Simulations for FASTPAC and the Standard 4-2 db Full- Threshold Strategy of the Humphrey Field Analyzer

Transcription

1 Simulations for and the Standard 4-2 db Full- Threshold Strategy of the Humphrey Field Analyzer Elisabeth Glass, Markus Schaumberger, and BernhardJ. Lachenmayr Purpose. This study evaluates the accuracy, reproducibility, and efficiency of, a new fast strategy for automated perimetry using 3-dB steps with single threshold crossing, compared to the standard 4-2 db full threshold strategy by means of computer simulations. Method. An "artificial patient" module was developed to create responses to stimuli by a Monte-Carlo technique from a given probability distribution. The authors performed 10,200 simulations with direshold values ranging from 0 to 50 db. Results. Results demonstrate an 18% decrease in the number of presentations per threshold determination, which is equal to a similar reduction in testing time. For both strategies, there is a considerable influence of the starting deviation (difference between starting value and actual threshold) on threshold error (difference between estimated threshold and actual threshold): negative starting deviations lead to negative threshold errors and vice versa. This relationship is more pronounced for (slope 0.18 db/db, P < ) than for the full-threshold strategy (slope 0.13 db/db, P < ). In addition, fluctuations of the determined thresholds, described as the distance between the 16th and 84th percentiles of the threshold errors, increase with increasing absolute starting deviations. This is particularly true of. Conclusions. The influence of the starting value on the threshold determination may lead to a considerable underestimation of visual field defects, accompanied by a higher fluctuation. This is an intrinsic property of both staircase procedures., however, is more affected than the standard 4-2 db full-threshold strategy., therefore, provides time reduction at the expense of accuracy and reliability. Invest Ophdialmol Vis Sci. 1995;36: V isual field testing is an important tool for the diagnosis and follow-up of various ophthalmologic disorders. An exact determination of the distribution of differential light sensitivity over the visual field, however, is time consuming and often requires a tremendous amount of patient cooperation over a long testing time. The consequence is loss of reliability and consistency in the results of automated perimetry, mostly attributed to "fatigue." Previous publications on this subject report a reduction in contrast sensitivity 1 ' 2 and higher fluctuations in the results' 3 with in- From the Section of Psychophysics and Physiological Optics, University Eye Hospital, Munich Germany. { 'resented in part at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasola, Florida, May Supported Ijy German Research Foundation grant La 517/6-1. Submitted for publication July 21, 1994; revised February 1, 1995; accepted April 5, Proprietary interest category: N. Reprint requests: Elisabeth Glass, Section of Psychophysics and Physiological Optics, University Eye Hospital, Mathildenslrasse 8, D Munich, Germany. creasing test duration. These effects of testing time were found to be more pronounced for patients with glaucoma than for normal subjects. 1 ' 2 Thus, a major effort in the development of new perimetric strategies is to find a reasonable trade-off between testing time and accuracy to minimize patient stress and simultaneously to improve reliability of results. Recently, Humphrey Instruments (San Leandro, CA) introduced a new fast strategy for the Humphrey Field Analyzer (HFA) called. This algorithm estimates diresholds from a single threshold crossing with a fixed step size of 3 db. It promises to achieve a considerable reduction in testing time compared to the standard 4-2 db full-threshold staircase strategy with double threshold crossing, which is commonly used in modern automated perimetry. 4 Our study evaluates the properties of and compares FAST- PAC to the standard 4-2 db full-threshold procedure. Both procedures are staircase methods widi predetermined step size for contrast variation. In contrast to Investigative Ophthalmology & Visual Science, August 1995, Vol. 36, No. 9 Copyright Association for Research in Vision and Ophthalmology 1847

2 1848 Investigative Ophthalmology & Visual Science, August 1995, Vol. 36, No. 9 brighter stimulus threshold darker stimulus o 3dB 4-2 db double threshold crossing 4dB 2dB : stimulus "seen" O : stimulus "not seen" FIGURE l. Threshold determination by {left) and the 4-2 db full-threshold strategy (right). The 4-2 db procedure continues presentation of stimuli until a second response reversal occurs, whereas terminates after the first response reversal, requiring on average less stimuli. The last seen stimulus is taken as the final estimate for the sensitivity (Humphrey Field Analyzer standard). the single threshold crossing of, the 4-2 db strategy performs a double crossing of the threshold requiring two response reversals, using 4-dB steps in the first stage and 2-dB steps in the second stage (Fig. 1). Various clinical studies that compared the practical viability of both strategies have given contradictory results. 5 " 11 We, therefore, use computer simulations as a more controllable and reproducible means to assess strategy characteristics during interaction with the patient. METHODS Our simulation software consists of two main components, an artificial patient module and a perimetry module (Fig. 2). Coupling these two elements provides the possibility of observing their interactive behavior and of investigating possible relationships between patient response behavior and properties of die strategy. Simulating the patient offers the important advantage of complete knowledge and control over his response characteristics. Thus, a direct comparison between predefined patient parameters (such as threshold) and the strategy results is possible. The perimetry module is composed of the "simulation control" and a "strategy module." The simulation control starts the simulation and records the resultant data and the main test parameters of each threshold determination. The strategy module contains the chosen perimetric strategy. It communicates with the patient, setting each current stimulus value to be presented to the patient on the basis of the decision criteria of the test algorithm. The "artificial patient module" can be divided into the interactive "patient routine" and the "psychometric function." The patient routine receives a stimulus from the perimetry module and generates and returns the corresponding patient response by a software interface. Its task, therefore, is to create these YES/NO answers (corresponding to "seen" or "not seen") from a given probability distribution by a Monte-Carlo simulation procedure. 12 This underlying probability distribution of positive responses is evaluated in the psychometric function module. It represents the threshold behavior of the patient as a function of the stimulus contrast at a specific retinal location. A typical psychometric function is s-shaped and is characterized by four parameters (Fig. 3): the threshold value a, the slope (3, and the probability of false-positive and false-negative responses y and 6. Their values are specific personal data of the patient and are initially set in the patient module by parameterized input. The parameter (3 is defined as the slope of the psychometric function and is, therefore, an indicator of the "sharpness" of the threshold. It is an inverse measure for the fluctuations of the answers for stimulus contrasts around the threshold value. The parameter y represents the probability of a positive answer for infinitesimally small (i.e., zero) stimulus contrast, usually labeled as a false-positive response, and 6 is defined as the probability of a negative answer for infinitely high contrast, attributable to a false-negative response. Values for y and 8 can be approximated by empirically counting the frequencies of false answers in the appropriate catch trials during a visual field determination. In our study, we describe the psychometric distribution analytically with the Weibull Function 13 as used by Harvey. 12 Our examinations included die testing of FAST- PAC and the 4-2 db full-threshold strategy, in both cases with three different values of the slope (3: 1.75 dbt\its half (0.875 dbt 1 ), and its double (3.5 dbt 1 ). These values were chosen to cover the range of experimental data for psychometric functions published, for example, by Weber and Rau, 14 who measured (3 values between 0.6 and 1.6 dbt x (transformed units) as well as by Chauhan et al 15 widi (3 at approximately 1.6 dbt 1 ; psychophysical measurements carried out in our laboratory in the course of this project 16 yielded values in the range of 1.8 to 3.1 db~ l. For each strategy and value (3, 10,200 threshold determinations were simulated, with threshold values a ranging from 0 to 50 db in steps of 1 db, corresponding to the stimulus range of the HFA. 4 We extracted die probability values of false-positive and false-negative responses from data collected by clinical surveys

3 Simulating and the 4-2 db Threshold Strategy 1849 input data properties of the patient threshold alpha * fluctuations beta» probability of false pos. answers probability of false neg. answers output data estimated threshold number of questions error messages etc. FIGURE 2. Configuration of the simulation system, consisting of the artificial patient module with his individual properties and the perimetry module. The psychometric function of the patient serves as a probability distribution for conversion into a response behavior in the patient module. stimulus psychometric^ function probability weibull function of response artificial patient module patient routine stimulus answer YES/NO strategy module 4/2 db double crossing or 3 db single crossing strategy start result perimetry module simulation control of the visual field parameters carried out in our group, 17 in which 144 normals were tested with the HFA. After reanalysis of the 144 visual fields evaluating the mean rates of false-positive and false-negative answers, we obtained the values (± SD) of y = (± 0.068) and 6 = (± 0.050), agreeing closely with those found by Johnson and Nelson-Quigg. 18 We fixed y and 6 to these values for all simulations. The starting point of the strategy was set to 25 db for all tests. The first presented stimulus was chosen slightly (4 db) brighter than the starting point, and the last seen stimulus value was taken as the threshold estimation, in the same way as is standard for the HFA. 8 All stimulus contrasts in this article will be given probability of response "YES" h 0.0 probability of false negative errors / slope/ /^threshold 2 3 stimulus intensity probability of false positve errors FIGURE 3. Typical psychometric function (in arbitrary units) characterized by four parameters: the threshold value a, the slope parameter /? (an inverse measure for the fluctuations), and the rates of false-positive and false-negative answers y and 6. in decibel units as defined for the HFA on the basis of its settings: E[dB] = 10 log (L max /L) with L max = asb = 3183 cd/ni 2 : maximum luminance, L: actual luminance. RESULTS Number of Stimulus Presentations To quantify the differences in testing time, we evaluated the number of stimulus presentations that were necessary to obtain a single threshold estimation (Fig. 4). Table 1 gives the mean number of stimuli averaged over all 10,200 simulations (regardless of their varying but equally distributed starting deviations). Here, FAS- TPAC required less stimulus presentations than the 4-2 db strategy: an 18% reduction was found for (3 = 1.75; for (3 = 3.5, it lies at approximately 15%; for (5 = 0.875, there is a decrease of 21%. With increasing P, both strategies tend to require slightly more trials per threshold determination (Table 1). Threshold Error To quantify the accuracy and reliability of the threshold determinations, we investigated the influence of various parameters on the "threshold error," which is given by the difference between the estimated threshold and the patient's actual threshold. An interesting parameter in the threshold determination process is the starting point of the strategy with respect to the patient's actual threshold. Is there any influence of the starting point on accuracy or reliability? To introduce this variable, we defined the parameter starting deviation as the difference between strategy

4 1850 number ol cases %] 6 = Investigative Ophthalmology 8c Visual Science, August 1995, Vol. 36, No db STRATEGY 4-2 db STRATEGY number ol cases (%] threshold error [db] 13 = threshold error [db] number ol stimuli per threshold determination number of stimuli per threshold determination 3 = 1.75 number ol cases (%) number ol cases [%] B = 1.75 threshold error [db] number ol stimuli per threshold determination number ol stimuli per threshold determination 13 = 3.5 number of cases [%] number of cases (%) = 3.5 threshold error [db] number of stimuli per threshold determination number of stimuli per threshold determination FIGURE 4. Relative frequency of the required number of presentations for a single threshold determination for different values of fi (, left, 4-2 db strategy, right, 10,200 simulations per plot or 200 simulations for each starting deviation). starting value and the patient's actual threshold. Figure 5 shows the threshold error as a function of the starting deviation. A remarkable relationship was found: negative starting deviations lead to negative threshold errors and vice versa. Nonparametric linear regression analysis 19 of the relation shows (Table 2) that this influence is significantly stronger for FAST- PAC than for the 4-2 db strategy (P < ). Fur FIGURE 5. Threshold error medians plotted as a function of the starting deviation. Black bars indicate the distance between the 16th and 84th percentiles. In all cases, the data presented an apparent influence of starting point on the resultant accuracy of the threshold determination (10,200 simulations per plot). thermore, this behavior becomes more evident with increasing fluctuations in the patient responses, i.e., with lower /? values, and tends to decrease more and more when approaching an ideal threshold behavior, i.e., a high ft value. TABLE l. Mean Number of Stimulus Presentations P Values TABLE 2. Relationship Between Threshold Error and Starting Deviation /3 Values Strategy Strategy db strategy db strategy 0.21 (0.57) 0.27 (0.58) 0.13 (0.46) 0.18 (0.46) 0.10 (0.41) 0.14 (0.40) Values represent the mean number of stimulus presentations required per threshold determination. (Means were determined in 10,200 stimulations.) Values are slopes (in units of db/db) and correlation coefficients r (in parentheses) of the linear regression analysis between threshold errors and starting deviation.

5 Simulating and the 4-2 db Threshold Strategy fluctuation width [db] dB strategy FIGURE 6. Fluctuation widths (16th to 84th percentiles) of the threshold errors as a function of the starting deviation. Fluctuation widths increase toward both ends of die abscissa, i.e., with rising absolute starting deviations for both strategies (10,200 simulations, (3 = 1.75). Fluctuations Fluctuations of threshold determination occurring under identical parameter settings may be used as an indicator of reproducibility. We consider the differences between the 16th and 84th percentiles of the threshold data as a reasonable indicator of the fluctuation width. This would correspond to a width of approximately 2 SD for normally distributed threshold values. The influence of the strategy starting point on reproducibility again shows a general trend: the bars in Figure 5, representing the fluctuation widths, indicate an increase in fluctuations with larger positive or negative starting deviations. Plotting the fluctuation values themselves for both strategies makes this effect even more visible (Fig. 6). Compared to the point of 0 db starting difference, the trend reaches statistically high significance (P < 0.001) at deviations greater than approximately ±12 db (nonparametric conover analysis 19 ). Fluctuation widths of the pooled threshold data of our simulations with each strategy and the various values of (3 are shown in Table 3. Two trends can be recognized in these results: higher fluctuations in the patient's threshold behavior (lower (3 in the psychometric function) lead to increasing fluctuation widths among determined thresholds (as expected); and, as opposed to the 4-2 db strategy, exhibits less reliable behavior, presenting substantially larger fluctuation widths for all values of (3 (Table 3). (A detailed description of the methods and results of this study can be found in Glass E. Psychometrische Funkitionen in der Perimetric: Entxuicklung und Erprobung eines Patient ensimulators. Munich: Ludwig-Maximilian University; thesis in preparation). DISCUSSION 1851 Versus 4-2 db Full-Threshold Strategy Our results confirm the claimed reduction in testing time with the procedure compared to the standard 4-2 db full-threshold strategy. Though not necessarily proportional to each other, it is still reasonable to compare qualitatively our reduction in the number of stimulus presentations with experimentally achieved reductions in clinical testing time, which are approximately 34% (depending on the study population). 5 ' 7 --'" It is because of its simpler strategy that needs a smaller number of stimuli per threshold determination: It demands only a single threshold crossing instead of a double crossing to determine the final threshold. The absolute size of threshold errors in our simulation increases for compared to the 4-2 db strategy. This is evident in the strong correlation between threshold errors and starting values, showing a significantly steeper regression slope for. In clinical examinations, it is not possible to determine the closeness of the detected threshold to the patient's actual threshold to have a measure of accuracy. Nevertheless, the mean deviation (MD) index, which is usually evaluated in a standard visual field examination of the HFA 1 and represents the mean deviation from age-corrected normal values, may be qualitatively linked with the threshold error: Changes in MD between and the 4-2 db strategy should basically reflect differences in the threshold values, provided that normative values are the same for both strategies. These differences appear in the simulation as changes in the threshold errors, hence, MD and threshold errors should show corresponding trends. For the purposes of tfiis study, we, therefore, qualitatively compared our results for possible trends in the mean MD to the results of other studies. Flanagan et al 8 and O'Brien et al 5 report significandy less negative MD values (i.e., smaller defects) generated by FAST- PAC for glaucomatous visual fields, whereas Iwase et al 9 found that the values were more negative for FAST- PAC (deeper defects). MD was also less negative in TABLE 3. Fluctuation Widths of Threshold Errors Strategy 4-2 db strategy P Values 1.75 Values are differences between the 16th and 84th percentiles of the pooled threshold errors (in db)

6 1852 Investigative Ophthalmology & Visual Science, August 1995, Vol. 36, No. 9 the study of Hoop et al, () but with insufficient significance. The discordance of these data could be owing to the fact that all the examinations are based on different populations with unknown parameters, such as the distribution of starting values, where opposite contributions could partly compensate for each other. Making the hypothetical assumption that in threshold determinations of glaucomatous visual fields the starting values are near normal and, therefore, that the starting deviations are predominantly greater than zero, our results would predict errors greater for FAS- TPAC than for the standard strategy. This is equivalent to a more pronounced underestimation of field loss with ; therefore, we would expect MD values to be slightly higher under these conditions (i.e., less negative), agreeing closely with studies cited above. 568 A clear trend was found for the fluctuations of measured threshold values. We obtained significant increases in fluctuation widths for of between 20% and 37%. In clinical studies, the reproducibility of visual field determinations generally is judged by the index of the short-term fluctuation.' 1 Publications on this subject consistently state that fluctuations are significantly higher for than for the 4-2 db strategy (increases vary between 14% and 43%, depending on the test population), b ~" confirming our finding of less reliability for. We conclude that achieves a considerable decrease in examination time, at the expense, however, of an equally significant loss in accuracy and reliability. It seems likely that this inverse relationship between efficiency and accuracy is of general validity for staircase procedures, as found by Johnson et al 20 in theoretical investigations. Heijl 21 inspected similar test logics and concluded that a quick, simple strategy is suitable for first examinations, such as screening tests, but in the follow-up of patients with glaucoma, a more complex algorithm with better reproducibility and reliability is desirable. Based on the results of our study, we suggest that for normal clinical purposes, the conventional 4-2 db staircase procedure should be used because it is still the better choice for perimetry, especially if considerable accuracy and reliability are necessary (as in followup examinations). For those patients for whom examination time is a limiting factor, can be a helpful alternative. Influence of the Starting Point Our results demonstrate a remarkable influence of the starting point of the staircase sequence on accuracy and reproducibility of the threshold determinations for both strategies. The thresholding procedure has the tendency to underestimate the threshold if the starting value is located below the "true" threshold and to overestimate it if it is above. At the same time, the fluctuations increase with absolute starting deviations. A possible reason for this effect could be the fact that for each presentation there is a certain probability of a false answer, which increases as the stimulus value approaches the threshold from one direction. Such a false answer would induce a response reversal and may then lead to a strategy termination before the testing stimulus has reached threshold. The resultant deviation, therefore, would occur in the same direction as the starting deviation; it would be correlated with its size and be accompanied by inherent fluctuations. The distortion caused by these false answers should be greater, the less response reversals are required for the strategy termination; this interpretation is confirmed by our observation of steeper regression slopes for. Indications of this kind of behavior have not been reported in the literature as yet, except for the article by Heijl 21 in which he simulates similar, but more specific, test logics for automated perimetry. He found a systematic displacement of the determined threshold relative to the actual threshold in the direction of the starting point if the process started a few steps away from the true threshold. Johnson et al, 20 who performed computer simulations on several staircase strategies using two or more threshold crossings, did notfindany influence of the starting position on accuracy. On the other hand, when looking at the influence of false answers, they noticed that a single response error in a staircase sequence does influence the accuracy of the threshold determination, a fact that fits into our interpretation. The influence of the starting point is a probability effect and is due to the nonideal shape of psychometric functions: For any given stimulus intensity, a response reversal becomes more likely for flatter psychometric functions (i.e., for smaller values of /?). This could explain the steeper regression slopes for lower P, as well as the fact that the required amount of stimuli is less in these cases because of the earlier termination of the threshold search. Even though the effect would disappear with a steplike shape in the patient's threshold region (very high value of/?), these systematic errors and increased fluctuations are not caused directly by the patient but by the strategy's termination criterion during the dynamic interaction with the patient. Thus, the reason for increased fluctuations in visual field defects is not necessarily purely physiological. It might be possible to explain in part the increased fluctuations found in patients with pathologic fields 22 " 24 which until now have generally been attributed to physiological changes by the influence of the strategy start. Unfortunately, the starting conditions under which these experiments have taken place are not known (they are generally not recorded with

7 Simulating and the 4-2 db Threshold Strategy 1853 the data). To estimate the degree of influence of strategy start, further investigation has to be undertaken, particularly taking into account the specific starting procedures of the perimeters. It is, nevertheless, most likely that a part of the fluctuations is caused by this strategy effect because at locations of lowered sensitivity, the majority of starting values usually lies above the actual threshold levels, shifting the starting deviations into a region in which underestimation of the defect and higher fluctuations are provoked. On the other hand, the effect cannot be used to explain increased threshold variations that precede glaucomatous defects 22 ' 25 ' 26 (assuming that unchanged starting values were used). Furthermore, direct measurements of psychometric functions as performed by Weber and Rau 14 detected a positive correlation between the slope and sensitivity value of the frequency-of-seeing curve, indicating that there are physiologically heightened fluctuations if sensitivity is low. We conclude that there is a combination of both a physiological increase in variability and a "feign" increase from heightened fluctuations and systematic errors caused by the strategy. These considerations highlight the important fact that we do not have an independent measurement method: An ideal measuring apparatus should not show any interference from its own starting conditions. This finding should be taken into account whenever perimetric data are compared. Under clinical settings, one has to be careful when interpreting inter-session variations of visual field data or increased fluctuations as diagnostic clues for pathologic change, as discussed in the literature. 22 " 24 ' 26 The behavior of the threshold strategy, especially at the limits of the scale of starting deviations, is accompanied by systematic errors. This may cause an underestimation of visual field defects, particularly if the strategy starts at or near normal values. Key Words computer simulations,, fluctuation, perimetry, threshold strategies References 1. Heijl A. Time changes of contrast thresholds during automatic perimetry. Acta Ophthalmol. 1977; 55: Johnson CA, Adams CW, Lewis RA. Fatigue effects in automated perimetry. Appl Opt. 1988; 27: Flammer J, Niesel P. Die Reproduzierbarkeit perimetrischer Untersuchungsergebnisse. Klin Mbl Augenheilk. 1984; 184: In German. 4. Haley MJ. Field Analyzer Fibel. Karlsruhe: Allergan Humphrey GmbH O'Brien C, Poinoosawmy S, Wu J, Hitchings R. Evaluation of the Humphrey threshold program in glaucoma. BrJ Ophthalmol. 1994;78: Hoop J, Harris A, Shoemaker J, Sponsel WE, Cantor LB. A comparison of global indices from the Humphrey 24-2 Statpac and Fastpac programs in normal and glaucomatous eyes. ARVO Abstracts. Invest Ophthalmol Vis Sci. 1993; 34: Flanagan JG, Moss ID, Wild JM, et al. Evaluation of : A new strategy for threshold estimation with the Humphrey Field Analyzer. Graefe's Arch Clin Exp Ophthalmol. 1993;231: Flanagan JG, WildJM, Trope GE. Evaluation of FAST- PAC, a new strategy for threshold estimation with the Humphrey Field Analyzer, in a glaucomatous population. Ophthalmology. 1993; 100: Iwase A, Kitazawa Y, Kato Y. Clinical value of Fastpac: A comparative study with the standard full threshold method. In: Mills RP, ed. Perimetry Update 1992/93. Proceedings of the Xth International Perimetric Society Meeting; Kyoto, Japan; October 20-23, Amsterdam: Kugler Publications; 1993: Moss ID, Hudson C, Dengler-Harles M, WildJM, Whitaker DJ, O'Neill EC. A 3 db step single crossing algorithm for threshold automated perimetry. ARVO Abstracts. Invest Ophthalmol Vis Sci. 1992; 33: Schafer B, Lachenmayr BJ, Schaumberger M, Oepke D, Gleissner M. Comparison of Fastpac/4-2 db standard strategy of the Humphrey Field Analyzer in normal and glaucomatous eyes. ARVO Abstracts. Invest Ophthalmol Vis Sci. 1993; 34: Harvey LO Jr. Efficient estimation of sensory thresholds. Behav Res Meth Instrum Comput. 1986; 18: Weibull W. A statistical distribution function of wide applicability. Jour Appl Mech. 1951; 18: Weber J, Rau S. The properties of perimetric thresholds in normal and glaucomatous eyes. GerJ Ophthalmol. 1992; 1: Chauhan BC, Tompkins JD, LeBlanc RP, McCormick TA. Characteristics of frequency-of-seeing curves in glaucoma. In: Mills RP, ed. Perimetry Update 1992/93. Proceedings of the Xth International Perimetric Society Meeting; Kyoto, Japan; October 20-23, Amsterdam: Kugler Publications; 1993: Elbel OK, Schaumberger MM, Lachenmayr BJ. Psychometric functions in light sense perimetry: Influence of eccentricity and mathematical modelling in normal subjects. DOG Abstracts. Ger J Ophthalmol. 1994; 3: Lachenmayr BJ, Angstwurm K, Bachmayer B, Kojetinsky S, Schaumberger M. The normal visual field in light-sense, flicker and resolution perimetry. In: Mills RP, ed. Perimetry Update 1992/93. Proceedings of the Xth International Perimetric Society Meeting; Kyoto, Japan; October 20-23,1992. Amsterdam: Kugler Publications; 1993: Johnson CA, Nelson-Quigg JM. A prospective threeyear study of response properties of normal subjects and patients during automated perimetry. Ophthalmology. 1993; 100: Conover WJ. Practical Nonparametric Statistics. 2nd ed. New York: John Wiley & Sons; 1980.

8 1854 Investigative Ophthalmology & Visual Science, August 1995, Vol. 36, No Johnson CA, Chauhan BC, Shapiro LR. Properties of staircase procedures for estimating thresholds in automated perimetry. Invest Ophthalmol Vis Sri. 1992; 33: Heijl A. Computer test logics in automatic perimetry. Ada Ophthalmol. 1977; 55: Flammer J, Drance SM, Zulauf M. Differential light threshold. Short- and long-term fluctuation in patients with glaucoma, normal controls, and patients with suspected glaucoma. Arch Ophthalmol. 1984; 102: Flammer J, Drance SM, Fankhauser F, Augustiny L. Differential light threshold in automated static perimetry: Factors influencing short-term fluctuation. Arch Ophthalmol. 1984; 102: SturmerJ, Gloor B, Tobler HJ. Wie sehen Glaukomgesichtsfelder wirklich aus? Klin Mbl Augenheilk. 1984; 184: In German. 25. Werner EB, Drance SM. Early visual field disturbance in glaucoma. Arch Ophthalmol. 1977; 95: Heijl A. A simple routine for demonstrating increased threshold scatter by comparing stored computer fields. In: Heijl A, Greve EL, eds. Proceedings of the 6th Int Visual Field Symposium, May Dordrecht: Dr W.Junk; 1985:35-38.