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(Investigative Ophthalmology and Visual Science. 2006;47:2896-2903.)
© 2006 by The Association for Research in Vision and Ophthalmology, Inc.
DOI:  10.1167/iovs.05-1079
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Pointwise Linear Regression Analysis for Detection of Visual Field Progression with Absolute versus Corrected Threshold Sensitivities

Anita Manassakorn, Kouros Nouri-Mahdavi, Behrooz Koucheki, Simon K. Law, and Joseph Caprioli

From the Glaucoma Division, Jules Stein Eye Institute, University of California Los Angeles, Los Angeles, California.


   Abstract
Top
 Abstract
Materials and Methods
 Results
 Discussion
 References
 
PURPOSE. To compare the performance of point-wise linear regression analysis (PLR) with total deviation (TD) versus corrected or pattern deviation (PD) threshold sensitivities for detection of visual field progression.

METHODS. Four hundred two eyes (402 patients) enrolled in the Advanced Glaucoma Intervention Study (AGIS) were selected. Criteria for progression according to PLR were a slope ≤ –1 dB/year with P ≤ 0.01 with ≥2 worsening points within the same Glaucoma Hemifield Test cluster. PLR was performed on TD and PD threshold sensitivities and compared to clinical evaluation. Eyes were classified into three groups based on mean deviation (MD): mild (MD ≥ –6 dB), moderately advanced (–6 dB > MD ≥ –12 dB), and advanced (MD < –12 dB) glaucoma.

RESULTS. Visual field progression was observed in 154 (38%), 85 (21%), and 175 (44%) eyes, according to PLR(TD) and PLR(PD), and clinical evaluation. The pair-wise agreement between clinicians and PLR(TD) was significantly greater than that of clinicians and PLR(PD) ({kappa} = 0.48, 95% CI: 0.44–0.52 vs. {kappa} = 0.31, 95% CI: 0.27–0.35). Agreement between PLR(TD) and PLR(PD) decreased with increasing glaucoma severity: {kappa} (95% CI) = 0.60 (0.52–0.67), 0.41 (0.35–0.47), and 0.33 (0.27–0.40) for mild, moderately advanced, and advanced glaucoma, respectively.

CONCLUSIONS. Point-wise linear regression analysis on TD threshold sensitivities performed better than the same analysis on PD when clinical evaluation was used as a reference. Agreement between the two methods was less in moderately advanced and advanced glaucoma.

Reliable detection of glaucomatous progression is a major challenge in the management of glaucoma. Both structural and functional approaches have been used to detect disease progression. Although structural damage can usually be detected before functional damage, evaluation of a longitudinal series of visual fields remains one of the most frequently used methods to detect early evidence of glaucoma and to observe patients.1 2 3 4 5 Various techniques such as the judgment of clinicians, defect classification systems, trend analyses (linear regression analysis), and event analyses (glaucoma change probability plots)6 have been evaluated for determining visual field progression. Point-wise linear regression (PLR) analysis has been used frequently in research settings to detect visual field progression.7 8 9 10 11 It examines the trend of threshold sensitivity at each test location over time and provides an estimate for the rate of change at each location in the visual field.

The Humphrey Visual Field Analyzer (HFA; Carl Zeiss Meditec, Dublin, CA) printout provides the clinician with two sets of plots: the total deviation (TD) and the pattern deviation (PD) plots. The TD numbers represent the difference between the measured absolute threshold sensitivity at each test location and the age-matched value from a control group of normal individuals. The PD plots use the seventh highest threshold sensitivity as a general height of the hill of vision. The difference in this test location from its normal value is deducted from all test locations.12 Its intent is to emphasize the detection of focal defect patterns in the early stages of glaucoma. However, glaucomatous visual field loss may have both generalized and localized patterns.13 14 15 With progression of the visual field defects, a large number of points will eventually be involved, and therefore correction of test locations based on the seventh highest value on the TD plot would potentially lead to apparent improvement of all test locations and could mask the real extent of damage or disease progression. Recently, Åsman et al.16 have suggested that the use of PD for detection of field progression may result in an underestimation of such changes. This is important, because in randomized clinical trials such as the Early Manifest Glaucoma Trial,17 Glaucoma Change Probability Maps (GCPMs) based on PD data were used for the detection of visual field progression. In previous investigations with PLR absolute threshold sensitivities have been used. The potential problem with this approach is the confounding effect of cataract or other nonglaucomatous sources of generalized field depression for correction of which there is no established approach. There is little evidence in the literature about whether TD or PD values are more appropriate for detection of glaucomatous visual field progression.18 We hypothesized that PLR on PD would underestimate true visual field progression, especially in advanced cases. The purpose of the present study was to evaluate the performance of point-wise linear regression analysis for the detection of visual field progression with TD versus PD values and to compare them with clinical evaluation of visual field series.


   Materials and Methods
Top
 Abstract
 Materials and Methods
Results
 Discussion
 References
 
We selected a subset of patients with glaucoma enrolled in the Advanced Glaucoma Intervention Study (AGIS) for the purposes of this study. The AGIS design and methods are provided in detail elsewhere.19 Individual institutional review boards approved the protocol, which complied with the tenants of the Declarations of Helsinki. The Institutional Review Board at University of California Los Angeles also approved the current investigation. From the original group of enrolled patients (789 eyes of 591 patients), 402 eyes of 402 patients, which met the following criteria, were enrolled: (1) a baseline AGIS visual field score ≤16; (2) at least 3 years of follow-up; and (3) a minimum of seven visual field examinations with a reliability score of 2 or better. In cases in which both eyes of the same patient were available, the eye with the better mean deviation (MD) was included.

Visual field tests were conducted with a perimeter (Humphrey Visual Field Analyzer I; Carl Zeiss Ophthalmic Systems, Inc., Dublin, CA). A central 24-2 full-threshold test, size III white stimulus, with the foveal threshold test turned on was performed in all examinations. The electronic visual field data were exported to a computer (Peridata ver. 1.9.0; Peridata Software GmbH, Hürth, Germany). Point-wise linear regression was then performed (SPSS software ver. 12.0; SPSS Inc., Chicago, IL). Our methodology for definition of change versus stability at each test location is described in detail elsewhere.20 21 In summary, a point was considered to be progressing if the regression slope was ≤ –1.0 dB/year with P ≤ 0.01. Improvement at a test location was described as a regression slope ≥ 1.0 dB/year in the presence of P ≤ 0.01. We performed two sets of PLR for each visual field series. First, the TD threshold sensitivities were regressed against time. Second, PD thresholds were analyzed in the same way. The change in a visual field series was defined when at least two test locations belonging to the same Glaucoma Hemifield Test cluster showed the same direction of change. If a given eye met the criteria for both progression and improvement, we compared the number of worsening and improving test locations. If the number of worsening test locations was equal or more than twice than the number of the improving test locations, we considered that visual field series as progressing and vice versa. If these criteria were not fulfilled, we defined that eye as indeterminate with regard to stability and direction of change.

Two experienced clinicians (KNM and SKL) evaluated the visual field series with single Humphrey visual field printouts. The graders agreed on the following qualitative approach: Each series would be judged for the magnitude of long-term fluctuation, and change was determined when the overall trend exceeded this magnitude. Progression had to be consistent with glaucomatous patterns. The reviewers independently graded each visual field series as progressing, stable, or improving while masked to all other clinical data. In cases in which there was disagreement, the two clinicians reviewed the visual field series together and reached a consensus regarding visual field status.

We classified study eyes into three groups according to visual field MD at baseline: mild glaucoma, MD ≥ –6 dB; moderately advanced glaucoma, –6 dB > MD ≥ –12 dB; and advanced glaucoma, MD < –12 dB. We also categorized the study eyes according to their having undergone cataract surgery. The analyses were repeated in the same manner in the subgroups.

Kappa ({kappa}) statistics and percentage of agreement were used to compare the performance of PLR on TD and PD values to that of clinical evaluation. The agreement according to the {kappa} statistic is interpreted as follows: slight, ≤ 0.20; fair, 0.21 to 0.40; moderate, 0.41 to 0.60; substantial, 0.61 to 0.80; and excellent, >0.80.22 The Wilcoxon signed-rank test was used to compare the demographic and other nonnormally distributed numerical data, and the McNemar test was used to compare proportions between groups.


   Results
Top
 Abstract
 Materials and Methods
 Results
Discussion
 References
 
Four hundred two eyes of 402 patients were recruited from the AGIS database. The demographic and clinical characteristics of the study sample are shown in Table 1 . One hundred fourteen (28.4%), 144 (35.8%), and 144 (35.8%) eyes were classified as having mild, moderately advanced, and advanced glaucoma, respectively.


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  		TABLE 1. Demographic Characteristics of the Study Sample

 
Visual field progression was noted in 154 (38.3%), 85 (21.1%), and 175 (43.5%) eyes with PLR(TD), PLR(PD), and clinical evaluation. Point-wise linear regression on TD threshold sensitivities detected a significantly larger number of progressing eyes compared with PD values (P < 0.001, = 0.004, <0.001, and <0.001 for the entire, mild, moderately advanced, and advanced glaucoma groups; McNemar test). The proportion of progressing eyes according to clinical assessment of field series was higher than both PLR methods (P = 0.04 and P < 0.001 for comparison between clinical assessment and PLR[TD] and PLR[PD], respectively; McNemar test). No statistically significant difference for improvement was observed between PLR(TD) and PLR(PD) (P = 0.43, McNemar test), whereas clinicians assessed improvement less than PLR(TD) and PLR(PD) (P = 0.003 and P = 0.07, McNemar test). The proportion of progressing and improving eyes according to glaucoma severity is shown in Figure 1 .


Figure 1
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  		FIGURE 1. Comparison of the results of PLR analysis on absolute threshold sensitivities (PLR[TD]) and pattern deviation thresholds (PLR[PD]) according to severity of glaucoma at baseline.

 
There were six eyes in the PLR on TD values that met the criteria for both progression and improvement at the same time. After comparing the number of progressing and improving test locations, as described in the Methods section, four eyes were classified as progressing and two as indeterminate. Both indeterminate eyes had advanced glaucoma. The AGIS scores at baseline were 11 and 15. One of the indeterminate eyes had nearly the same number of progressing and improving points and was considered stable by clinical evaluation. The other eye that progressed by clinical evaluation had several progressing test locations that was considerably greater than the number of improving test locations.

Three eyes were considered to have progressed and improved by PLR on PD values. Two eyes had moderate glaucoma and one eye had advanced glaucoma. All progressed by clinical assessment. The number of progressing and improving test locations was not much different. There were 12 (3.0%) eyes that progressed with PLR on TD values and improved with PLR on PD values. Four and nine eyes were classified to have moderately advanced and advanced glaucoma, respectively. All were considered to have progressed by clinical assessment. These "mixed" findings may be explained by the long-term fluctuation that usually is found in advanced disease.

The {kappa} statistic for pair-wise agreement of PLR(TD) versus PLR(PD) was 0.43 (95% CI: 0.40–0.47) with an observed percentage agreement (95% CI) of 72% (70%–74%). The number and percent of agreement among three methods are shown in Figure 2 . The {kappa} statistics (95% CI) in the entire group for agreement of clinical evaluation and PLR(TD) or PLR(PD) values was 0.48 (0.44–0.52) and 0.31 (0.27–0.35), respectively. The {kappa} statistics and percentage agreements between results of PLR(TD), PLR(PD) and clinical evaluation according to glaucoma severity are shown in Table 2 . Figures 3 and 4 provide examples of field series according to PLR(TD), PLR(PD), and clinical evaluation. The average rate of worsening per test location per year (regression slopes) was –1.8 dB when regression analysis was performed on PLR(TD) compared with –1.5 dB on PLR(PD) (P < 0.001; Wilcoxon signed-rank test), whereas the reverse was true for improving eyes (P < 0.001). The {kappa} statistic (95% CI) for the agreement between the two clinicians in the entire group was 0.58 (0.54–0.62) with a percentage agreement (95% CI) of 78% (76%–80%). The {kappa} statistics for agreement of clinicians (95% CI) in different glaucoma groups were not significantly different: 0.62 (0.55–0.69) versus 0.55 (0.49–0.61) versus 0.57 (0.51–0.64) for the early, moderately advanced, and advanced glaucoma groups, respectively.


Figure 2
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  		FIGURE 2. Agreement between PLR analysis for detection of progression on TD and PD values in the entire group (A) and in the mild (B), moderately advanced (C), and advanced glaucoma (D) groups. Numbers in circles represent the number of progressing eyes.

 

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  		TABLE 2. Comparison of Agreement of Point-Wise Linear Regression Analysis on Raw and Corrected Threshold Sensitivities, according to Cataract Surgery

 

Figure 3
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  		FIGURE 3. An example of a visual field series defined as progressing by both PLR analysis on TD sensitivities and clinical assessment but considered to be stable by PLR analysis on PD data.

 

Figure 4
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  		FIGURE 4. An example of a visual field series defined as progressing by both PLR analysis on PD data and clinical assessment but considered stable by PLR analysis on TD sensitivities.

 
The average MD at baseline was –9.9 and –10.3 dB for patients who underwent cataract surgery and those who did not (P = 0.64; Mann-Whitney test). In the group of patients who had cataract surgery, progression was found in 67 (16.7%) and 41 (10.2%) eyes with PLR(TD) and PLR(PD) (P < 0.001, Wilcoxon signed-rank test), and improvement was found in nine (2.2%) and eight (2.0%) eyes with PLR(TD) and PLR(PD) (P = 0.78, McNemar test), respectively. In the group that did not undergo cataract surgery, progression was found in 87 (21.6%) and 44 (10.9%) (P < 0.001, McNemar test) and improvement was observed in 12 (3.0%) and 12 (3.0%) with PLR(TD) and PLR(PD), respectively (P = 1.0, McNemar test). The average number of worsening test locations per eye in patients who underwent cataract surgery was 7.7 and 2.4 on PLR(TD) and PLR(PD) (P < 0.001, Wilcoxon’s signed rank test) and 6.5 and 2.7 in those patients who did not required cataract surgery (P < 0.001, Wilcoxon’s signed rank test). The detection of worsening eyes between patients who underwent cataract surgery and those who did not was not significantly different according to PLR(TD) (P = 0.08). However, PLR(PD) detected worsening eyes in the cataract surgery group more the other group (P = 0.03). There was no significantly different for detection of improving eyes between cataract surgery and noncataract surgery groups regarding to PLR(TD) and PLR(PD) (P = 0.64 and P = 0.86).


   Discussion
Top
 Abstract
 Materials and Methods
 Results
 Discussion
References
 
The present study shows that PLR on TD threshold sensitivities can detect significantly more progressing eyes than the same analysis on PD thresholds, especially in eyes with moderately advanced and advanced glaucoma (P = 0.003 in the early glaucoma group and <.001 in the moderately advanced and advanced glaucoma groups). The {kappa} statistic and percent agreement between the two methods was moderate in the mild glaucoma group ({kappa} = 0.60; 95% CI: 0.52–0.67) and progressively decreased with advancing glaucomatous damage: {kappa} (95% CI) = 0.41 (0.35–0.47) and 0.33 (0.27–0.40) in the moderately advanced and advanced glaucoma groups, respectively. The {kappa} statistic for the early glaucoma group were significantly higher than either the moderately advanced or advanced group. Point-wise linear regression on TD thresholds also agreed better with clinical evaluation of visual fields by experienced observers than did PLR(PD). The agreement was statistically significant in the entire group: {kappa} = 0.48 and 0.31 for comparison between clinical evaluation and PLR(TD) and PLR(PD) and the early and moderately advanced glaucoma subgroups ({kappa} = 0.59 vs. 0.43 and 0.50 vs. 0.27 in the two groups). However, no significant difference was found in the advanced groups ({kappa} = 0.37 vs. 0.27; Table 3 ). As expected, PLR(TD) led to larger average regression slopes and a greater number of progressing points per eye than did PLR(PD) (P < 0.001). The results did not change after the study eyes were divided according to performance of cataract surgery (results not shown).


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  		TABLE 3. Comparison of Results of PLR Analysis on Absolute (PLR[TD]) and Corrected Threshold (PLR[PD]) Sensitivities according to Cataract Surgery

 
There were 12 (3.0%) eyes that were found to have progression with PLR(TD) and improvement with PLR(PD). Four and nine eyes were classified as moderately advanced and advanced glaucoma, respectively. All of them were considered to have progression by clinical assessment. Eight of 12 eyes were observed until the late stage of disease and presented with tunnel vision. Obviously, MD in these eyes went beyond –20 dB, with >50 test locations on TD plots having P < 0.5%; the PD plots showed only a minimal degree of abnormality.

The performance of Glaucoma Change Probability Analysis (GCPA) with TD and PD has been evaluated. Lee et al.23 compared visual field progression according to clinical criteria and GCPA on TD and PD data. Consistent with our results, clinicians detected visual field progression more frequently than did GCPA on TD values, and GCPA with TDs detected more progressing eyes than did the same method with PDs. In a similar investigation, Katz18 compared results of GCPA on TD and PD data and found that in half of patients, glaucoma that was detected as progressing based on TD data was not detected on GCPA with PD. The mean deviation was –7.4 dB in that study and the agreement for progression was only moderate between GCPA results on TD and PD data ({kappa} = 0.48; percent agreement = 79%). Similarly, we found moderate agreement ({kappa} = 0.43; percent agreement = 72%) between results of PLR on TD and PD thresholds despite the fact that the average MD in our study was lower (–10.1 dB). Katz found that the rate of visual field progression as judged by clinicians was similar to GCPA on PD data, but the agreement between clinicians and TD data was higher. In our study, we found that the progression rate for PLR(TD) and PLR(PD) were similar to those of Katz and that pair-wise agreement was better between clinical assessment of field series and PLR(TD) ({kappa} = 0.48; 73% agreement) than did PLR(PD) ({kappa} = 0.31; 65% agreement).

The Early Manifest Glaucoma Trial (EMGT) also used GCPA based on PD data to detect visual field progression.24 One of the inclusion criteria for that study was MD > –16 dB. The average MD in that group was –4.7 dB. They found that GCPA on PD data had high sensitivity and specificity for detecting definite visual field progression compared with clinical evaluation.17 The GCPA based on PD data is probably sensitive enough to detect changes in early glaucoma, because visual field loss in such cases usually has a prominent focal component and is commonly located on one side of the horizontal meridian.25

Åsman et al.16 found that the mean change in the visual field general height index (the difference from normal at the seventh best point) did not depend on the depth of visual field defect, but rather depended on the number of point locations involved in the glaucomatous process. With advancing glaucomatous damage, more test locations become involved (i.e., more diffuse loss) and the visual field general height index is more likely to change, which would lead to a potential overestimation of the correction factor that is used to outline the diffuse loss; as a result, underestimation of the corrected threshold sensitivities occurs. Henson et al.26 reported a diffuse pattern of visual field loss in an early stage of glaucoma (median MD = –3.1 ± 2.4 dB). A group of 10 best sensitivities of each visual field was 1.0 to 2.0 dB lower than the normal age-matched eye. This would translate into lower threshold sensitivity at the seventh best point in the visual field, and therefore, underestimation of the PDs. In more advanced glaucoma cases, more test locations get involved and the PD threshold sensitivities are more likely to be affected.

In this study, we used clinical evaluation as the external standard. The main shortcoming of the clinical judgment is the high inter- and intraobserver variability.27 28 It is possible that the results of this investigation would have been somewhat different if a different group of reviewers had evaluated the visual field series. It is also possible that clinicians might rely too much on the gray-scale schematic in the visual field printout, which is probably the most misleading part. We believe that this was not very likely to occur, given the fact that experienced clinicians reviewed the visual fields. In contrast, clinicians are less likely to call clinically dubious changes as real. In addition, they tend to be less sensitive to diagnose diffuse changes of the visual fields as glaucomatous progression. Clinicians are also more likely to flag learning effects, artifacts, or sudden reversible changes of the visual field progression. The higher agreement of clinicians with results of PLR(TD) values in this study is unexpected, since clinicians tend to put more weight on PD plots for determining the extent of field loss and detection of visual field progression, especially if existing or progressive media opacity is a concern.

Although PLR is a useful method in the research setting, it also has limitations.6 29 30 31 32 33 34 35 36 37 Visual field test locations are assumed to be independent in time and space, which is not a valid assumption. In addition, to achieve acceptable sensitivity and high specificity, PLR requires at least six visual field examinations, and perhaps more.37 38 A large number of comparisons were performed in the present study. Many of those were potentially correlated, and therefore it was difficult to adjust the probabilities correctly, to keep the {alpha} error at 0.05. Considering the exploratory nature of our study, we decided not to implement any type of correction for multiple comparisons.

In conclusion, we found that PLR analysis of corrected threshold sensitivities performed less adequately than did the same technique using absolute threshold sensitivities, especially in moderately advanced to advanced glaucoma, where a large number of test locations are abnormal. Our data suggest that although using corrected threshold sensitivities for PLR may be appropriate in early glaucoma, it is not a good approach in eyes with more advanced glaucomatous damage. In addition, comparison of the two approaches may be more useful in eyes with suspected progression.


   Footnotes
 
Supported by a grant from Research to Prevent Blindness and National Eye Institute Grant R01 EY12738.

Submitted for publication August 15, 2005; revised December 7, 2005; accepted April 28, 2006.

Disclosure: A. Manassakorn, None; K. Nouri-Mahdavi, None; B. Koucheki, None; S.K. Law, None; J. Caprioli, None

The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Corresponding author: Joseph Caprioli, Glaucoma Division, Jules Stein Eye Institute, 100 Stein Plaza, Los Angeles, CA 90095; caprioli{at}jsei.ucla.edu.


   References
Top
 Abstract
 Materials and Methods
 Results
 Discussion
 References
 

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S. Hong, G. J. Seong, and Y. J. Hong
Long-term Intraocular Pressure Fluctuation and Progressive Visual Field Deterioration in Patients With Glaucoma and Low Intraocular Pressures After a Triple Procedure
Arch Ophthalmol, August 1, 2007; 125(8): 1010 - 1013.
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