A C T A 0 P HT HA L M 0 L 0 G I C A
70 (1992)679-686
Spatial analyses of glaucomatous visual fields; a comparison with traditional visual field indices Peter Asman', Anders Heijl', Jonny OIsson2 and Holger Rootzen2 Departments of Ophthalmology' in Malmo and Mathematical Statisticszin Lund, University of Lund, Sweden
Abstract. Interpretation of numeric automated threshold visual field results is often difficult. A large amount of data is obtained for every single field tested. Various approaches to summarize this data have been suggested, most commonly the mean and standard deviation of departures from age-corrected normal threshold values. These visual field indices differ substantially from subjective field interpretation where spatial relationships are important. We have previously devised two methods for automated field interpretation which take spatial information into account - regional up-down comparisons and arcuate cluster analysis. We now studied the merits of using these new spatial methods and compared them to traditional visual field indices for discrimination between normal and glaucomatous field results. Central static 30" field results in 101 eyes of 101 normal subjects and 101 eyes of 101 patients with glaucoma were discriminated using logistic regression analysis. The best field classification was obtained with a spatial visual field model combining up-down differences and arcuate clusters. The advantages of the spatial model were confirmed in an independent material of 163 eyes of 163 normal subjects and 76 eyes of 76 patients with glaucoma where eyes with large field defects had been removed. In this material the spatial model gave 87%sensitivity and 83% specificity while the best non-spatialmodel gave 82%sensitivity and 80%specificity. Visual field interpretation in glaucoma may be significantly enhanced if detection is focused on circumscribed field loss rather than on averages of differential light sensitivities and similar indices which do not take spatial relationships into consideration.
Key words: perimetry - computer-assistedfield interpretation - visual field indices - hemifield analysis - arcuate cluster analysis - glaucoma - classification - spatial indices.
Automated threshold perimetry is an important diagnostic tool in glaucoma. However, the large and complex physiologic variability of field results often makes intuitive judgement difficult. The results of studies of normal populations (Flammer et al. 1984; Heijl et al. 1987a) have enabled the construction of age-corrected normal reference fields. Visual field indices representing the sum of pointwise differential light sensitivityvalues (Holmin & Krakau 1980), and subsequently the mean and standard deviation of departures from age-corrected normal threshold values have been used for a number of years (Bebie 1985; Flammer et al. 1985; Heijl et al. 198713).Each of these traditional, or standard, indices reduce visual field data from several locations into a single number that allows a crude classification of the measured visual field. A drawback of these indices, however, is the loss of spatial information which makes them unable to discriminate, e.g., between a few scattered abnormal points and a few abnormal points arranged in a typical glaucomatous defect (Chauhan et al. 1989). We believed that data reduction that takes geo679
graphical factors into account would improve the quality of automated field interpretation. Probability maps, that graphically display test point sensitivities in terms of their significance, provide such data reduction on a point by point basis without loss of geographical information (Heijl et al. 1987b), and have facilitated the interpretation of automated visual field results (Asman & Heijl 1988; Anderson 1992). Further reduction of the data in these probability maps is often desirable and has been applied in e.g. the Glaucoma Hemifield Test of the Statpac 2 program (Humphrey Instruments Inc, San Leandro, Calif) (Heijl et al. 1991),and in cluster analysis (Asman & Heijl 1991). Both the Glaucoma Hemifield Test and cluster analysis differ from standard visual field indices in that they take spatial relationships into account. The aim of this paper was to study the ability of a spatial approach to discriminate between normal and glaucomatous visual fields and compare it with an approach based on traditional non-spatial visual field indices.
Materialand Methods Field test results in a normal group and a group of patients with glaucoma (model population) were analyzed using logistic regression to obtain models that predict glaucoma based on standard visual field indices, up-down differences, and arcuate clusters. The resulting models were afterwards applied on visual field results of a separate group of normal subjects and patients with glaucoma (control population) to independently evaluate the different models. Model population
Static differential light sensitivity in the central 30" field had been measured with the 30-2 full threshold program of the Humphrey perimeter (Humphrey Inc, San Leandro, Calif) in each study eye. The normal subjects were part of the normal data base used in the construction of a package for statistical visual field analysis, Statpac (Humphrey Inc, San Leandro, Calif) (Heijl et al. 1987b).In the present study we used 101 eyes of 101 subjects. Eightyeight of the subjects were selected from a random sample of the population of Malmo, Sweden (Heijl et al. 1987a). The remaining 13 subjects were recruited and tested in Oakland, Calif. Subjects who 680
had pathologic findings which could affect the visual field were removed, but no subject was disqualified because of apparent visual field abnormalities if careful history and examination were unable to explain such findings. Field tests were available from two or three test sessions in each eye. To avoid learning effects, tests obtained at the first test session were not used (Wood et al. 1987; Heijl et al. 1989). One of the remaining tests in each subject was randomly selected for this study. Mean age in this normal group was 50 years (range 20-79). The glaucoma group consisted of 101 eyes of 101 patients selected on the basis of optic disc findings without knowledge of their perimetric results. Optic discs in 656 eyes of 388 patients followed at the Department of Ophthalmology in Malmo, Sweden for suspect or manifest glaucoma were classified subjectively and independently by two of the authors, A.H. and P.A. Eyes with pathological findings other than glaucoma or cataract were removed from the study if effects on the visual field could be suspected. Classification of the discs was normal, uncertain, or glaucoma. One hundred seventy-five eyes were reclassified jointly because of initial disagreement in the classification.Among patients with perimetric experience the examiners agreed on a diagnosis of glaucoma in 169 eyes of 130 patients. All eyes had a visual acuity of 20/40 or better. The visual fields of these eyes were then retrieved. Fields with defects exceeding group I1 in the classification of Aulhorn and Harms (Aulhorn & Harms 1966) were removed since they would be obviously abnormal with any of the methods employed in this study. Of the remaining tests, one was randomly selected from each subject, leaving the mentioned 101 eyes. Mean age in the glaucoma group was 68 years (range 23-85). Fields had been obtained within one year of the disc photograph. Control population
One. field test in each of 163 eyes of 163 normal subjects and 76 eyes of 76 patients with glaucoma were used to study the sensitivity and specificity of the various models. None of these subjects were part of the model population. The normal group has previously been described in detail (Asman & Heijl 1992a) and was mainly healthy volunteers tested at three different centres (Malmo, Sweden (41 subjects),Irvine, Calif (61 subjects),and Detroit, Mich (61 subjects)).As in
the model population, all subjects had normal results on ophthalmologicalexamination, visual acuity of 20140 or better, and previous experience with automated perimetry. Mean age was 53 years (range 22-88). The glaucoma control group was selected in the same way as the glaucoma model group. Optic discs of 537 eyes of 310 patients were used for this purpose. Both authors agreed on a diagnosis of glaucoma in 132 eyes of 98 subjects. After exclusion of large field defects (cf. above) 94 eyes of 76 eyes remained. One eye was then randomly selected in each patient. In this glaucoma group mean age was 68 years (range 36-87).
Arcuate cluster
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,
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We wanted to analyze the relative importance of several possible visual field indices and parameters for correct classification of visual fields as normal or glaucomatous. We decided to use logistic regression for this purpose. Three standard visual field indices were calculated in each field: Mean Deviation,MD (Heijlet al. 1987b),which is the location-weighted average departure from age-corrected normal threshold values, Pattern Standard Deviation, PSD (Heijl et al. 1987b),which is the location-weighted standard deviation of these departures, and General Height, GH, which is an estimate of the general level of the measured visual field. GH is based on a subset of the best points in the field (Olsson 1991) and is therefore not influenced by localized field loss. These indices will be referred to as non-spatial since they are not devised to take the spatial relationship between the test locations into account. Two types of spatial analyses were also performed in each field. The first was the calculation of up-down differences of probability scores (Heijl et al. 1991) in each of the 5 mirror image sectors used in the Glaucoma Hemifield Test. The probability scores were based on the significance reached in the pattern deviation map of the Statpac program, p < 0.05 giving a score of 2, p < 0.02 a score of 5, and p < 0.01 a score of 10. Below the p = 0.01 limit the score was multiplied with the pattern deviation divided by the p = 0.01 limit. Each of the five up-down differences was divided by the number of points in the corresponding sector (3, 4, 5, 6, and 4 points for the 5 sector pairs, respectively). The maximum of these up-down differenceswas
Fig. 1. Arcuate cluster of significantly depressed points in pattern deviation probability map. Clustered points are interconnected by lines corresponding to anatomy of normal retinal nerve fibre layer (dashed lines).
used as a measure of up-down difference in a field and will be referred to as A:., The second spatial analysis was an arcuate cluster analysis (Asman & Heijl 1992b).This analysis identifies clusters of significant points in the pattern deviation probability map which are oriented along the directions of the normal retinal nerve fiber layer (Fig. 1).The volume of each identified cluster was defined as the sum of probability scores of its points. Arcuate cluster volumes were weighted according to location as described elsewhere (Asman & Heijl 1992b). The largest weighted arcuate cluster volume, referred to as V:&, was used as a measure of clustering. Building models
In analyzing the data using logistic regression, we followed the guidelines for model building and assessment suggested by Hosmer and Lemeshow (Hosmer & Lemeshow 1989).In a first step we analyzed each variable (index) individually. For each variable various mathematical transformations were tested. The transformation giving the best fit to the logistic regression model was used. A large number of models that included two or more variables were then tested. Variables were 681
Table 1.
Variable
Univariate results in model population.
I
Loglikelihood function
Range-
In (1+V;;J A 1/PSD MD GH
0-3.22 0-6.46 0.07-0.73 -24.7-3.16 - 17.1-6.05
:;:
5.02 0.79 -15.1 -0.70 -0.71
entered manually. Improvement of a model as a result of the addition of a variable was tested for significance using the likelihood ratio test (Hosmer& Lemeshow 1989). Testing models also included evaluation of possible interactions between variables in the model. In each field a predicted probability of glaucoma 5( x ) ( x is the value or values of one or several variables in a model) was determined. This value ranged from 0 (normal) to 1 (glaucoma) and was dependent on the model under consideration. A field could thus have a high 5( x ) if analysis was based on a model containing a certain set of variables and a low 72 ( x ) ifa different set of variables were used. A formal description of the 72 (x)-estimatesand their calculation is found elsewhere (Hosmer & Lemeshow 1989).The likelihood function for a given model is the product of 5(x)-valuesin the glaucoma group and the (1-5 (x))-valuesin the normal group. The higher the value of the likelihood function, the better is the ability of the model to predict normal and glaucomatous results in the sample. Here we will use the conventional loglikelihood function, i.e. Zn (likelihood function). The sensitivity and specificity of the models
Table2. Univariate results in control population. Variable
In ( l + V $ 3
A:g 1/PSD MD GH
682
Sensitivity
Specificity
83 84 84 80 78
86 86 75 79 67
-45.9 -48.6 -61.7 -70.1 -92.2
I
Sensitivity (%)
I
Specificity
86 85 87 79 72
(%)
93 95 83 91 87
were determined using 5 ( x ) = 0.5 as a cut-off limit above which field results were classified as glaucomatous and below which they were considered normal. An increase in the average value of sensitivity and specificity in the control group with one model as compared with another model was tested for significance using a multinomial model (Asman & Heijl 1992a).
Results We used l/PSD and In ( l + V i 2 since these transformations gave the best fit to the models. The remaining variables, MD, GH, and A:& did not require transformation. Loglikelihood function, range, coefficients (f), sensitivity, and specificity in the model population for the individual variables are given in Table 1. Sensitivity and specificity achieved in the control population are given in Table 2. Best results were obtained with up-down differences followed by arcuate clusters. The non-spatial indices 1/PSD, MD, and GH achieved considerably lower values of the loglikelihood function. Values of the loglikelihood function for various models in the model population are given in Table 3 along with sensitivity and specificity. A model combining up-down differences and arcuate clusters was significantly better than each of its two components separately (p < 0.05 for adding A 2 and p < 0.001 for adding Vk2. This spatial model could not be significantly improved by including any of the remaining variables. When only standard field indices were used, two models were found to offer about equally good discrimination in the model group. These models were based on MD in association with either one of
Table3. Model results in model population. Variables in model
In (l+VAa,:A: 1/PSD; MD GH, MD
3.47 -10.6 1.72
0.30 -0.25 -1.91
l/PSD (non-spatial model I) or GH (non-spatial model II). Including the third and last standard visual field index did not significantlyimprove either of these two models. The model containing MD and 1/PSD was more sensitive to circumscribed field loss in glaucoma but also to trial lens artifacts than was the model including MD and GH. The coefficientsof the latter model showed that the dqf m c e between MD and GH was important. Thus, for a fixed level of MD an increase in the diffuse loss component as detected by a decrease in GH diminished the likelihood of glaucoma. No interaction between any of the variables was found. Differences in initial disc classification by the two authors (before the joint classification) were not found to be related to differences between the spatial and non-spatial models. Sensitivity and specifcity for the spatial and the non-spatial models in the control population are given in Table 4. Classification of fields in the control group using the spatial as compared to the two non-spatial models are given in Table 5. The average value of sensitivityand specificity of the spatial model was significantly better than that of both non-spatial models (p < 0.05). Four glaucoma fields were detected with the spatial model but missed with the non-spatial model I. These fields generally had shallow central or paracentral field loss (Fig. 2). Twelve fields from normal subjects
-42.9 -58.6 -58.0
88 88 85
93 86 92
were classified as glaucomatous by the first nonspatial model (MD, l/PSD) but labelled normal by the spatial model. Such fields generally showed disturbances in the mid-periphery (Fig. 3). Comparing the spatial model with the second non-spatial model gave similar results.
Discussion Several visual field indices have been suggested and used. These have been of two principally different kinds: indices that do not utilize the spatial information in the field chart and those that do. The present results indicate that spatial information in probability maps can result in significantly better recognition of glaucoma fields than can commonly used standard visual field indices. Cluster analysis and sectonvise up-down comparisons
Table5. Classificationin control group.
model
model I
Spatial model
Non-spatial model I1
Table4. Model results in control population. Variables in model
In (l+Vt2, A"& 1/PSD, MD GH, MD
Sensitivity
Specificity
87 83 82
83 79 80
683
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Fig. 2. Visual field in patient with glaucoma. Spatial model based on up-down differences and arcuate clusters detect field abnormality(arrow)[A = 0.941, passed undetected [A= 0.431 by non-spatialmodel in which MD and UPSD are employed.
reduce the risk that subtle defects are diluted by physiologic irregularities in other parts of the field. Experienced clinicians evaluate field charts according to similar principles. The present results also show that up-down comparisons and arcuate cluster analysis can be important and also have the potential of being used as complementing 'building blocks' in the construction of complex field analysis aids. Arcuate cluster analysis was more sensitive to shallow arcuate defects straddling the borders used for updown comparisons, while analysis of up-down differences was more sensitive to defects of less typical shape. The arcuate cluster analysis employed here differed from traditionally used cluster analyses in that knowledge of the normal retinal nerve fiber layer anatomy was incorporated. Taking arcuate 684
shape into account (Weber & Ulrich 1991) can significantly improve cluster analysis in glaucoma (Asman & Heijl 1991)and we therefore decided to use such enhanced cluster analysis in the present study. The non-spatial model employing MD and GH had clear similarities to the Mean Local Defect (MLD) index devised by Langerhorst (1988). In both, the total defect is adjusted for overall shifts in sensitivity, thereby isolating the localized component of the field loss. We avoided inclusionlexclusion criteria based on perimetric results when establishing our model population. The major part of the normal group (the Malmo subjects) was that part of a random sample of the population which remained after exclusion of subjects with pathologic findings detected by means other than perimetry. The same
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Fig. 3. Visual field in normal subject. Spatial model based on up-down differences and arcuate clusters confirms normality [J; = 0.071 while the non-spatial model in which MD and l/PSD are employed gave abnormal results [Jz = 0.651.
principles of exclusion were applied also for the Oakland group of healthy volunteers. The glaucoma group was also established without any knowledge of visual field results. It is likely that this approach in selecting materials can result in more robust visual field models than more conventional 'clinical' approaches where individual ideas of normal and glaucomatous fields will play an important role. Katz and coworkers (1991) found no significant differences between spatial analyses and standard visual field indices, but their material had been selected with perimetric inclusion criteria requiring normal field results in the normal group and a defect revealed with manual perimetry in the glaucoma group. In this way, a much larger proportion of obviously normal or pathological field results were obtained, which might have impaired the
ability to detect clinically important differences between the methods (Taube & Tholander 1990). The JZ(x)-valuesshould not be regarded as probabilities of glaucoma when applied outside the model population. Instead, the probability of glaucoma given a certain JZ(x)-valueis highly dependent on the population (Hosmer & Lemeshow 1989). Thus, a 4x)-value of 0.5 is more indicative of glaucoma in a population at high risk of having glaucoma, e.g. in a population with elevated intraocular pressure, than in the population at large. A model is expected to perform better in the material on which it was constructed than in other materials. The lower values of sensitivity and specificity in the control population than in the model population were therefore expected. The values would have been higher, however, if fields with large field defects had not been removed. The ad685
vantages of the spatial model clearly remained in the control population, however. This indicates that automated visual field interpretation based on traditional non-spatial visual field indices can be improved by spatial analyses in the form of updown comparisons and arcuate cluster analysis in probability maps. Thus, spatial analyses, like the ones described here can be valuable tools in the construction of aids for computer-assisted interpretation of visual fields in glaucoma.
Acknowledgments Supported in part by grants from the Herman Jarnhardt Foundation, Inez and Joel Carlsson’s Foundation, and Ingeborg and Ernst Ydman’s Foundation, Malmo, Sweden, and by grants No. 150 and No. 158 from the Medical Faculty of the University of Lund, Sweden and by grant from The Bank of Sweden Tercentenary Foundation. We thank P. Juhani Airaksinen, MD, and Anja Tuulonen, MD, Oulu, Finland, for providing data for the normal retinal nerve fibre layer anatomy. Parts of the normal material were supplied by Marcus D. Benedetto, Ph.D., Sinai Hospital of Detroit, Mich; by Ben R. Hasty, MD, Oak Knoll Naval Hospital, Oakland, Calif; and by Michael Patella, O.D., Allergan Humphrey, San Leandro, Calif, which is gratefully acknowledged.
References Anderson D R (1992): Automated Static Perimetry, chapter 7, pp 91-161. St. Louis, Mosby Year Book, Inc. Aulhorn E & Harms M (1966):Early visual field defects in glaucoma. In: Leydhecker W (ed). Glaucoma, Tutzing Symposium, pp 151-186. Basel, Karger. Bebie H (1985): Computerized techniques of visual field analysis. In:Drance S M & Anderson D R (eds). Automatic perimetry in glaucoma: a practical guide, pp 147-160. New York, Grune & Stratton. Chauhan B C, Drance S M & Lai C (1989):A cluster analysis for threshold perimetry. Graefes Arch Clin Exp Ophthalmol227: 216-220. Flammer J, Drance S M, Fankhauser F & Augustiny L (1984):Differential light threshold in automated static perimetry: factors influencing short-term fluctuation. Arch Ophthalmol 102: 876-879. Flammer J, Drance S M, Augustiny L & Funkhouser A (1985):Quantification of glaucomatous visual field defects with automated perimetry. Invest Ophthalmol Vis Sci 26: 176-181. Heijl A, Lindgren G & Olsson J (1987a): Normal variability of static perimetric threshold values across the central visual field. Arch Ophthalmol 105: 1544-1549.
686
Heijl A, Lindgren G & OlssonJ (1987b):A package for the statistical analysis of visual fields. Doc Ophthalmol 49: 153-168. Heijl A, Lindgren G & Olsson J (1989):The effect of perimetric experience in normal subjects. Arch Ophthalmol 107: 81-86. Heijl A, Lindgren G, Lindgren A, Olsson J, Asman P, Myers S & Patella M (1991):Extended empirical statistical package for evaluation of single and multiple fields in glaucoma.In: Mills R P & Heijl A (eds).Perimetry Update 1990/91, pp 303-315. Amsterdam, Kugler & Ghedini. Holmin C & Krakau C E T (1980): Visual field decay in normal subjects and in cases of chronic glaucoma. Graefes Arch Clin Exp Ophthalmol213: 291-298. Hosmer D W & Lemeshow S (1989): Applied Logistic Regression. New York, John Wiley & Sons. Katz J, Sommer A, Gaasterland D E & Anderson D R (1991): Comparison of analytic algorithms for detecting glaucomatous visual field loss. Arch Ophthalmol 109: 1684-1689. Langerhorst C T (1988): Automated perimetry in glaucoma: Fluctuation behavior and general and local reduction of sensitivity, chapter 4, pp 23-39. Amsterdam, Kugler & Ghedini. OlssonJ (1991): Statistics in perimetry. PhD thesis, Lund University, Department of Mathematical Statistics. pp 22-24. Taube A & Tholander B (1990):Over- and underestimation of the sensitivity of diagnostic malignancy test due to various selections of the study populations. Acta Oncol29: 971-975. Weber J & Ulrich H (1991): A penmetric nerve fiber bundle map. Int Ophthalmol 15: 193-200. Wood J M, Wild J M, Hussey M K & Crews S J (1987):Serial examination of the normal visual field using Octopus automated projection perimetry: Evidence for a learning effect. Acta Ophthalmol (Copenh) 65: 326333. Asman P & Heijl A (1988): A clinical study of penmetric probability maps. Arch Ophthalmol 107: 199-203. Asman P & Heijl A (1991): Cluster analysis in glaucoma. Invest Ophthalmol Vis Sci 32 (Suppl 4): 1191. Asman P & Heijl A (1992a): Evaluation of methods for automated hemifield analysis in perimetry. Arch Ophthalmol 110: 820-826. Asman P & Heijl A (1992b):Weighting according to location in computer-assisted glaucoma visual field analysis. Acta Ophthalmol (Copenh) 70: 671-678. Received on June 15th, 1992. Author’s address: Dr. Peter Asman, Department of Ophthalmology, Malmci General Hospital, S-214 01 Malmo, Sweden.
70 (1992)679-686
Spatial analyses of glaucomatous visual fields; a comparison with traditional visual field indices Peter Asman', Anders Heijl', Jonny OIsson2 and Holger Rootzen2 Departments of Ophthalmology' in Malmo and Mathematical Statisticszin Lund, University of Lund, Sweden
Abstract. Interpretation of numeric automated threshold visual field results is often difficult. A large amount of data is obtained for every single field tested. Various approaches to summarize this data have been suggested, most commonly the mean and standard deviation of departures from age-corrected normal threshold values. These visual field indices differ substantially from subjective field interpretation where spatial relationships are important. We have previously devised two methods for automated field interpretation which take spatial information into account - regional up-down comparisons and arcuate cluster analysis. We now studied the merits of using these new spatial methods and compared them to traditional visual field indices for discrimination between normal and glaucomatous field results. Central static 30" field results in 101 eyes of 101 normal subjects and 101 eyes of 101 patients with glaucoma were discriminated using logistic regression analysis. The best field classification was obtained with a spatial visual field model combining up-down differences and arcuate clusters. The advantages of the spatial model were confirmed in an independent material of 163 eyes of 163 normal subjects and 76 eyes of 76 patients with glaucoma where eyes with large field defects had been removed. In this material the spatial model gave 87%sensitivity and 83% specificity while the best non-spatialmodel gave 82%sensitivity and 80%specificity. Visual field interpretation in glaucoma may be significantly enhanced if detection is focused on circumscribed field loss rather than on averages of differential light sensitivities and similar indices which do not take spatial relationships into consideration.
Key words: perimetry - computer-assistedfield interpretation - visual field indices - hemifield analysis - arcuate cluster analysis - glaucoma - classification - spatial indices.
Automated threshold perimetry is an important diagnostic tool in glaucoma. However, the large and complex physiologic variability of field results often makes intuitive judgement difficult. The results of studies of normal populations (Flammer et al. 1984; Heijl et al. 1987a) have enabled the construction of age-corrected normal reference fields. Visual field indices representing the sum of pointwise differential light sensitivityvalues (Holmin & Krakau 1980), and subsequently the mean and standard deviation of departures from age-corrected normal threshold values have been used for a number of years (Bebie 1985; Flammer et al. 1985; Heijl et al. 198713).Each of these traditional, or standard, indices reduce visual field data from several locations into a single number that allows a crude classification of the measured visual field. A drawback of these indices, however, is the loss of spatial information which makes them unable to discriminate, e.g., between a few scattered abnormal points and a few abnormal points arranged in a typical glaucomatous defect (Chauhan et al. 1989). We believed that data reduction that takes geo679
graphical factors into account would improve the quality of automated field interpretation. Probability maps, that graphically display test point sensitivities in terms of their significance, provide such data reduction on a point by point basis without loss of geographical information (Heijl et al. 1987b), and have facilitated the interpretation of automated visual field results (Asman & Heijl 1988; Anderson 1992). Further reduction of the data in these probability maps is often desirable and has been applied in e.g. the Glaucoma Hemifield Test of the Statpac 2 program (Humphrey Instruments Inc, San Leandro, Calif) (Heijl et al. 1991),and in cluster analysis (Asman & Heijl 1991). Both the Glaucoma Hemifield Test and cluster analysis differ from standard visual field indices in that they take spatial relationships into account. The aim of this paper was to study the ability of a spatial approach to discriminate between normal and glaucomatous visual fields and compare it with an approach based on traditional non-spatial visual field indices.
Materialand Methods Field test results in a normal group and a group of patients with glaucoma (model population) were analyzed using logistic regression to obtain models that predict glaucoma based on standard visual field indices, up-down differences, and arcuate clusters. The resulting models were afterwards applied on visual field results of a separate group of normal subjects and patients with glaucoma (control population) to independently evaluate the different models. Model population
Static differential light sensitivity in the central 30" field had been measured with the 30-2 full threshold program of the Humphrey perimeter (Humphrey Inc, San Leandro, Calif) in each study eye. The normal subjects were part of the normal data base used in the construction of a package for statistical visual field analysis, Statpac (Humphrey Inc, San Leandro, Calif) (Heijl et al. 1987b).In the present study we used 101 eyes of 101 subjects. Eightyeight of the subjects were selected from a random sample of the population of Malmo, Sweden (Heijl et al. 1987a). The remaining 13 subjects were recruited and tested in Oakland, Calif. Subjects who 680
had pathologic findings which could affect the visual field were removed, but no subject was disqualified because of apparent visual field abnormalities if careful history and examination were unable to explain such findings. Field tests were available from two or three test sessions in each eye. To avoid learning effects, tests obtained at the first test session were not used (Wood et al. 1987; Heijl et al. 1989). One of the remaining tests in each subject was randomly selected for this study. Mean age in this normal group was 50 years (range 20-79). The glaucoma group consisted of 101 eyes of 101 patients selected on the basis of optic disc findings without knowledge of their perimetric results. Optic discs in 656 eyes of 388 patients followed at the Department of Ophthalmology in Malmo, Sweden for suspect or manifest glaucoma were classified subjectively and independently by two of the authors, A.H. and P.A. Eyes with pathological findings other than glaucoma or cataract were removed from the study if effects on the visual field could be suspected. Classification of the discs was normal, uncertain, or glaucoma. One hundred seventy-five eyes were reclassified jointly because of initial disagreement in the classification.Among patients with perimetric experience the examiners agreed on a diagnosis of glaucoma in 169 eyes of 130 patients. All eyes had a visual acuity of 20/40 or better. The visual fields of these eyes were then retrieved. Fields with defects exceeding group I1 in the classification of Aulhorn and Harms (Aulhorn & Harms 1966) were removed since they would be obviously abnormal with any of the methods employed in this study. Of the remaining tests, one was randomly selected from each subject, leaving the mentioned 101 eyes. Mean age in the glaucoma group was 68 years (range 23-85). Fields had been obtained within one year of the disc photograph. Control population
One. field test in each of 163 eyes of 163 normal subjects and 76 eyes of 76 patients with glaucoma were used to study the sensitivity and specificity of the various models. None of these subjects were part of the model population. The normal group has previously been described in detail (Asman & Heijl 1992a) and was mainly healthy volunteers tested at three different centres (Malmo, Sweden (41 subjects),Irvine, Calif (61 subjects),and Detroit, Mich (61 subjects)).As in
the model population, all subjects had normal results on ophthalmologicalexamination, visual acuity of 20140 or better, and previous experience with automated perimetry. Mean age was 53 years (range 22-88). The glaucoma control group was selected in the same way as the glaucoma model group. Optic discs of 537 eyes of 310 patients were used for this purpose. Both authors agreed on a diagnosis of glaucoma in 132 eyes of 98 subjects. After exclusion of large field defects (cf. above) 94 eyes of 76 eyes remained. One eye was then randomly selected in each patient. In this glaucoma group mean age was 68 years (range 36-87).
Arcuate cluster
\
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Visual field data
We wanted to analyze the relative importance of several possible visual field indices and parameters for correct classification of visual fields as normal or glaucomatous. We decided to use logistic regression for this purpose. Three standard visual field indices were calculated in each field: Mean Deviation,MD (Heijlet al. 1987b),which is the location-weighted average departure from age-corrected normal threshold values, Pattern Standard Deviation, PSD (Heijl et al. 1987b),which is the location-weighted standard deviation of these departures, and General Height, GH, which is an estimate of the general level of the measured visual field. GH is based on a subset of the best points in the field (Olsson 1991) and is therefore not influenced by localized field loss. These indices will be referred to as non-spatial since they are not devised to take the spatial relationship between the test locations into account. Two types of spatial analyses were also performed in each field. The first was the calculation of up-down differences of probability scores (Heijl et al. 1991) in each of the 5 mirror image sectors used in the Glaucoma Hemifield Test. The probability scores were based on the significance reached in the pattern deviation map of the Statpac program, p < 0.05 giving a score of 2, p < 0.02 a score of 5, and p < 0.01 a score of 10. Below the p = 0.01 limit the score was multiplied with the pattern deviation divided by the p = 0.01 limit. Each of the five up-down differences was divided by the number of points in the corresponding sector (3, 4, 5, 6, and 4 points for the 5 sector pairs, respectively). The maximum of these up-down differenceswas
Fig. 1. Arcuate cluster of significantly depressed points in pattern deviation probability map. Clustered points are interconnected by lines corresponding to anatomy of normal retinal nerve fibre layer (dashed lines).
used as a measure of up-down difference in a field and will be referred to as A:., The second spatial analysis was an arcuate cluster analysis (Asman & Heijl 1992b).This analysis identifies clusters of significant points in the pattern deviation probability map which are oriented along the directions of the normal retinal nerve fiber layer (Fig. 1).The volume of each identified cluster was defined as the sum of probability scores of its points. Arcuate cluster volumes were weighted according to location as described elsewhere (Asman & Heijl 1992b). The largest weighted arcuate cluster volume, referred to as V:&, was used as a measure of clustering. Building models
In analyzing the data using logistic regression, we followed the guidelines for model building and assessment suggested by Hosmer and Lemeshow (Hosmer & Lemeshow 1989).In a first step we analyzed each variable (index) individually. For each variable various mathematical transformations were tested. The transformation giving the best fit to the logistic regression model was used. A large number of models that included two or more variables were then tested. Variables were 681
Table 1.
Variable
Univariate results in model population.
I
Loglikelihood function
Range-
In (1+V;;J A 1/PSD MD GH
0-3.22 0-6.46 0.07-0.73 -24.7-3.16 - 17.1-6.05
:;:
5.02 0.79 -15.1 -0.70 -0.71
entered manually. Improvement of a model as a result of the addition of a variable was tested for significance using the likelihood ratio test (Hosmer& Lemeshow 1989). Testing models also included evaluation of possible interactions between variables in the model. In each field a predicted probability of glaucoma 5( x ) ( x is the value or values of one or several variables in a model) was determined. This value ranged from 0 (normal) to 1 (glaucoma) and was dependent on the model under consideration. A field could thus have a high 5( x ) if analysis was based on a model containing a certain set of variables and a low 72 ( x ) ifa different set of variables were used. A formal description of the 72 (x)-estimatesand their calculation is found elsewhere (Hosmer & Lemeshow 1989).The likelihood function for a given model is the product of 5(x)-valuesin the glaucoma group and the (1-5 (x))-valuesin the normal group. The higher the value of the likelihood function, the better is the ability of the model to predict normal and glaucomatous results in the sample. Here we will use the conventional loglikelihood function, i.e. Zn (likelihood function). The sensitivity and specificity of the models
Table2. Univariate results in control population. Variable
In ( l + V $ 3
A:g 1/PSD MD GH
682
Sensitivity
Specificity
83 84 84 80 78
86 86 75 79 67
-45.9 -48.6 -61.7 -70.1 -92.2
I
Sensitivity (%)
I
Specificity
86 85 87 79 72
(%)
93 95 83 91 87
were determined using 5 ( x ) = 0.5 as a cut-off limit above which field results were classified as glaucomatous and below which they were considered normal. An increase in the average value of sensitivity and specificity in the control group with one model as compared with another model was tested for significance using a multinomial model (Asman & Heijl 1992a).
Results We used l/PSD and In ( l + V i 2 since these transformations gave the best fit to the models. The remaining variables, MD, GH, and A:& did not require transformation. Loglikelihood function, range, coefficients (f), sensitivity, and specificity in the model population for the individual variables are given in Table 1. Sensitivity and specificity achieved in the control population are given in Table 2. Best results were obtained with up-down differences followed by arcuate clusters. The non-spatial indices 1/PSD, MD, and GH achieved considerably lower values of the loglikelihood function. Values of the loglikelihood function for various models in the model population are given in Table 3 along with sensitivity and specificity. A model combining up-down differences and arcuate clusters was significantly better than each of its two components separately (p < 0.05 for adding A 2 and p < 0.001 for adding Vk2. This spatial model could not be significantly improved by including any of the remaining variables. When only standard field indices were used, two models were found to offer about equally good discrimination in the model group. These models were based on MD in association with either one of
Table3. Model results in model population. Variables in model
In (l+VAa,:A: 1/PSD; MD GH, MD
3.47 -10.6 1.72
0.30 -0.25 -1.91
l/PSD (non-spatial model I) or GH (non-spatial model II). Including the third and last standard visual field index did not significantlyimprove either of these two models. The model containing MD and 1/PSD was more sensitive to circumscribed field loss in glaucoma but also to trial lens artifacts than was the model including MD and GH. The coefficientsof the latter model showed that the dqf m c e between MD and GH was important. Thus, for a fixed level of MD an increase in the diffuse loss component as detected by a decrease in GH diminished the likelihood of glaucoma. No interaction between any of the variables was found. Differences in initial disc classification by the two authors (before the joint classification) were not found to be related to differences between the spatial and non-spatial models. Sensitivity and specifcity for the spatial and the non-spatial models in the control population are given in Table 4. Classification of fields in the control group using the spatial as compared to the two non-spatial models are given in Table 5. The average value of sensitivityand specificity of the spatial model was significantly better than that of both non-spatial models (p < 0.05). Four glaucoma fields were detected with the spatial model but missed with the non-spatial model I. These fields generally had shallow central or paracentral field loss (Fig. 2). Twelve fields from normal subjects
-42.9 -58.6 -58.0
88 88 85
93 86 92
were classified as glaucomatous by the first nonspatial model (MD, l/PSD) but labelled normal by the spatial model. Such fields generally showed disturbances in the mid-periphery (Fig. 3). Comparing the spatial model with the second non-spatial model gave similar results.
Discussion Several visual field indices have been suggested and used. These have been of two principally different kinds: indices that do not utilize the spatial information in the field chart and those that do. The present results indicate that spatial information in probability maps can result in significantly better recognition of glaucoma fields than can commonly used standard visual field indices. Cluster analysis and sectonvise up-down comparisons
Table5. Classificationin control group.
model
model I
Spatial model
Non-spatial model I1
Table4. Model results in control population. Variables in model
In (l+Vt2, A"& 1/PSD, MD GH, MD
Sensitivity
Specificity
87 83 82
83 79 80
683
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Fig. 2. Visual field in patient with glaucoma. Spatial model based on up-down differences and arcuate clusters detect field abnormality(arrow)[A = 0.941, passed undetected [A= 0.431 by non-spatialmodel in which MD and UPSD are employed.
reduce the risk that subtle defects are diluted by physiologic irregularities in other parts of the field. Experienced clinicians evaluate field charts according to similar principles. The present results also show that up-down comparisons and arcuate cluster analysis can be important and also have the potential of being used as complementing 'building blocks' in the construction of complex field analysis aids. Arcuate cluster analysis was more sensitive to shallow arcuate defects straddling the borders used for updown comparisons, while analysis of up-down differences was more sensitive to defects of less typical shape. The arcuate cluster analysis employed here differed from traditionally used cluster analyses in that knowledge of the normal retinal nerve fiber layer anatomy was incorporated. Taking arcuate 684
shape into account (Weber & Ulrich 1991) can significantly improve cluster analysis in glaucoma (Asman & Heijl 1991)and we therefore decided to use such enhanced cluster analysis in the present study. The non-spatial model employing MD and GH had clear similarities to the Mean Local Defect (MLD) index devised by Langerhorst (1988). In both, the total defect is adjusted for overall shifts in sensitivity, thereby isolating the localized component of the field loss. We avoided inclusionlexclusion criteria based on perimetric results when establishing our model population. The major part of the normal group (the Malmo subjects) was that part of a random sample of the population which remained after exclusion of subjects with pathologic findings detected by means other than perimetry. The same
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Fig. 3. Visual field in normal subject. Spatial model based on up-down differences and arcuate clusters confirms normality [J; = 0.071 while the non-spatial model in which MD and l/PSD are employed gave abnormal results [Jz = 0.651.
principles of exclusion were applied also for the Oakland group of healthy volunteers. The glaucoma group was also established without any knowledge of visual field results. It is likely that this approach in selecting materials can result in more robust visual field models than more conventional 'clinical' approaches where individual ideas of normal and glaucomatous fields will play an important role. Katz and coworkers (1991) found no significant differences between spatial analyses and standard visual field indices, but their material had been selected with perimetric inclusion criteria requiring normal field results in the normal group and a defect revealed with manual perimetry in the glaucoma group. In this way, a much larger proportion of obviously normal or pathological field results were obtained, which might have impaired the
ability to detect clinically important differences between the methods (Taube & Tholander 1990). The JZ(x)-valuesshould not be regarded as probabilities of glaucoma when applied outside the model population. Instead, the probability of glaucoma given a certain JZ(x)-valueis highly dependent on the population (Hosmer & Lemeshow 1989). Thus, a 4x)-value of 0.5 is more indicative of glaucoma in a population at high risk of having glaucoma, e.g. in a population with elevated intraocular pressure, than in the population at large. A model is expected to perform better in the material on which it was constructed than in other materials. The lower values of sensitivity and specificity in the control population than in the model population were therefore expected. The values would have been higher, however, if fields with large field defects had not been removed. The ad685
vantages of the spatial model clearly remained in the control population, however. This indicates that automated visual field interpretation based on traditional non-spatial visual field indices can be improved by spatial analyses in the form of updown comparisons and arcuate cluster analysis in probability maps. Thus, spatial analyses, like the ones described here can be valuable tools in the construction of aids for computer-assisted interpretation of visual fields in glaucoma.
Acknowledgments Supported in part by grants from the Herman Jarnhardt Foundation, Inez and Joel Carlsson’s Foundation, and Ingeborg and Ernst Ydman’s Foundation, Malmo, Sweden, and by grants No. 150 and No. 158 from the Medical Faculty of the University of Lund, Sweden and by grant from The Bank of Sweden Tercentenary Foundation. We thank P. Juhani Airaksinen, MD, and Anja Tuulonen, MD, Oulu, Finland, for providing data for the normal retinal nerve fibre layer anatomy. Parts of the normal material were supplied by Marcus D. Benedetto, Ph.D., Sinai Hospital of Detroit, Mich; by Ben R. Hasty, MD, Oak Knoll Naval Hospital, Oakland, Calif; and by Michael Patella, O.D., Allergan Humphrey, San Leandro, Calif, which is gratefully acknowledged.
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Heijl A, Lindgren G & OlssonJ (1987b):A package for the statistical analysis of visual fields. Doc Ophthalmol 49: 153-168. Heijl A, Lindgren G & Olsson J (1989):The effect of perimetric experience in normal subjects. Arch Ophthalmol 107: 81-86. Heijl A, Lindgren G, Lindgren A, Olsson J, Asman P, Myers S & Patella M (1991):Extended empirical statistical package for evaluation of single and multiple fields in glaucoma.In: Mills R P & Heijl A (eds).Perimetry Update 1990/91, pp 303-315. Amsterdam, Kugler & Ghedini. Holmin C & Krakau C E T (1980): Visual field decay in normal subjects and in cases of chronic glaucoma. Graefes Arch Clin Exp Ophthalmol213: 291-298. Hosmer D W & Lemeshow S (1989): Applied Logistic Regression. New York, John Wiley & Sons. Katz J, Sommer A, Gaasterland D E & Anderson D R (1991): Comparison of analytic algorithms for detecting glaucomatous visual field loss. Arch Ophthalmol 109: 1684-1689. Langerhorst C T (1988): Automated perimetry in glaucoma: Fluctuation behavior and general and local reduction of sensitivity, chapter 4, pp 23-39. Amsterdam, Kugler & Ghedini. OlssonJ (1991): Statistics in perimetry. PhD thesis, Lund University, Department of Mathematical Statistics. pp 22-24. Taube A & Tholander B (1990):Over- and underestimation of the sensitivity of diagnostic malignancy test due to various selections of the study populations. Acta Oncol29: 971-975. Weber J & Ulrich H (1991): A penmetric nerve fiber bundle map. Int Ophthalmol 15: 193-200. Wood J M, Wild J M, Hussey M K & Crews S J (1987):Serial examination of the normal visual field using Octopus automated projection perimetry: Evidence for a learning effect. Acta Ophthalmol (Copenh) 65: 326333. Asman P & Heijl A (1988): A clinical study of penmetric probability maps. Arch Ophthalmol 107: 199-203. Asman P & Heijl A (1991): Cluster analysis in glaucoma. Invest Ophthalmol Vis Sci 32 (Suppl 4): 1191. Asman P & Heijl A (1992a): Evaluation of methods for automated hemifield analysis in perimetry. Arch Ophthalmol 110: 820-826. Asman P & Heijl A (1992b):Weighting according to location in computer-assisted glaucoma visual field analysis. Acta Ophthalmol (Copenh) 70: 671-678. Received on June 15th, 1992. Author’s address: Dr. Peter Asman, Department of Ophthalmology, Malmci General Hospital, S-214 01 Malmo, Sweden.
