments that are deemed inconsequential might unexpectedly affect threshold. For example, the exact algorithm and criterion used to determine threshold may have effects that we cannot predict. Even the face tilt (determined by relative position of the chin rest and forehead bar) may affect the threshold in the superior part of the field. We undertook this study to determine empirically the relationship between threshold values determined with different instruments to see if a usable formula could be found to match the threshold values and to determine how variable the match is. We studied the standard manual perimeter (Goldmann)':" and three automated perimeters available to us (Dicon,':" Humphrey,3,4,14,15 and OctopuS 2,14,16.21) that are capable of static threshold perimetry and seem to be among the most frequently used such instruments, at least in the United States. 14,22 Subjects underwent field testing twice on each of the four instruments to provide matched threshold values in the same individuals at representative field locations. Available normal values for age (representing different samples, but all, we hope, representative of the population at large) were also used to help confirm the formulas for the difference between instruments. Material and Methods

We tested 49 eyes of 35 subjects aged 27 to 80 years (mean ± S.D., 59.44 ± 14.02 years). Refractive errors ranged from -7.125 to +9.25 (mean ± S.D., -0.12 ± 2.87 diopters). All but one of the eyes had a visual acuity of 20/80 or better, and 40 had 20/20 or better. Twelve eyes had normal visual fields, and 37 eyes had mild to moderate glaucomatous defects so that we could obtain data in the lower range of visual sensitivity as well as in the normal range. With the approval of the Institutional Review Board of the University of Miami, subjects who gave

May, 1989

written consent underwent eight visual field examinations of one or both eyes, twice on each of the four instruments studied. No testing session included more than two field examinations (equivalent to the effort required to undergo field testing in the right and left eyes in a typical clinical examination). Sometimes two such sessions were conducted in the morning and the afternoon of the same day, but more typically the sessions were on four separate days. Nineteen subjects (54%) completed their participation within one month. If the participation was spread out over a longer time, the medical records were carefully reviewed to ensure that there was no reason to suspect there had been any change in ocular status between the first and the last visual field tests. This review resulted in the elimination of one field examination from analysis. All subjects completed at least four field examinations, 45 eyes completed at least six of the planned eight field examinations, and 32 completed all eight. In those cases in which patients elected not to complete the entire series of eight field examinations, the data could be used for only some of the interinstrument comparisons. The Goldmann perimeter (Haag-Streit model 940) was calibrated and used to plot several representative isopters according to the method used at our institution." Program 32 was used for the Octopus perimeter model 201 (Interzeag, Schlieren, Switzerlandj.v'v":" Program 30-2 was used with the Humphrey Field Analyzerv':":" model 620 (Humphrey Instruments, Palo Alto, Calif.). We used the central threshold program of the Dicon Auto Perimeter AP20005,14 (which we obtained when the instrument was marketed by CooperVision Diagnostics, San Diego, Calif.). The geometric distribution of test locations was not the same for all instruments. Therefore, 19 locations in the right eye and 18 locations in the left eye were selected at which a point in the grid of 76 points tested in program 32 of the Octopus perimeter (and the identical 30-2 pattern of the Humphrey perimeter) coincided within 2 degrees of a point in the radially arranged test points of the Dicon perimeter. The selected points were not the same for the right and left eyes. None of the points fell in the upper two rows of the pattern 32 of the Octopus perimeter or 30-2 of the Humphrey perimeter, thereby avoiding the more variable points in the uppermost part of the field. For the Goldmann perimeter, the threshold values at the points were obtained by interpolation

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Threshold Equivalence Between Perimeters

from the plotted isopters. Goldmann values were assigned only when one of the selected points fell on a plotted isopter or the contour of the hill of vision in the region was sufficiently smooth, and the plotted isopter sufficiently nearby, that a reasonable interpolation could be made. Because of these requirements, there were many fewer data points for the Goldmann perimeter than for the others. The Goldmann value was expressed in decibels (1 dB = 0.1 log unit) of attenuation of a size I stimulus from the maximal intensity of 1,000 asb (1 4e = 0 dB, 14d = 1 dB, ... he = 5 dB, 13d = 6 dB, ... II. = 19 dB). The II4e stimulus was assigned a value of -5 dB and III4e a value of -10 dB. The following strategy was used for analysis of these data. The right eye data from all patients were used to determine prediction equations, while the left eye data were reserved for their validation. The validation data set is thus not completely independent, but we believe this approach provides maximum use of the data. To obtain prediction equations that were based on points with a wide range of sensitivities, we wished to include all of the 19 measurements contributed by each right eye in the study. For this reason, relationships were assessed using three related techniques. For the Humphrey and Octopus data, analysis of covariance was used to evaluate the homogeneity of regression coefficients at different points in the field. As there was no difference in the derived slopes for the 19 points, we did not analyze the points separately in the rest of the analysis. Our second analysis, implemented with the Statistical Analysis Software PROC MATRIX (SAS Institute Inc., Cary, North Carolina), was to estimate the intraclass correlations in the data for each perimeter pair. 23 The first two analyses were performed on the averages of two determinations made for each perimeter pair at each location. Our third analysis was a weighted linear regression analysis of each perimeter pair. For this, all points were treated as independent observations, but weighted inversely to their pooled test-retest variances. Each perimeter was used once as the dependent and once as the independent variable in these analyses. For the three automated perimeters, zero values provide less information than non-zero measurements. The first two analyses were practical only with equal numbers of measurements per eye. However, for the third analysis, points that included a zero for either perimeter were discarded.

495

We also analyzed normative data available for the Octopus, Humphrey, and Goldmann perimeters at ages 30, 50, and 79 years. The Octopus data for ages 30 and 50 years for the pattern of points in Program 31 were obtained from the Octopus Visual Field Atlas." For age 79 years, Octopus threshold values for the points in Program 32 were obtained from the "compare" (CO) printout of the field test on a patient of that age. For the Humphrey perimeter, values were obtained from dummy Statpac printouts" of pattern 30-1 for ages 30 and 50 years, pattern 30-2 for age 79 years. For the Goldmann perimeter, the kinetic data of Johnson" and the data of Egge" were digitized at points corresponding to test locations of the static instruments by interpolation from kinetic isopter locations with 14e corresponding to 0 dB. Results

Figure 1 shows the relationship in our empiric data between the threshold values for the six pairings of the four perimeters. The normal points behave linearly, but the relationships are not as tight for the abnormal points with reduced sensitivity. We could find no systematic differences in the slopes of the perimeter pair equations at our 19 different locations in the field. The analysis of covariance did demonstrate some statistically significant differences, but the range of the slopes was small (Octopus to Humphrey: 0.7 to 1.1; Humphrey to Octopus: 0.8 to 1.2) and there was no evidence that the larger or smaller slopes tended to be either central, nasal, temporal, superior, or inferior. Table 1 shows three formulas for each perimeter pair, as obtained by linear regression analysis of data from right eyes only with exclusion of data points in which either perimeter gave a value of 0 dB. The first is the equation that produces the smallest error (smallest least squares residual of the dependent variable weighted inversely according to test-retest variance) in predicting the threshold value of one perimeter from the threshold determined by the other. The second equation is obtained for each perimeter pair by exchanging the dependent and independent variables and repeating the regression analysis to obtain the least squares formula for prediction in the opposite direction. A third formula was obtained for each instrument pair by the least squares method, but requiring the slope to be 1. When the

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Fig. 1 (Anderson and associates). Top left, Relationship between Humphrey threshold values and Octopus threshold values (n = 613 paired duplicate observations). Top right, Relationship between Humphrey threshold values and Goldmann threshold values (n = 201 paired duplicate observations). Middle left, Relationship between Humphrey threshold values and Dicon threshold values (n = 705 paired duplicate observations). Middle right, Relationship between Octopus threshold values and Goldmann threshold values (n = 207 paired duplicate observations). Bottom left, Relationship between Octopus threshold values and Dicon threshold values (n = 685 paired duplicate observations). Bottom right, Relationship between Goldmann threshold values and Dicon threshold values (n = 223 paired duplicate observations).

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Threshold Equivalence Between Perimeters

497

TABLE 1 WEIGHTED LINEAR REGRESSION ANALYSIS OF SIX PAIRED COMBINATIONS WITH DATA FROM RIGHT EYES ONLY LINEAR REGRESSION, SLOPE NOT FIXED

LINEAR REGRESSION WITH SLOPE = 1

FORMULAS PERIMETER PAIR (XIY)

Octopus/Humphrey (n = 343) Goldmann/Humphrey (n = 157) DiconiHumphrey (n = 386) Goldmann/Octopus (n = 147) Dicon/Octopus (n = 344) DiconiGoldmann (n = 163)

(x ON Y & Y ON xl

o= H= G= H= D= H= G= 0= D= o= D= G=

1.00 H - 3.22 0.790 + 8.73 0.74 H - 10.62 0.99 G + 17.16 0.66 H + 2.60 1.11 D + 4.18 0.64 0 - 5.60 1.10 G + 12.79 0.62 0 + 5.33 1.05 D + 2,39 0.91 G + 11.43 0.67 D - 4.82

slope is fixed at 1, the constant term (yintercept) derived, to minimize the squared residual error is the difference between the average threshold values of the two perimeters. A conversion formula with a slope of 1 greatly simplifies the conversion to the simple addition or subtraction of a constant. The use of a single conversion term also makes the conversion from one perimeter to another identical with the inverse conversion. Requiring a slope of 1 did not reduce the correlation (R2, Table 1) or increase the prediction error (Table 2) by much. Overall, the formulas with the slope of 1 predicted the actual values on the other perimeters within 2 dB about 50% to 65% of the time and within 4 dB about 61% to 86% of the time when we tested the formulas (derived from only the right eye data) on the separate data set obtained on left eyes (Table 2). Interconversions between the static perimeters were particularly close (within 4 dB 75% to 80% of the time), with a less close relationship when converting between automated static and manual kinetic perimetry. By way of comparison, the threshold values obtained on the first test with a given instrument predicted the values on the second test with the same instrument within 2 dB about 60% to 80% of the time and within 4 dB about 79% to 91% of the time (Table 3). Thus, only 10% of the time are the interperimeter relationships not as close as intraperimeter prediction. These limits of intraperimeter prediction represent measurement irreproducibility (short-term

R2

0.78 0.74 0.74 0.70 0.65 0.61

R2

FORMULAS

.37 .31 .87 .42 .22 .42 .50 .32 .16 .42 .02 .87

0= H= G= H= D= H= G= 0= D= 0= D= G=

H - 3.32 0 + 3.32 H - 17.09 G + 17.09 H - 6.52 D + 6.52 0 - 13.62 G + 13.62 0 - 3.45 D + 3.45 G + 10.79 D - 10.79

.78 .71 .65 .74 .54 .73 .49 .70 .59 .65 .60 .45

TABLE 2 ACCURACY OF PREDICTION FROM FORMULAS (DERIVED FROM RIGHT EYE DATA) TESTED ON DATA FROM LEFT EYE FORMULA SLOPE NOT FIXED

SLOPE FIXEDTO 1 MACHINE PAIR PREDICTION PREDICTION PREDICTION PREDICTION WITHIN WITHIN WITHIN WITHIN CONVERSION NO. ± 2 dB ± 4 dB ± 2 dB ± 4 dB FROMITO

Humphreyl 244 Octopus Octopusl 244 Humphrey Humphreyl 38 Goldmann Goldmannl 38 Humphrey Humphreyl 301 Dicon Diconl 301 Humphrey Octopusl 56 Goldmann Goldmannl 56 Octopus Octopus/ 321 Dicon Diconl 321 Octopus Goldmannl 60 Dicon Diconl 60 Goldmann

57%

77%

57%

77%

59%

79%

57%

77%

52%

71%

53%

61%

53%

61%

53%

65%

81%

56%

75%

58%

75%

56%

75%

60%

86%

61%

75%

59%

77%

61%

75%

57%

83%

55%

80%

56%

80%

55%

80%

62%

74%

62%

73%

65%

78%

62%

73%

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TABLE 3 ACCURACY OF PREDICTION OF THRESHOLD ON SECOND EXAMINATION (2) FROM THE THRESHOLD OF THE FIRST EXAMINATION (1) CONVERSION FROMITO

Humphrey 1/Humph rey2 Octopus 1IOctopus2 Goldmann 1IGoidmann2 Dicon1IDicon2

NO.

PREDICTION WITHIN:!: 2dB

PREDICTION WITHIN:!: 4dB

79%

294

60%

315

73%

91%

61

80%

91%

378

72%

84%

fluctuation) plus physiologic long-term fluctuations. 28.29 Because we used many data points from the same eye, we checked the intraclass correlation coefficients" (rj, Table 1), which were between 0.31 and 0.42, except for the conversion of Humphrey to Goldmann (r, = 0.866, n = 63), Dicon to Goldmann (r, = 0.869, n = 63), and Octopus to Goldmann (r, = 0.503, n = 63). These were the only cases in which the intraclass correlation and adjusted coefficients were substantially different from the ordinary least squares equation. The average normal values for the Octopus." Humphrey," and Coldrnannw" perimeters are shown in Figures 2 and 3. A point-by-point subtraction of these values by perimeter pairs is shown in Figures 4, 5, and 6. The difference values in Figures 4 through 6 correspond with the constant that needs to be added or subtract-

IUrphrey : lJ y/o 27 2929292929 lJ 31 31 31 31 31 31 ll3233333333323232 31 33 34 35 35 34 33 lJ32333535 35 3333 323335353535 33 31 33 34 34 34 34 34 33 34 32323333333333 31 32 32 32 32 31 Octopus : lJ y/0

26 27 28 27 27 26 28 27 29 28 29 29 29 282929lJll29292929 28 2931 32 32 32 29 29 29 28 29 31 32 33 37 33 lJ 10 lJ 29 29 n 32 32 32 32 31 29 II 27 n lJ lJ 31 31 29 II 28 28 29 lJ 29 31 29 II 27 29 29 29 29 28

HlJTllhrey : 50 y/o 24 27 27 27 27 26 28291111292928 28 lJ 31 32 32 31 31 II 29 31 33 33 33 33 28 lJ 32 33 34 34 30 32 33 34 34 34 29 31 32 33 33 33 32 32 lJ 31 31 32 32 32 31 29 II II n n 29

ed in our formulas with a slope of 1 (Table 1), except for three details: (1) When the Octopus or Goldmann values are subtracted from the Humphrey values, the upper quarter of the field shows a smaller difference than is found elsewhere, suggesting that on the average the upper field is physiologically more depressed with the Humphrey instrument than with the others. This position of the field, however, is not represented in the points sampled for our regression analysis. (2) When comparisons involve the Octopus at age 79 years, the obtained difference values do not correspond with the differences at other ages or to the prediction formulas found in our empiric data. The direction of the discrepancy suggests the Octopus normal values for age 79 years are too high. (3) The Goldmann values in Johnson's normal data" are 20 dB lower than the Humphrey normal data, while the Egge normal data" are 18 dB lower than the Humphrey normal values, but the Goldmann values are 17 dB less than the Humphrey values in our empiric data.

Discussion Humphrey-Octopus comparison-These two perimeters have the closest relationship, both being projection perimeters that determine threshold intensity of a static size 3 stimulus. There is a 10-dB difference in the designation of the same stimulus intensity (a 100-asb stimulus

fiJ!lJhrey : 79y/o

29 31 31 31 31 32

Octopus : 50 y/o

22 2426 25 24 24 25 26 26 28 26 27 26 24 26 28 29 lJ 28 28 27 27 26 28 II II II 29 28 29 27 25 26 lJ 31 32 35 31 24 10 29 28 27 29 lJ 32 32 31 28 27 28 26 28 29 lJ lJ lJ 29 29 28 26 27 29 28 II II 29 25 27 27 28 28 25

232322 21 25 26 26 26 25 25 26 28 28 29 28 28 27 26 25 27 29 31 31 II II 29 28 26 26 28 31 32 32 32 31 29 28 26 29 31 32 33 33 32 29 28 25 28 II 32 32 32 31 II 29 28 27 29 II 31 31 II II 29 27 28 29 29 29 28 26 27 27 27 27 Octopus : 79y/o

19191920 20 21 21 21 21 21 21 22 23 23 23 23 22 22 20 22 23 24 25 24 24 23 22 22 22 23 25 26 27 27 25 24 23 23 22 23 25 26 27 27 26 25 24 23 21 23 24 25 25 26 25 24 23 22 22 23 24 24 25 24 24 23 22 22 23 24 24 23 21 22 2323

Fig. 2 (Anderson and associates). Normal threshold values for Humphrey and Octopus perimeters at age 30, SO, and 79 years.

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Threshold Equivalence Between Perimeters

GolclJwwl (J): IJ y/o

Goldnm (J): 50 y/o

GolclTmn (J): 79 y/o

8 910101010 9111212121211 9 11 13 14 14 14 13 12 11 10 12 14 15 16 15 14 13 12 8 10 12 14 17 17 15 14 12 11 10 12 14 16 16 15 14 13 12 9 11 13 14 14 14 13 12 11 10111212121211 10111111 10 9

89998 9101111111010 8 10 12 13 14 13 12 11 10 9 11 13 16 16 15 14 13 11 8 10 12 14 16 16 14 13 12 11 9 12 13 15 16 15 14 13 11 9 10 12 13 14 13 13 12 9101112111111 89999 8

6

344 3 4 566 5 6 788 7 79111110 810151310 810151510 79101110 6 8 9 9 8 5 7 7 7 7 566 6

GolclJwwl (E): IJ y/o

Golctncrm (E): 50 y/o

10 1112121211 12131313131312 12 13 15 15 15 15 15 14 13 16 15 15 13 15 16 11 13 15 17 15 19 15 13 14 17 12 13 15 16 17 16 16 15 13 12 13 14 15 14 14 14 1112131313 11

8 910101010 10 11 12 13 12 12 12 10 12 13 14 15 14 14 13 12 11 13 15 17 17 17 16 14 13 10 12 14 16 17 17 16 15 14 12 12 13 15 17 17 17 15 14 13 11 12 14 14 15 15 14 13 12 12121313131312 1011 12 12 11 10

is 10 dB for the Octopus and 20 dB for the Humphrey, for example). However, the Octopus background (4 asb) is 9 dB less intense than the 31.6-dB background of the Humphrey instrument. Therefore, when visibility is expressed as the ratio of the projected stimulus to the background (Weber fraction), there is a net discrepancy of only 1 dB, with the 9-dB Octopus stimulus (125.9 asb) having nearly the same proportion to a 4-asb background as a 10-dB (l,OOO-asb) stimulus has to a 31.6-asb background. If the threshold Weber fraction were the same at the two background intensities, there would thus be only a I-dB difference between the two perimeters, but the threshold Weber fraction is increased by 3 to 4 dB at the 4-asb background intensity," bringing the theoretical discrepancy to 4 to 5 dB. However, after matching background intensity, there is an approximate 3-dB difference in reported threshold by the two instruments. 11 This instru-

H- 0 Diff IJ y/o

2 3 2 3 3 4

2 3 4 2 3 3 4

3 4 4 3 3 3 4 3 4

1 2 3 4 2 3 4 3 3

1 2 3 3 3 3 3 4 4 4

2 2 4 2 2 3 3 2 3

3 2 2 3 3 3 4 3 4 3 5 3 6 4 3 3

3 4 4 4

4 5 6 6 6 5

4 3 3 4 3 3

4 4 3 2 3 3 4

1 4 3 4 2 3 3 2 3

2 3 3 2 3 2 3 4 3 4

4 3 3 4 3 3 3 2 3

2 3 2 3 3 2 4 3 3 3 3 3 4 2 3 2

5 7 7 8 7 7

5 6 6 6

Fig. 3 (Anderson and associates). Normal threshold values for the Goldmann perimeter from the data of Johnson26 and the data of Egge.27

ment difference reduces the theoretical 4 to 5 dB threshold difference, but the reasons for the instrument difference are not known. It is not explained by the 0.2-second stimulation duration of the Humphrey perimeter compared to O.l-second stimulus of the Octopus because temporal summation with a 4-asb background is complete within 0.1 second.s" A feature that should tend to raise the Octopus value relative to the Humphrey Field Analyzer is that the Humphrey records as threshold the weakest stimulus seen, whereas the Octopus records the threshold as midway between the weakest stimulus seen and the strongest stimulus not seen, but this accounts for only a I-dB difference in threshold notation. It seems doubtful that the larger pupil size at the weaker background of the Octopus perimeter would be sufficient to account for much of the instrument difference. The complexity of predicting equivalence

H- 0 Diff 50 y/o 3 3 3 3 2 3 3 4 4

4 6 8 9 9 9 8 6 6

499

H- 0 Diff 79y/o

5 5 5 4 5 4 6 4 5 5

4 5 5 7 6 6 7

4 5 6 6 5 6 7 6 6 7 5 6 6 5 5 5 6 6 6 6 6

3 1

5 4 4

5 6 5 6 6

5 5 4 6 6 6 4 6 6 5 5 5 6 6 6 6 6

6 6 6 6 5 5 5

4 4

Fig. 4 (Anderson and associates). Point-by-point difference between normal values of Humphrey and Octopus perimeters determined from data in Figure 2.

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H - G(J) Diff 3D y/o mean=20.5

H - G(J) Diff 50 y/o mean=19.5

H - G(J) Diff 79 y/o mean=21.3

19 21 19 19 19 19 21 20 19 19 19 ~9 20 21 21 21 19 19 19 19 20 21 21 20 20 19 19 22 22 21 21 18 18 22 21 21 20 19 20 22 22 21 20 20 20 21 21 22 21 21 21 21 22 22 21 22 21 22 22 22

18 19 19 19 19 18 20 19 19 19 18 19 19 20 20 19 19 19 18 19 19 20 20 20 18 17 18 20 21 20 19 18 18 21 21 20 19 18 19 21 21 20 20 19 20 19 20 22 21 20 21 21 21 21 21 21 21 22 21 21

20 19 18 18 21 21 20 20 20 21 22 22 21 21 20 21 21 21 22 22 22 22 20 19 20 22 22 22 22 23 22 17 19 21 22 22 23 23 22 18 18 22 22 21 23 23 23 22 21 21 22 22 22 23 22 23 23 22 23 23 22 22 22 22 22 22 21 21 21 22

21 21 21 22 22 23

19 20 19 20 20

H - G(E) Diff 30 y/o mean=18.4

H - G(E) Diff 50 y/o mean=17.9

17 18 17 17 17 18 18 18 18 18 18 18 18 19 18 18 18 18 17 19 19 18 19 19 18 18 20 19 19 19 20 19 18 17 18 18 20 19 19 18 19 19 20 20 19 19 20 20

16 18 17 17 17 16 18 18 18 17 17 17 16 18 19 18 18 17 17 17 17 17 18 18 18 17 16 17 18 19 18 18 17 17 17 18 19 18 19 18 18 17 18 18 18 19 19 19 18 18 18 19 20 19 19 19 19 19 20 19 19 19 18 19 19 19

19 18 19 18 18 14 18 18 21 20

from theoretical considerations illustrates the need to determine the relationship empirically. The 2- to 3-dB difference in the present study is smaller than the difference found by Johnson, Keltner, and Lewis" among 40-year-old normal subjects (5.36-dB average difference inside 10 degrees, 5.67-dB average difference from 10 to 20 degrees, and 6.25-dB average difference between 20 and 30 degrees eccentrically [CO A. Johnson, M.D., oral communication, June 24, 1988], and 5. 9-dB average difference derived by simultaneous solution of their regression equations" relating Humphrey and Octopus Model 500, which would yield the average Humphrey and Octopus values). Conversely, the present result of a 2- to 3-dB difference is slightly larger than the average 1.6- to 1.7-dB difference found in studies with natural sized pupils ll •32,33 and the average 0.9-dB difference found in normal subjects with fully dilated pupils." We cannot explain the discrepancies in various data sets, except that different sets of points went into the averages used and there may be some difference between models of instruments if the algorithm for determining threshold were altered. However, we are satisfied with our present results, which are within the range of values found by other studies. The present study is also in keeping with our clinical impression and with the analysis of population normal

21 22 22 22

Fig. 5 (Anderson and associates). Point-by-point difference between normal values of Humphrey and Goldmann perimeters determined from data in Figures 2 and 3.

data (Fig. 4) if the extrapolation to age 79 years is ignored.

Relationship of Goldmann size I to projected static perimetry size III-The background intensities

of the Goldmann and Humphrey instruments are the same. The threshold expressed in decibels is different because (1) the maximal stimulus, in each instrument designated as 0 dB, is 1,000 asb for the Goldmann and 10,000 asb for the Humphrey perimeter, and (2) a size I stimulus is standardly used with the Goldmann instrument and a size III with the Humphrey instrument. Thus, in principle, these instruments should differ by 20 dB: 10 dB for the difference in the intensity of the O-dB maximal stimulus and an additional 10 dB because the change in size from I to III is meant to correspond to a I-log unit (lO-dB) increase in intensity at an average retinal location. However, the size-to-intensity relationship is not the same at all retinal locations." The relationship is described by the formula NI, where A is the area and I the intensity. The value for the exponent k varies from 0.55 near the fovea to 0.9 at 45 degrees nasally. Goldmann used k = 0.83 for the conversion formula for the field as a whole, which may differ from the optimum formula for an average relationship when considering only points in the central 30 degrees. Moreover, kinetic stimuli on the Goldmann

Vol. 107, No.5

o - G(J)

Oiff 30 y/o mean=17.3

18 18 18 17 17 16 19 16 17 16 17 17 18 19 18 17 16 16 15 16 17 18 18 17 17 17 16 17 15 16 17 20 19 19 18 16 16 18 18 19 18 18 16 16 17 17 16 18 18 19 17 16 17 17 16 18 17 18 18 18 17 19 18 19 17 18 18 18 19 19

o - G(E)

Oiff 30 y/o mean=15.3

16 16 16 15 15 15 16 14 16 15 16 16 17 16 16 14 15 15 14 14 15 16 16 14 15 13 14 14 17 16 16 15 15 10 16 16 15 15 15 17 15 14 14 15 13 15 15 16 16 16 14 17 15 16 16 17 16 16 16 17

Threshold Equivalence Between Perimeters

o - G(J)

Oiff 50 y/o mean=16.4

16 16 17 16 15 16 16 16 15 17 15 17 16 16 16 16 16 16 15 16 16 17 17 17 14 14 14 14 16 17 17 18 17 16 15 18 17 17 17 16 16 14 14 18 18 17 17 16 17 16 17 18 17 18 16 19 19 18 17 18 18 19 19 17

o - G(E)

14 15 15 14 15 15

15 14 15 16 16 16 15

17 16 17 17 17

Oiff 50 y/o mean=14.8

501

H - G(J) Oiff 79 Y/o mean=15.9

16 15 15 17 16 16 15 15 16 17 17 16 16 15 15 16 16 17 17 17 16 15 14 13 14 16 16 17 18 17 17 16 12 14 15 16 16 17 18 17 17 16 12 12 16 17 17 17 17 18 17 16 15 15 15 16 16 16 17 17 16 16 17 16 17 17 17 16 16 17 17 17 16 16 17 18

Fig. 6 (Anderson and associates). Point-by-point difference between normal values of Octopus and Goldmann perimeters determined from the data in Figures 2 and 3.

14 15 16 15 14 14 15 14 15 14 15 14 15 15 15 14 14 14 15 15 13 13 13 12 15 14 15 15 14 15 16 15 15 15 14 13 13 15 16 16 15 15 15 16 16 15 16 15 17 17 17 15 16 15 16 17 15

perimeter are being compared with static stimuli on the Humphrey instrument. Thus, empiric determination of the stimulus equivalence is wise. We found that 17 dB was the best correction term, which corresponds to a reduced effect of area change (k < 0.83) in the central 30 degrees as compared to the field as a whole. The data of Johnson, Keltner, and LewiS 31 suggest only a 4-dB change instead of the 5-dB change when going from Humphrey size 3 to size 2. Our data correspond more closely to the analysis of the normal data (Fig. 5) of Egge." although the data of johnson" are closer to the 20-dB difference predicted by the Goldmann's assumed average relationship. We found a 14-dB difference between the Goldmann and Octopus 201 values, which added to the 3-dB difference between Humphrey and Octopus is in keeping with the 17-dB difference between the Goldmann and Humphrey in our data. The 14-dB difference we found is slightly larger than the data of Klewin and Radius." who found an 11.2-dB average difference between the Goldmann kinetic and Octopus 2000 static threshold values. Figure 6 shows the comparisons of population normal data, which suggests a 15- to 17-dB average difference. Conversion formulas to and from values of Goldmann perimetry are less reliable than the

others. Translation of isopter diagrams to digital values is not an exact procedure (but requires interpolation between isopters). In deriving our formulas we had fewer data points with which to work because we made translation into decibel values only when the isopter configuration made us certain of the value. Another reason for less certainty in the Goldmann conversion formulas in our data is that intraclass correlations were a substantial problem only on those perimeter pairs that included the Goldmann perimeter. Thus, kinetic values do not correlate to static threshold values as tightly as two types of static threshold correlate with each other. More importantly, it may be that the same conversion term may not be applicable in all clinics if slightly different techniques are used. For example, Johnson (oral communication, June 24, 1988) found that if movement of the stimulus in kinetic perimetry is at a rate for maximal visibility (about 4 to 5 degrees per second), the isopter is about 6 degrees external to the location when the static stimulus is visible, which corresponds to about a 2-dB difference in sensitivity. Extrapolation of data from another study" suggests the opposite (that static sensitivity is greater) with the manual kinetic 12• isopter (10 dB) occupying a position of about 34 degrees in the 45-degree merid-

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ian and approximately a 12-dB sensitivity at that location when static threshold is determined by automated ascending method of limits. The reaction time between where the stimulus is first detectable and where the patient's response is recorded may cause the isopter to be recorded internal to the actual kinetic isopter. In principle, if the stimulus is moved slowly enough, the stimulus movement does not contribute to visibility, so that it becomes essentially a static stimulus, and the reaction time is less influential, so that static and kinetic thresholds become identical. 12 In any event, manual kinetic perimetry is inherently more variable from one patient and perimetrist to another, so that the conversion values involving Goldmann perimetry are certainly less exact than the other conversions. Conversions between Dicon and other instruments-Empiric determinations are also necessary in the case of the Dicon Auto Perimeter, because the stimulus is a light emitting diode of a nonstandard 2-mm 2 area,6,8 between size 2 (1 mm") and size 3 (4 mm") in the Goldmann perimeter notation. Additionally, the presentation of the yellow-green stimulus (550 to 600 nm, peak of 570 nm") in a dark hole surrounded by white light may alter its perception, especially in retinal regions of high sensitivity. 7,8 The manufacturer designates the l,OOO-asb stimulus (10 dB) against a background of 32.5 asb as equivalent to a Goldmann I4e (0 dB) stimulus, which is also a 1,000-asb stimulus against a 32.5-asb background, but is of different size (0.25 mm"). Our empiric finding of an ll-dB difference between the Dicon and Goldmann perimeters suggests that the equivalence designation by the manufacturer, which takes into account only the stimulus intensity, is within 1 dB of being correct, despite an eightfold difference in stimulus area. The effect of area difference must be counterbalanced by effects of using a monochromatic light emitting diode stimulus in a dark hole, the details of the static thresholding algorithm, and the difference between static and kinetic perimetry. The approximate correctness of the manufacturer's designated equivalence was also confirmed by Hart and Cordon," who found that the static threshold intensity measured by the bracketing technique in the Dicon corresponded closely with the static threshold intensity of a size I Goldmann stimulus determined by the manual ascending method of limits. (The equivalence varied slightly with retinal location because of a flatter field profile with the Dicon.)

May, 1989

When comparing the Dicon stimulus with a size III Goldmann stimulus, Mills and Drance" found that the maximal 10,OOO-asb stimulus (0 dB) approximated the Goldmann III4e stimulus (as designated by the manufacturer based on the average size-intensity conversion formula that Goldmann used). However, Esterman and coworkers" found on empiric testing the Goldmann III4e to be equivalent to a 2,500-asb Dicon stimulus, a 6-dB discrepancy. Our findings relating the Dicon instrument to the Octopus are comparable to the data of Johnson, Keltner, and Lewis." but the relationship we found with the Humphrey perimeter differed inexplicably from their data. Johnson found (oral communication, June 24, 1988) an Octopus-Dicon difference of 3.14 dB inside 10 degrees, 4.37 dB from 10 to 20 degrees, and 3.41 dB between 20 and 30 degrees of eccentricity; overall, from simultaneous solution of published regression equations;" there was a difference of 3.6 dB. Johnson, Keltner, and Lewis" found a Humphrey-Dicon difference of 8.5 dB from 0 to 10 degrees, 10.04 dB from 10 to 20 degrees, and 9.6 dB from 20 to 30 degrees, and overall 9.4 dB. The discrepancy between the data sets for the Humphrey-Dicon comparison is like the discrepancy in the HumphreyOctopus comparisons; our Humphrey threshold values are 3 dB low relative to theirs. Confirmation of conversion terms from population normal data-With all three perimeters for which normal data were available, the upper part of the central field shows a slight physiologic depression compared to the inferior hemifield (Fig. 2). The depression in the upper quarter of the field is more marked with the Humphrey instrument than with the others, so that a different conversion constant should be used when comparing the top two rows of the 30-2 pattern of points with the Humphrey instrument. None of the data points we used in deriving empiric formulas in Table 1 came from the upper quarter of the field where this slight discrepancy exists. We suspect that one reason for the difference between instruments is a greater forward face tilt with the Humphrey instrument when the head is in position on the chin rest and the forehead is against the bar. For this reason, the eyebrows or eyelids may more often shade the upper field in some people, bringing down the population's average sensitivity in the upper field. Another apparent irregularity in the normal data comparison is a higher relative sensitivity of the field at age 79 years with the Octopus than with the other instruments. We do not

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Threshold Equivalence Between Perimeters

take this to mean that the conversion formulas do not apply to older individuals. Rather, the discrepancy means that the "normal values" for older individuals were not equivalently obtained for all instruments. At least some of the values were extrapolations from data obtained on a greater number of younger individuals, assuming a constant linear decline with age. Practical application-Overall, the conversion between static threshold values of the automated instruments is almost as reliable as could be expected given test-retest error (short-term and physiologic long-term fluctuation) f1uctuation. 28.29 Two consecutive fields on two different machines are nearly as comparable as two consecutive fields on the same machine (Tables 2 and 3), as was also found by Johnson, Keltner, and Lewis." From OUT data, by fixing the slope of the regression equation to 1, the conversion simplifies to the rules in Table 4. These rules are in keeping with the normal values available for the Humphrey and Octopus instruments, if the Octopus normal values at age 79 years are set aside for the present purpose. Because of greater variability in manual kinetic fields, the correlations between the Goldmann and other instruments was not as good as between two automated static perimeters, such as the Octopus and Humphrey values. TABLE 4 PROCEDURES TO CONVERTING FROM ONE PERIMETER TO ANOTHER TO CONVERT FROMITO

PROCEDURE

Add 3 (add 2 in upper 2 rows) Subtract3 Subtract 14 Subtract 3 (subtract 2 in upper 2 rows) Subtract 7 Subtract 17 (subtract 16 in upper 2 rows) Add 7 Add 3 Subtract 11 Add 14 Add 17 (add 16 in upper 2 rows) Add 11

Octopus/Humphrey OctopuS/Oicon Octopus/Goldmann' Humphrey/Octopus Humphrey/Oicon Humphrey/Goldmann' Oicon/Humphrey Olcon/Octopus Olcon/Goldmann' Goldmann'/Octopus Goldmann'/Humphrey Goldmann'/Oicon

'11148 = -10 dB; 11 48 dB; 110 = 15 dB.

= -5 dB; 148

=

0 dB; b.

= 5 dB; 12•

=

10

503

Even with simplified formulas, the point-bypoint conversion from one field map into the units of another instrument is bound to be tedious. It is especially tedious (and less accurate) when converting kinetic field plots to static threshold values. However, it may be worthwhile in particular regions of the field where there is particular suspicion of possible progression and the clinical circumstances force one to make a comparison between field tests performed with two different instruments. An easy method to compare static fields to kinetic Goldmann fields would be to draw isopters for 17, 22, 27, and 32 on the numerical printout of the Humphrey perimeter and compare these to the 14e , 13e , b, and lIe isopters of the Goldmann plot. The equivalent on the Octopus printout would be to plot isopters corresponding to 13.6, 18.6, 23.6, and 28.6 dB. Any of the conversions has an expected error in matching the values actually obtained on a second instrument. The conversion can be no better than the threshold measurement accuracy (short-term fluctuation). This and physiologic variation from one time to another (longterm fluctuation)28.29 needs to be taken into account when comparing fields at two different times conducted with two different instruments, just as when judging progression from one occasion to another by comparing the field tests on the same instrument. The test-retest variability of each perimeter and the prediction inaccuracy between perimeters are both greater for points with reduced sensitivity than for points with normal sensitivity. The conversion formulas can also be applied to correction of the mean sensitivity values. Comparison of two averages is not completely valid, however, unless the same pattern of test points made up the average (for example, program 32 of the Octopus and 30-2 of the Humphrey instrument). A comparison of the mean value of the Octopus or Humphrey instrument could not be made as accurately with a mean Dicon threshold value in the central 30 degrees because the pattern of points that make up the average is different. In a similar way, a comparison of mean sensitivity of Octopus program 31 could not be made with the mean value of a different Humphrey pattern (for example, 30-2 or 24-2). Finally, current definitions of disability or degree of impairment by most agencies use the III4e test stimulus of the Goldmann perimeter. As automated static perimetry becomes more commonly used, knowing the equivalence of III4e Goldmann stimulus on the other perime-

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ters will be necessary. In attempting to make such a conversion from our data, it must be kept in mind that nearly all of our data (which led to conversion terms in Table 4) consisted of a size I Goldmann stimulus of various intensities compared to a size 3 stimulus of the Humphrey and Octopus perimeters (and a nonstandard size for the Dicon). With the size-intensity relationship Goldmann used when designing his perimeter, shifting to stimulus size III on the Goldmann perimeter is intended to be equivalent to -10 dB. Therefore, if a Goldmann I,e (0 dB) is equivalent to a 17-dB Humphrey stimulus, then the Goldmann Ill.; should be equivalent to a 7-dB Humphrey stimulus. In a similar way, the Goldmann Ill., equates to a 4-dB Octopus stimulus and a I-dB Dicon stimulus. The data of Klewin and Radius" suggest that increasing from size 1 to sizes 2 and 3 of the Goldmann perimeter does correspond to sand la-dB changes in static threshold intensity respectively on the Octopus 2000 perimeter. However, the data of Johnson, Keltner, and Lewis" suggest a smaller change in intensity corresponds in such changes from size II to size III (2.70 dB for a to 10 degrees eccentrically, 3.29 dB for 10 to 20 degrees eccentrically, and 4.5 dB for 20 to 30 degrees eccentrically). However, the size-intensity relationship may not be 10 dB for a size change from I to III. If it were, the Humphrey perimeter equivalent to Goldmann III,e should be 10 dB (not 6 dB), because the Goldmann III,e and Humphrey 10dB stimuli are identical: they are both 1,000-asb stimuli and are of identical size on an identical 31.6-asb background. Part of the explanation for our finding a 6-dB instead of a Hl-dll equivalence is probably that the size-intensity relationship in the central 30 degrees is not the average value for the whole field used by Goldmann. Additionally, the Humphrey stimulus is static and of D.2-second duration, whereas the Goldmann stimulus is moving and provides opportunity for full temporal summation if longer than 0.2 second is required. In kinetic perimetry the patient can also wait for the stimulus to become more certainly visible before deciding whether or not to respond. For all these reasons, despite identity of size, intensity, and background, the equivalent Humphrey stimulus may be under 10 dB. It may be safe to conclude, however, that the Ill., equivalent is somewhere in the rather narrow range of 7 to 10 dB for the Humphrey perimeter. Similarly, it may be estimated that the Octopus stimulus of 4 to 7 dB should equate to the Goldmann III,e

stimulus. The Dicon stimulus of a dB (10,000 asb) is intended to be equivalent to the Goldmann III,e, and our empiric finding of 1 dB is close. Mills and Drance" agreed that a a-dB Dicon stimulus approximates the Goldmann III,e, although Estermanand associates" found a 6-dB (2,500-asb) stimulus to be equal to III4e. With these approximate equivalents of the Goldmann lII,e, expressed as a range, it may be abundantly clear from available static perirnetric examination performed for diagnostic purposes that an individual meets the current definition for visual disability without the need to obtain a separate kinetic field examination for disability determination. Thus, for example, if a 7-dB Humphrey stimulus (or a 4-dB Octopus stimulus or a-dB Dicon stimulus) is not seen outside 10 degrees, it is clear that the field would be limited to 10 degrees or less with a III4e Goldmann stimulus. In the future, agencies may find it better to adopt a certain static threshold level for each instrument as the standard, not because of its equivalence to the arbitrary standard of the Goldmann III4e, but in its own right. After all, there is more variability from one patient and perimetrist to another with the Goldmann perimeter than with the automated static perimeters, so there would be greater consistency by adopting a new static threshold standard. Whatever static threshold is chosen as a standard, it will be no less arbitrary than the original selection of the III4e Goldmann stimulus.

References 1. Goldmann, H.: Ein selbstregistrierendes Projektionskugelperimeter. Ophthalmologica 109:71, 1945. 2. Fankhauser, F.: Problems related to the design of automatic perimeters. Doc. Ophthalmol. 47:89, 1979. 3. Heijl, A.: The Humphrey field analyzer, construction and concepts. Doc. Ophthalmol. Proc. Ser. 42:77,1985. 4. Heijl, A.: The Humphrey field analyzer. Concepts and clinical results. Doc. Ophthalmol. Proc. Ser. 43:55, 1985. 5. Mills, R. P.: Quantitative perimetry. Dicon. In Drance, S. M., and Anderson, D. R. (eds.): Automatic Perimetry in Glaucoma. A Practical Guide. New York, Grune and Stratton, Inc., 1985, pp. 99-112. 6. Hart, W. M., Jr., and Gordon, M. 0.: Calibration of the Dicon Auto Perimeter 2000 compared with that of the Goldmann perimeter. Am. J. Ophthalmol. 96:744, 1983.

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7. Britt, J. M., and Mills, R. P.: The black hole effect in perimetry. Invest. Ophthalmol. Vis. Sci. 29:795, 1988. 8. Desjardins, D., and Anderson, D. R.: Threshold variability with an automated LED perimeter. Invest. Ophthalmol. Vis. Sci. 29:915, 1988. 9. Aulhorn, E., and Harms, H.: Visual perimetry. In Jameson, D., and Hurvich, L. M. (eds.): Visual Psychophysics. Handbook of Sensory Physiology. New York, Springer Verlag, 1972, vol. 7, no. 4, pp. 102-145. 10. Greve, E. L.: Single and multiple stimulus static perimetry in glaucoma. The two phases of perimetry. Doc. Ophthalmol. 36:1, 1973. 11. Heuer, D. K., Anderson, D. R., Feuer, W. J., Knighton, R. W., Gressel, M. G., and Fantes, F. E.: The influence of simulated media opacities on threshold measurements. Doc. Ophthalmol. Proc. Ser. 49:15, 1987. 12. Sloan, L. L.: Area and luminance of test object as variables in examination of the visual field by projection perimetry. Vision Res. 1:121, 1961. 13. Anderson, D. R.: Perimetry With and Without Automation, ed. 2. St. Louis, C. V. Mosby Co., 1987, pp. 347-413. 14. Lieberman, M. F., and Drake, M. V.: A Simplified Guide to Computerized Perimetry. Thorofare, N.J., Slack Inc., 1987. 15. Heijl, A.: Humphrey Field Analyzer. In Drance, S. M., and Anderson, D. R. (eds.): Automatic Perimetry in Glaucoma. A Practical Guide. New York, Grune and Stratton, Inc., 1985, pp. 129-140. 16. Spahr, J.: Zur Automatisierung der Perimetrie. I. Die Anwendung eines computergesteuerten Perimeters. Graefes Arch. Klin. Exp. Ophthalmol. 188:323, 1973. 17. Fankhauser, F., Spahr, J., and Bebie, H.: Three years of experience with the Octopus automatic perimeter. Doc. Ophthalmol. Proc. Ser. 14:7, 1977. 18. [enni, A., Fankhauser, F., and Bebie, H.: Neue Programme fur das automatische Perimeter Octopus. Klin. Monatsbl. Augenheilkd. 176:536, 1980. 19. Fankhauser, F.: The development of computerized perimetry. In Whalen, W. R., and Spaeth, G. L. (eds.): Computerized Visual Fields. What They Are and How to Use Them. Thorofare, N.J., Slack Inc., 1985, pp. 11-27. 20. Bebie, H.: Computerized techniques of threshold determination. In Whalen, W. R., and Spaeth, G. L. (eds.): Computerized Visual Fields. What They Are and How to Use Them. Thorofare, N.J., Slack Inc., 1985, pp. 29-44. 21. LeBlanc, R. P.: The Octopus system. In Drance, S. M., and Anderson, D. R. (eds.): Automatic Perimetry in Glaucoma. A Practical Guide. New York, Grune and Stratton, Inc., 1985, pp. 69-87. 22. Silverstone, D. E., and Hirsch, j.: Automated

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Visual Field Testing; Techniques of Examination and Interpretation. Norwalk, Conn., Appleton-CenturyCrofts, 1986. 23. Rosner, B.: Multivariate methods in ophthalmology with application to other paired-data situations. Biometrics 40:1025, 1984. 24. Zuhlke, G. (ed.): Octopus. Visual Field Atlas, ed. 2. Schlieren, Switzerland, Interzeag, 1978, pp. N2.9 and N3.9. 25. Heijl, A., Lindgren, G., and Olsson, J.: A package for the statistical analysis of visual fields. Doc. Ophthalmol. Proc. Ser. 49:153, 1987. 26. Johnson, c., cited by Anderson, D. R.: Perimetry With and Without Automation, ed. 2. St. Louis, C. V. Mosby Co., 1987, pp. 258-261. 27. Egge, K.: The visual field in normal subjects. Acta Ophthalmol. 169(suppl):I, 1984. 28. Flammer, J., Drance, S. M., and Schulzer, M.: Covariates of the long-term fluctuation of the differential light threshold. Arch. Ophthalmol. 102:880, 1984. 29. Flammer, J.: Fluctuations in the visual field. In Drance, S. M., and Anderson, D. R. (eds.): Automatic Perimetry in Glaucoma. A Practical Guide. New York, Grune and Stratton, Inc., 1985, pp. 161-173. 30. Fankhauser, F., Bebie, H., and Flammer, J.: Threshold fluctuations in the Humphrey field analyzer and in the Octopus automated perimeter. Invest. Ophthalmol. Vis. Sci. 29:1466, 1988. 31. Johnson, C. A., Keltner, J. L., and Lewis, R. A.: JAWS (joint automated weighting statistic). A method of converting results between automated perimeters. Doc. Ophthalmol. Proc. Ser. 49:563, 1987. 32. Heuer, D. K., Anderson, D. R., Knighton, R. W., Feuer, W. J., and Gressel, M. G.: The influence of simulated light scattering on automated perimetric threshold measurements. Arch. Ophthalmol. 106:1247,1988. 33. Brenton, R. S., and Argus, W. A.: Fluctuations on the Humphrey and Octopus perimeters. Invest. Ophthalmol. Vis. Sci. 28:767, 1987. 34. Klewin, K. M., and Radius, R. L: Static threshold determination and kinetic perimetry. Glaucoma 9:61, 1987. 35. Parrish, R. K., II, Schiffman, J., and Anderson, D. R.: Static and kinetic visual field testing. Reproducibility in normal volunteers. Arch. Ophthalmol. 102:1497,1984. 36. Mills, R. P., and Drance, S. M.: Esterman disability rating in severe glaucoma. Ophthalmology 93:371, 1986. 37. Esterman, B., Blanche, E., Wallach, M., and Bonelli, A.: Computerized scoring of the functional field. Preliminary report. Doc. Ophthalmol. Proc. Ser. 42:333, 1985.