a comparison of the mean defect and mean deviation

Jpn J Ophthalmol Vol 34: 414-420,1990

A COMPARISON OF THE MEAN DEFECT AND MEAN DEVIATION INDICES WITHIN THE CENTRAL 28° OF THE GLAUCOMATOUS VISUAL FIELD A.T. FUNKHOUSER and F. FANKHAUSER Summary: The mean defect index of Flammer and the mean deviation index of Heijl have been compared based on a study of 169 glaucomatous visual fields. It is shown that in the cases studied the differences between the two indices are negligible for Octopus G 1 program results and that they may thus be used interchangeably.

Key Words:

Automated perimetry, glaucoma, mean defect, mean deviation, visual field Introduction

The mean defect index, along with the corrected loss variance and the short-term fluctuation indices among others, was introduced by Flammer in 19853 as one means of characterizing visual fields measured with the Octopus G1 programv". It provides the perimetrist with information about the overall depression of the visual field as compared with the age-corrected normal field", and is calculated as follows: 1 n MDr= - ~ (z, - Xi) (1) n i=1 where MDr is the mean defect index according to Flammer, z: is the age-corrected normal value at location i, Xi is the mean differential light sensitivity (DLS) at location i (averaged over the repetitions of the measurement at that location [the G1 program measures with two phases]), and n is the number of test locations (=59 for the G1 program). In 1986, Heijl introduced the mean deviation index for the same purpose'. Its calculation takes into account the interindividual fluctuation at each test location and is made according to the formula:

1 n -~n

i=1

1

(2)

S2i

where MDh is the mean deviation index according to Heijl and S2i is the variance at location i (z, is the same as above, and Xi is now the measured DLS, rather than a mean value, since the mean deviation index is not defined for multi-phase examinations). Inspection of equations (1) and (2) shows that with increasing loss in the visual field, the mean defect index increases (is more positive) while the mean deviation index decreases (becomes more negative). The supposed advantage of the mean deviation index over the mean defect index is that test locations more centrally located, where DLS fluctuations are lower, are given more weight Received: July 7,1990 University Eye Clinic, Bern, Switzerland Reprint requests to: Dr. AT. FUNKHOUSER,

University Eye Clinic, Insel Hospital,

3010 Bern, Switzerland

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in the calculation of the index than those which are more peripheral, where fluctuations are larger. Further, it was argued that paracentral depressions are thus more reliable and have a higher likelihood of representing abnormality than depressions in the periphery, which could be due to normal fluctuation'"?", One asks, therefore, if there is a significant difference in the results based on these two indices which would predispose the use of one over the other. In other words, a question is raised whether the calculation including the local fluctuation information would lead to values which are significantly different from the results without doing so. The relevance of using such transformed threshold values in the calculation has never been analyzed. In particular, the recommendation of Heijl and co-workers to weight global visual field indices according to fluctuation within the visual field has never been verified. It was such considerations which prompted the following relatively simple and straightforward investigation. Materials and Methods One hundred and sixty-nine eyes with slight to very heavy glaucomatous damage were examined using the Octopus Gl program on both Octopus 201 and Octopus 500 automated perimeters. The data for this study were obtained from the out- and inpatient departments of the University Eye Clinics of Bern and Basel. Cases of both high tension and normal tension glaucoma were included. The second examinations of the eyes involved were utilized in order to avoid learning effects. The following inclusion criteria were employed: 1) If damage were present, it had to be of a type consistent with the diagnosis of glaucoma. 2) For high tension glaucoma, average lOP values greater than 22.5 mmHg, together with a recorded maximum lOP greater than or equal to 30 mmHg, had to be present. 3) For normal tension glaucoma, recorded lOP values were never greater than 20 mmHg. 4) Alterations of the optic disc, if present, were those compatible with glaucoma. 5) Patients had visual acuities 0.8 or better. 6) Refractive errors were less than or equal to ±3 diopters. 7) Concomitant pathology had to be absent, in particular opacities of the media. Using the software developed specially for this purpose, the two indices, mean defect and mean deviation, were calculated based on visual field results from the first phase of the Gl examinations (the first phase was employed in order to best match examining with program 30-2 [Humphrey J). The local fluctuation data used in the calculation of mean deviation were derived from a multi-center normal value study ofGl examinations (R LeBlanc,] Flammer, M Zulauf: unpublished results). The data consisted of the local standard deviations of the results from 274 second examinations of 274 volunteers, one per subject. Results Figure 1 contains plots of the standard deviations of the thresholds as a function of eccentricity: a) as obtained with the Octopus Gl program, and b) those published for the Humphrey 30-2 program (Figure 6 in Reference 7). The local fluctuations shown in Figure la are those obtained for the 274 non-first examinations (corresponding to the s, used for calculating mean deviations according to equation 2). As mentioned above, the results are from the first phase of G1 examinations of normal eyes, one per person. Since for many

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a.

OF OPHTHALMOLOGY

Octopus G 1 standard Standard

deviations

deviation (dB)

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(degrees)

30- 2 standard

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Figure

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(degrees)

Dependence of interindividual DLS threshold variations on eccentricity: a) for non-first examinations made with Octopus program Gl, and b) those published for the Humphrey program 30-2'. Standard deviations from age-corrected normal DLS thresholds at each test location. (For further explanation, see text.)

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INDICES

Humphrey 30-2 and Octopus G1 deviations 6.-----------------------------------------------------------------,

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Octopus Gl

°OL---------~5~--------~1~0----------~1~5----------~20~--------~2~5~--------~30 Eccentricity Figure

2.

Comparison of mean automated perimeters.

local fluctuation

(degrees)

as function

of eccentricity

for Humphrey

and

Octopus

eccentricities there are usually several test locations (along various meridians), the local fluctuation results on both plots are shown shifted slightly horizontally (to the left for locations in the superior part of the visual field and to the right for locations in the inferior part). The rather elevated value for a test location at around 23° eccentricity in Figure la denotes results from a point in the preliminary version of the Gl program that was deemed too close to the blind spot (ie, fluctuations were large); it was shifted 2° horizontally, further away from the blind spot, in the final version. Figure 2 shows a more direct comparison of the same local fluctuation data shown in Figure l. Here, the mean values and standard deviations for the local fluctuation results at each eccentricity are shown. The dashed curve, which shows the mean Humphrey fluctuations, can be compared with the curve in Figure 2 of Reference 6, which is a profile of the fluctuations along the 270° to 90° meridian. Figure 3, which shows the results of the current investigation, is a plot of the mean deviations for the 169 glaucomatous examinations versus the corresponding mean defects. One sees that the two indices yield results which are remarkably similar, except for a difference in sign. The correlation coefficient for the entire range of MDr and MDh values as shown in Figure 3 is -0.998 with a standard error of estimate amounting to 0.47 dB, which is negligible

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Comparison of Flammer and Heijl Indices 5 ----------------------------------------------------------,

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Mean defect (dB) Figure 3.

Mean deviation (Heijl) versus mean defect (Flammer) represents linear regression curve.

for 169 glaucomatous

visual fields. Line

for most purposes (the maximum difference between the two indices amounted to 1.5 dB for a mean defect of 15.8 dB). If the range of the two indices is restricted to -4 to 4 dB, the correlation coefficient becomes -0.993 and the standard error amounts to only 0.l8 dB (with a maximum difference of 1 dB for a mean defect of 1.3 dB). This seems to indicate that in the early stages of glaucoma, where damage to the visual field is relatively small, the two indices are virtually identical. Discussion From Figure 2 it-can be concluded that the local fluctuation at the center is larger for the Octopus perimenters than for the Humphrey instrument. This is most likely due to the fact that the 274 examinations used in the normal value study included measurements made with the Octopus 201 which necessitates tilting the subject's head position when measuring the central five test locations. This often entails adaption changes with resulting fluctuations in the DLS measured there. For 5° out to around 189, the fluctuations appear to be about the same.

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For eccentricities greater than around 23°, they are larger for the Humphrey instruments than for the Octopus perimeters. The reason for this difference is not clear, though it may have to do with the inclusion criteria for the normal populations involved and/or with differences in the measurement accuracy and stimulus exposure durations of the two instruments". At first glance, it may seem surprising that there is so little difference evident between the two indices in Figure 3. Two facts, however, need to be considered. The first is that local fluctuations as seen in the standard deviations of the DLS values, shown in Figure 1, do not vary enormously within the central 28° of the visual field when determined with the Gl program on Octopus automated perimeters. They range from 1.9 to 2.6 dB near the center out to about 3 dB in the periphery (in contrast to those from the Humphrey 30-2 program which are reported as being larger than 5 dB at eccentricities near 28°). The great majority lie between 2 and 2.5 dB. This means that the weighting of the local loss values as performed in calculating the mean deviation, at least within this part of the visual field, affects the resulting mean deviation value, as compared with the unweighted mean defect value, very slightly. (Mathematically, this can be seen by comparing equations 1 and 2: if the fluctuations were constant for all visual field locations, the weighting has no effect and the two indices are identical.) For more peripheral parts of the visual field, especially where fluctuations are higher, such as near correcting lens edges and near the blind spot, weighting in the calculation of the index might be of greater value and thus more important. Furthermore, the excellent correlation of the two indices might also be due to the fact that glaucomatous field damage tends to be located in the central, paracentral or midperipheral regions of the visual field, both in early phases of the disease and in later stages. More precisely, in a hypothetical case, where visual field damage is only peripheral, MDc will be larger than the absolute value of MDh. For only paracentral damage, on the other hand, the reverse is true. Since in individual cases both situations tend to be present, they average out. It might be worthwhile noting that for purely diffuse visual damage, (ie, where the loss is constant for all the examined test locations), the two indices are once again identical, as can be seen by inspecting equations 1 and 2. From general considerations, there are good reasons to believe that the approximate equality of the two indices will hold, moreover, for other disease situations as well. The only instances in which this would not be true are those where there is heavy damage that is concentrated only at the periphery or only in the central and/or paracentral regions. Therefore, it seems reasonable to conclude that, at least for glaucomatous eyes in the central 28° of the visual field, the two indices calculated from program Gl examination results can be used interchangeably and are virtually identical. This seems to be especially true when the detection of early glaucomatous damage is attempted. The results as obtained here also point to the fact that probability weighting of DLS threshold determinations in the central, paracentral and midperipheral visual field does not tend to provide any advantage in the interpretation of visual field damage, when these two indices are used. This statement does not cover artifacts such as disturbances caused by the blind spot, correction lens edges or others. It is the opinion of the authors that the interpretation in such cases should be left to an experienced perimetrist who is then able to decide for him or herself whether apparent abnormalities should be assigned to such disturbances or might be due to actual pathology.

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Acknowledgements: This work was supported in part by the Swiss National Science Foundation Grant 32-27563.89 and in part by the Swiss Foundation to Prevent and Combat Blindness.

REFERENCES 1. (Anonymous): (1986) STATPAC: User's Guide. Allergan-Humphrey, San Leandro, CA, USA 2. Fankhauser F, Bebie H & Flammer j: (1988) Threshold fluctuations in the Humphrey Field Analyzer and in the Octopus Automated Perimeter. Invest Ophthalmol Vis Sci 29: 1466 3. Flammer j, Drance SM, Augustiny L & Funkhouser A: (1985) Quantification of glaucomatous visual field defects with automated perimetry. Invest Ophthalmol Vis Sci 26: 176-181 4. Flammer J: (1986) The concept of visual field indices. Graefes Arch Clin Exp Ophthalmol 224: 389-392 5. Flammer j,jenni A, Keller B & Bebie H: (1987) The Octopus glaucoma program Gl. Glaucoma 9: 67-72 6. Heijl A: (1987) The implications of the results of computerized perimetry in normals for the statistical evaluation of glaucomatous visual fields, Ed Kriegelstein GK, Glaucoma Update III: 115-122. Springer-Verlag, Heidelberg 7. Heijl A, Lingren G & Olsson J: (1987) Normal variability of static perimetry threshold values across the central visual field. Arch Ophthalmol 105: 1544-1549 8. Heijl A, Lingren G & Olsson J: (1987) A package for the statistical analysis of visual fields. Doc Ophthalmol Proc Ser 49: 153-168 9. Heijl A, Lingren G, Olsson j et al: (1988) Visual field interpretation with empiric probability maps. Arch Ophthalmol107: 204-208 10. Heijl A & Asman P: (1989) A clinical study of perimetric probability maps. Arch Ophthalmol 107: 199-203