Prediction of Visual Field Progression in Glaucoma

Abstract

purpose. To determine the probability of future glaucomatous visual field (VF) progression with clinical and perimetric data.

methods. One hundred sixty-one eyes of patients (161) enrolled in the Advanced Glaucoma Intervention Study (AGIS) with ≥8 years of follow-up and a baseline VF score ≤16 were selected. VF progression at 8 years was determined with point-wise linear regression (PLR) analysis, using a two-omitting algorithm. The course of VF series over the first 4 years of follow-up was quantified by an index, the sum of slopes, which is the sum of all slopes of VF thresholds with P < 0.05 when PLR was performed on the 4-year data. The following parameters were included in a logistic regression model to predict 8-year outcomes from the first 4 years of follow-up: intervention sequence, age, AGIS VF score, mean IOP, IOP fluctuation, and sum of slopes.

results. Sixty-four (40%) eyes progressed after 8 years as determined by PLR analysis. Two parameters were predictive of subsequent VF progression, as identified at 8 years (predictive power: 76%): more negative sum of slopes (i.e., faster or more extensive deterioration; P < 0.001) and older age at 4 years (P = 0.049). When sum of slopes alone was used to predict outcomes at 8 years, the predictive power was the same.

conclusions. The VF sum of slopes can be used to estimate the probability of subsequent VF worsening with reasonable, clinically useful accuracy. This probability may be combined with other clinical information for more effective clinical predictions and treatment decisions.

Recent analyses of data from the Advanced Glaucoma Intervention Study (AGIS) ¹ and previous AGIS reports ^{2 3} have shown the most important predictors for visual field (VF) progression to be older age at the time of first glaucoma intervention, greater intraocular pressure (IOP) fluctuation, higher mean IOP, and lower baseline AGIS VF score. Length of follow-up and number of glaucoma interventions have also been found to be less important, but significant, risk factors for glaucomatous VF progression. Clinicians often have available VF series obtained during earlier follow-up and depend on both kinds of data to make an informed decision about glaucoma treatment in a given patient. No study has been undertaken to investigate whether and how combining these different types of clinical information would be helpful for predicting the subsequent course of glaucoma in an individual patient. 

The purpose of this study was to investigate whether clinical or perimetric data gathered during follow-up can provide the clinician with a probability estimate for subsequent glaucomatous VF progression. 

Methods

The AGIS design and methods are described in detail elsewhere and therefore will be summarized briefly. ⁴ Phakic patients, 35 to 80 years of age, with open-angle glaucoma no longer controlled by maximally tolerated medical treatment were recruited. The eligible eyes had to have a best corrected visual acuity score of at least 56 letters (Early Treatment Diabetic Retinopathy Study charts) and meet specified criteria for combinations of consistently elevated IOP, despite maximum-tolerated and effective medical therapy, glaucomatous VF defect, and/or optic disc rim deterioration. ⁴ Between 1988 and 1992, investigators at 12 participating AGIS clinical centers enrolled 789 eyes of 591 patients. Eyes were randomly assigned to one of two surgical-intervention sequences: argon laser trabeculoplasty–trabeculectomy–trabeculectomy (ATT) or trabeculectomy–argon laser trabeculoplasty–trabeculectomy (TAT). Follow-up study visits were scheduled 3 and 6 months after enrollment and every 6 months thereafter. The institutional review boards at each of the participating centers approved the AGIS protocol, and all patients provided informed consent. The research was conducted in accordance with the tenets of the Declaration of Helsinki. Data in this report are based on database closure of March 31, 2001. 

VF tests were conducted with a field perimeter (Humphrey Visual Field Analyzer I, set for the central 24-2 threshold test, size III white stimulus, and full threshold strategy; Carl Zeiss Meditec, Dublin, CA). VF defect scores ranged from 0 (no defect) to 20 (advanced glaucoma). ⁵ Study measurements were made at baseline, 3 months after initial intervention, and at each 6-month follow-up examination. Baseline, or reference, measurements were performed after the eligibility measurements but before the first surgical intervention, to avoid the effect of regression to the mean. 

All patients enrolled in AGIS who had at least 8 years of follow-up, reliable VFs (AGIS reliability score ≤ 2), and a reference VF score of 16 or less were included. In addition, these eyes also underwent a minimum of six VF exams during the first 4 years and 6 or more additional VF examinations during the latter part of follow-up. We selected only one eye of each patient. When both eyes of a patient were either stable or progressing, we randomly chose one of the eyes. In cases where one eye remained stable and the fellow eye was progressing, we selected the progressing eye to increase the power of subsequent logistic regression analyses. 

Statistical Methods

A computer (with SPSS, ver. 11.5; SPSS Inc., Chicago IL) was used to perform point-wise linear regression analyses. Our methodology is described in detail elsewhere. ⁶ We used the two-omitting regression algorithm recently described by Gardiner and Crabb ⁷ for definition of change versus stability at each point at 8 years. In summary, a test location is considered progressing or improving during the follow-up period if the regression slope is statistically and clinically significant (as defined later) in both of the following regression analyses: (1) after omitting the last threshold in a series and (2) after deleting the threshold before last for the same series. This approach has been shown, in simulation experiments, to be more specific than using all the data points for a single regression analysis, and it maintains a sensitivity comparable to other stringent algorithms used for the same purpose, such as two of two ⁸ or three of four. ^{9 10} Regression slopes were considered significant if ≥1.00 dB/year or ≤−1.0 dB/year in presence of P ≤0.01. 

For evaluation of VF series after 8 years of follow-up, we used the most clinically rigorous set of criteria explored in the aforementioned investigation ⁶ : the two point Glaucoma Hemifield Test (GHT) change criterion. According to this criterion, a VF series is designated as changing if two test locations belonging to the same GHT cluster demonstrate change in the same direction. This set of criteria was found to be the most conservative among various PLR approaches. VF outcomes from PLR at 8 years were classified as progressing or nonprogressing. Improving and stable eyes were categorized together as nonprogressing. 

As a comparison, we also used the AGIS criteria as an alternative outcome measure for VF progression at 8 years. VF progression according to AGIS criteria was defined as the first occurrence in an eye, at three consecutive 6-month visits, of a worsening in VF defect score of 4 or more from the baseline value. Changes in AGIS VF defect score were measured from preintervention reference values. 

To summarize VF data over the first 4 years of follow-up, we defined a new index based on PLR that we called sum of slopes at 4 years. A single point-wise linear regression analysis was performed on all VF thresholds gathered during the first 4 years of follow-up. The sum of slopes was calculated as the arithmetic sum of all regression slopes with *P < 0.05. 

Multivariate logistic regression was used to predict the 8-year VF outcomes from 4-year perimetric and clinical data. Preoperative and postoperative factors that were associated with VF progression in univariate analyses (χ² test, unpaired t-test, or Mann-Whitney test, depending on the type of data) at P ≤ 0.20 were included in the final model. In addition, we included all clinically relevant variables that might predict or confound detection of VF progression. The following risk factors or potentially confounding factors were entered into the final logistic model for prediction of VF worsening at 8 years: intervention sequence, age at 4-year follow-up, mean IOP and IOP fluctuation during the first 4 years of follow-up, AGIS VF score, and sum of slopes at 4 years. Standard deviation of the IOP at all visits after the initial surgery was used as a measure of IOP fluctuation. 

Multivariate logistic regression is usually used to predict a binary variable or group assignment with a defined cutoff point. The resultant values for the dependent variable in the logistic regression equation can vary from 0 to 1. Ordinarily, values below 0.5 or another selected cutoff point are assigned to one group and higher values to the other group. 

Alternatively, these probabilities can be interpreted as an estimate of probability for occurrence of the dependent variable (here VF progression at 8 years). Once predictive factors have been determined and a valid regression equation is established, the probability estimates may be used to assist informed decision making about further management of glaucoma after an initial period of follow-up. 

The binary results of logistic regression or the probability of progression at 8 years can therefore be estimated for each eye using the logistic regression equation after inclusion of predictive factors for VF progression at 8 years:  

\[P_{x}\ {=}\ 1/1\ {+}\ e^{{-}(b_{0}{+}b_{1}X_{1}{+}b_{2}X_{2}{+}{\ldots}{+}b_{n}X_{n})}\]

where P _x is the probability of occurrence of an outcome (VF progression here), e is the root of the natural logarithm, b ₀ is the intercept, b _{1… n} is the regression coefficient(s) for independent variable(s), and X _{1… n} is independent variable(s) included in the logistic regression equation. 

The cutoff point for classification by logistic regression was set at 0.50 in this study. Variables with P ≤ 0.05 or less were considered statistically significant. 

Results

A total of 161 eyes (of 161 patients) were evaluated. The mean (± SD) number of available VF examinations at 4 and 8 years were 9.6 ± 1.0 (range, 6–11) and 18.9 ± 1.8 (range, 13–21), respectively. In 64 (40%) eyes the VF became worse after 8 years, according to the two-omitting PLR algorithm. Forty-five (28%) eyes progressed based on AGIS criteria. The following variables were found to be significantly different between the progressing and nonprogressing groups (according to PLR) on univariate analysis (Table 1) : sum of slopes during the first 4 years (P < 0.001; Mann-Whitney test, Fig. 1 ), age at 4-year follow-up (P < 0.001; unpaired t-test), and AGIS scores at 4 years (P = 0.001, unpaired t-test). Neither average IOP nor IOP fluctuation during the first 4 years of follow-up was significantly different between the progressing and nonprogressing eyes. On multivariate analysis, the following two variables were associated with VF progression (Table 2) : a more negative sum of slopes during the first 4 years (P < 0.001) and older age at 4 years of follow-up (P = 0.049). 

Use of the two significant predictive factors found with multivariate analysis (sum of slopes at 4 years, age at 4 years) provided a prediction accuracy of 76%. When sum of slopes was investigated as the only predictive variable, the prediction accuracy was the same. When age at 4 years of follow-up was investigated as the only predictive variable, the prediction accuracy was 56%. The best cutoff point for predicting progression versus stability was approximately –2.6 dB/year. The sensitivity and specificity at this cutoff point were 86% and 73%, respectively. With the specificity fixed at 80% and 90%, the respective sensitivities were 75% and 56%. The sum of slopes at 4 years remained the only consistent and statistically significant predictor of VF progression at 8 years when the analyses were repeated separately on the two groups of eyes that did or did not undergo cataract surgery during follow-up (Table 3) . We investigated whether the results of PLR of 4-year data with the same criteria used at 8 years (regression slope ≥ 1.00 dB/year in the presence of P ≤ 0.01) had any predictive power for the fate of VF series at 8 years. We found that PLR at 4 years missed 67% (43/64 eyes) of progressing eyes, whereas it rarely detected progression (1/ 97 eyes, 1%) in the absence of worsening at 8 years. 

We also investigated whether the change in AGIS VF score during the first 4 years of follow-up had any predictive value for VF status at 8 years, in addition to the sum of slopes. However, it was not found to provide any additional information in the presence of sum of slopes (data not shown). When the AGIS criteria were used to define VF progression at 8 years, sum of slopes at 4 years was the only statistically significant variable associated with worsening of VFs (P < 0.001). 

Figure 2 shows an example of a stable series of VFs as determined by point-wise linear regression analysis. The probability estimate, derived from the logistic equation, for VF progression at 8 years was 20%, and this series was therefore classified as nonprogressing. This probability of progression at 8 years can be considered low. Conversely, Figure 3 demonstrates an example of a worsening series of VFs. The probability estimate, derived from the logistic equation, for VF progression at 8 years was 66%. The likelihood for progression of glaucomatous field damage in this eye can be considered fairly high. 

Discussion

We investigated the possibility of predicting the future course of treated glaucoma with clinical and VF data gathered during earlier follow-up of patients enrolled in AGIS. We applied strict PLR criteria at 8 years to define VF outcomes. Then, the first 4 years of data were used to predict the VF outcomes at 8 years. We found that the “sum of slopes” derived from point-wise linear regression analysis on VFs performed during the first 4 years after recruitment of patients was the strongest predictor of VF status at 8 years. Although older age during the first 4 years of follow-up was also significantly associated with VF status at 8 years, the influence of the sum of slopes far exceeded that of age. 

In a preliminary study, McNaught et al. ¹¹ compared different curve-fitting models for predicting individual VF thresholds over time. They found that PLR was the best model for prediction of threshold sensitivity at individual test locations when the first five VFs were used to predict the threshold sensitivity at selected test locations on the 15th VF examination performed during follow-up of patients with normal-tension glaucoma. Our study is different in that we addressed the problem of predicting the course of the entire VF series at 8 years using information available during the first 4 years of follow-up, including clinical and perimetric data. The AGIS database was considered an appropriate database for this investigation, because a large proportion of patients enrolled in AGIS were followed for >8 years. The AGIS patients also had regular VF examinations every 6 months during the course of the study, making this database an excellent medium for application of PLR. However, it must be emphasized that AGIS patients represent a subgroup of patients with advanced glaucoma who are no longer controlled on medical treatment. Hence, the rate and pattern of glaucoma progression is not necessarily generalizable to patients at large with primary open-angle glaucoma. This, though, does not diminish the value of the model presented in this investigation. 

The major advantage of using sum of slopes to summarize the course of VFs is that no empiric interim judgment or assumptions regarding progression of VF series is required at 4 years. It also enabled us to summarize the data derived from the VFs as a single number. Given the lack of a gold standard for the detection of VF progression, a given eye may need to be followed for a long time before a definite decision regarding the course of the VF series can be reached. Therefore, use of a summary index, such as sum of slopes, would allow the clinician to calculate a probability for future worsening of glaucoma. Clinicians can then combine this probability estimate with other available clinical information, such as age and indices of IOP control to make a more informed decision regarding continuing care of individual patients. Figures 2 and 3 show examples of how the probability estimate can replace the binary—yes or no—outcome of the logistic equation. Although based on a cutoff point of 0.5, we expected that the examples would be classified as nonprogressing and progressing, respectively, the probability estimates derived from the same analysis (P _x : 20% and 66%) provide quantitative probabilities that are more meaningful and can be taken into account along with other clinical findings for better clinical decision making. 

The sum of slopes can also provide quantitative information regarding the rate of progression, although there is loss of spatial information. When we applied the same PLR criteria for definition of VF progression during the first 4 years of follow-up, the resultant binary findings were not as strongly associated with VF status at 8 years. Point-wise linear regression analysis is the only currently used technique (in addition to Glaucoma Change Probability Analysis of the Humphrey Field Analyzer; Carl Zeiss Meditec) for which commercial software (Progressor; OBF Laboratories UK Ltd., Wiltshire, UK) is available. The sum of slopes index could be easily integrated into software and used clinically. 

A previous AGIS report and a recent analysis of the AGIS database with PLR have found that mean IOP and IOP fluctuation, defined as the standard deviation of all IOP measurements after initial surgery, were strong risk factors for predicting VF progression. ^{1 2} In the present study, neither mean IOP nor IOP fluctuation during the first 4 years of follow-up had predictive value for the VF status at 8 years. We speculate that there may be an inadequate number of IOP measurements during the first 4 years for a robust estimate of mean IOP or IOP fluctuation. These results do not necessarily contradict the findings of the aforementioned studies. 

A limitation of PLR is the requirement of a minimum of six to eight fields before the results are meaningful. ^{12 13 14} Therefore, assuming that VFs are performed every 6 months after the baseline examination, PLR can be applied only after three or more years of follow-up. 

We have previously shown that AGIS and PLR criteria agree in two thirds of the eyes in AGIS. ⁶ Of note, when AGIS criteria were used for definition of VF outcomes at 8 years, the sum of slopes was still the strongest and only significant predictor of subsequent VF change. This confirms the value of sum of slopes for forecasting the subsequent course of VFs. 

In conclusion, we have presented evidence that the index sum of slope, derived from point-wise linear regression analysis of VF data obtained during early follow-up of patients with glaucoma is a useful and relevant predictor of the future course of VF series. The probability estimate provided by the logistic regression analysis can be combined with other clinical data to make better-informed decisions regarding continuing care of patients with glaucoma. 

 Presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Fort Lauderdale, Florida, April 2004; and at the annual meeting of the American Glaucoma Society, Sarasota, Florida, March 2004.

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

 Submitted for publication February 24, 2004; revised May 5, 2004; accepted May 12, 2004.

 Disclosure: K. Nouri-Mahdavi, None; D. Hoffman, None; D. Gaasterland, 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.

 

Table 1.

 

Characteristics of the Study Sample According to Visual Field Outcomes at 8 Years

	Progressing			Nonprogressing
		No.	%	No.	%	P
Total	64	39.8	97	60.2
Eye
Right	36	56.3	40	41.2	0.060
Left	28	43.8	57	58.8
Gender
Male	29	44.4	48	49.5	0.518
Female	35	55.6	49	50.5
Race
Black	35	54.7	47	48.5	0.687
White	28	43.8	49	50.5
Hispanic	1	1.6	1	1.0
Age after 4 years of follow-up (y)
Mean		71		66	< 0.001*
SD		6.7		10.8
Range		49–82		45–85
Intervention sequence
ATT	32	50	51	52.6	0.749
TAT	32	50	46	47.4
Cataract surgery during follow-up
No	34	53.1	58	59.8	0.403
Yes	30	46.9	39	40.2
No. of visual field exams per eye during first 4 years
Mean		9.6		9.6	0.370
SD		0.9		1
Range		6–11		6–11
Mean IOP during first 4 years (mm Hg)
Mean		16.6		15.7	0.080
SD		3		3.4
Range		7.2–22.7		6.9–22.3
IOP fluctuation (mm Hg)
Mean		3.2		2.8	0.190
SD		1.9		2
Range		1.0–12.0		0.7–15.9
AGIS visual field score at 4 years
Mean		9.5		7	0.001*
SD		4.1		4.5
Range		0–16		0–16
Sum of slopes at 4 years (dB/y)
Mean		−28.7		1.9	< 0.001, †
SD		38.9		14.5
Range		−236.9 to +10.4		−58.6 to +42.2

 Outcomes were measured by the two point Glaucoma Hemifield Test set of criteria for pointwise linear regression analysis.

*  Unpaired t-test.

†  Mann-Whitney test.

Figure 1.

 

Mean sum of slopes at 4 years of follow-up based on VF progression at 8 years, as detected by point-wise linear regression analysis. The whiskers represent one SE.

Table 2.

 

Results of Logistic Regression

	P	Odds Ratio	95% CI for OR
						Lower	Upper
Intervention sequence (TAT sequence)	0.709	1.172	0.509	2.699
Age at 4 years of follow-up (y)	0.049	1.048	1.000	1.097
AGIS VF score at 4 years	0.590	1.028	0.931	1.135
Mean IOP during the first 4 years (mm Hg)	0.246	1.083	0.947	1.238
IOP fluctuation during the first 4 years (mm Hg)	0.966	0.995	0.803	1.233
Sum of slopes at 4 years (dB/y)	< 0.001	0.918	0.886	0.951

 The two-point Glaucoma Hemifield Test-change criteria for pointwise linear regression analysis was used as the outcome measure for visual field progression.

Table 3.

 

Results of Logistic Regression According to Performance of Cataract Surgery with Pointwise Linear Regression Analysis Used to Determine Visual Field Progression

	P	Odds Ratio	95% CI for OR
						Lower	Upper
No cataract extraction
Intervention sequence (TAT sequence)	0.827	0.891	0.316	2.510
Age at 4 years of follow-up (years)	0.040	1.068	1.003	1.138
AGIS VF score at 4 years	0.061	1.128	0.995	1.279
Mean IOP during the first 4 years (mm Hg)	0.740	0.971	0.819	1.152
IOP fluctuation during the first 4 years (mm Hg)	0.540	1.115	0.786	1.582
Sum of slopes at 4 years (dB/year)	0.027	0.952	0.912	0.994
Cataract extraction during follow-up
Intervention sequence (TAT sequence)	0.693	1.439	0.237	8.759
Age at 4 years of follow-up (years)	0.371	1.046	0.947	1.156
AGIS VF score at 4 years	0.076	0.799	0.623	1.024
Mean IOP during the first 4 years (mm Hg)	0.362	1.170	0.834	1.641
IOP fluctuation during the first 4 years (mm Hg)	0.542	1.108	0.797	1.540
Sum of slopes at 4 years (dB/year)	0.001	0.826	0.737	0.927

Figure 2.

 

An example of a stable series of VFs as determined by point-wise linear regression analysis. The first VF (A) represents the baseline field. The second field (B) demonstrates the VF status at 4 years. The probability estimate, derived from the logistic equation, for VF progression at 8 years was 20% at this point. (C) The final VF examination at 8 years.

Figure 3.

 

An example of a worsening series of VFs as determined by point-wise linear regression analysis. (A) Is the baseline field (11-27-89). Some long-term variability can be observed during the first 4 years: (B) year 1 (09-11-90); (C) year 3 (10-29-92); and (D) year 4 (08-2-93). (D) VF status at year 4. No definite progression can be concluded at that time point. The probability estimate, derived from the logistic equation, for VF progression at 8 years was 66%. (E, F) VF status after 5 (08-22-94) and 8 (09-1-97) years, respectively.

The authors thank all the AGIS investigators for their contributions.