Pointwise Methods to Measure Long-term Visual Field Progression in Glaucoma

Key Points

Question  What is the relative performance of 3 pointwise methods to detect visual field progression in primary open angle glaucoma?

Findings  In this cohort study of 567 patients with primary open-angle glaucoma, the glaucoma rate index had the highest detection rate for progression and detected progression earlier than pointwise linear regression or guided progression analysis while maintaining a low rate of false-positive estimates. Agreement among methods was moderate at best and showed differences depending on baseline severity.

Meaning  These results suggest that the glaucoma rate index is a sensitive and specific method that can detect long-term visual field progression in glaucoma earlier than pointwise linear regression or guided progression analysis.

Importance  Rates of visual field (VF) progression vary among patients with glaucoma. Knowing the rate of progression of individual patients would allow appropriately aggressive therapy for patients with high rates of visual loss and protect those with low rates from unnecessary therapy.

Objective  To compare 3 pointwise methods of estimating the rate of VF progression in glaucoma.

Design, Setting, and Participants  This retrospective, observational cohort study included 729 eyes of 567 consecutive patients with primary open-angle glaucoma who had at least 6 reliable VFs and at least 3 years of follow-up. One hundred seventy-six patients (257 eyes) were treated at a tertiary glaucoma center; in addition, data were collected from 391 participants (472 eyes) in the Advanced Glaucoma Intervention Study. Data were collected from May 1988 to November 2004 and analyzed from October 2018 to February 2019.

Exposures  Estimates of VF progression were measured with guided progression analysis (GPA), pointwise linear regression (PLR), and the glaucoma rate index (GRI). A subgroup analysis was performed in a subset of patients with likely VF progression and likely VF stability.

Main Outcomes and Measures  Proportion of VF series detected as progressing, estimates of false-positive proportions, time to detect progression, and agreement among measures.

Results  Among the 567 patients included in the analysis, mean (SD) age was 65.6 (9.7) years, 300 (52.9%) were female, and 295 (52.0%) were white. The median baseline mean deviation was −6.7 (interquartile range [IQR], −11.6 to −3.5) dB; the median follow-up time, 8.9 (IQR, 7.3-10.4) years. The proportion of eyes labeled as progressing was 27.7% according to the GPA, 33.5% according to the PLR, and 52.9% according to the GRI; pairwise differences for GRI vs PLR were 20% (95% CI, 17%-23%); for GRI vs GPA, 25% (95% CI, 22%-29%); and for PLR vs GPA, 6% (95% CI, 3%-9%; P < .001 for all comparisons, McNemar test). The shortest median time to progression was with the GRI (8.8 [IQR, 2.4-10.5 years), compared with the GPA and PLR (both >16 years). The hazard ratio of VF progression for GRI vs PLR (reference) was 11.3 (95% CI, 9.2-13.7); for GRI vs GPA (reference), 18.1 (95% CI, 14.5-22.6); and for PLR vs GPA (reference), 1.5 (95% CI, 1.3-1.9; P < .001 for all comparisons, Cox proportional hazards regression). These results held in the subgroup with likely progression; the proportions of progressing eyes were 73.7% (115 of 156) for GPA, 81.4% (127 of 156) for PLR, and 92.9% (145 of 156) for GRI. Pairwise difference for GRI vs PLR was 11.5% (95% CI, 7.4%-17.6%; P < .001, McNemar test); for GRI vs GPA, 19.2% (95% CI, 12.6%-26.4%; P < .001, McNemar test); and for PLR vs GPA, 7.7% (95% CI, 0.3%-15.7%; P = .08, McNemar test).

Conclusions and Relevance  These results suggest GRI can detect long-term VF progression in glaucoma earlier than PLR or GPA. Validation with prospective designs may strengthen the generalizability and value of this method.

Glaucoma is a progressive optic neuropathy and a leading cause of irreversible blindness worldwide.^1,2 Longitudinal visual field (VF) testing with standard achromatic perimetry continues to be a mainstay for assessing progression of visual loss. Measures of VF are correlated with vision-related quality-of-life measures and are often used as the primary outcome in clinical trials of glaucoma treatment.^3-5 The detection of true VF change is confounded by the considerable variability of perimetric measurements.^6,7

Methods for detecting perimetric progression include qualitative clinical judgment, event-based analyses, and trend-based analyses. Event-based analyses detect progression if a global index or a defined number of test locations show decreased sensitivity that exceeds a predefined prediction limit of variability.⁸ Trend-based techniques define progression by performing regression analyses on all the available VFs in a given series and provide estimates of the rate of change.

Rates of progression vary among patients with glaucoma.^9,10 Knowledge of the rate of progression of individual patients, including changes along their clinical course, together with an estimate of their longevity, provides an opportunity to optimize treatment by providing appropriately aggressive treatment to those with high rates of visual loss and sparing those with low rates the morbidity of unnecessary treatments.¹¹

Event- and trend-based methods can be applied to global parameters, such as mean deviation (MD) or visual field index; regional parameters, such as sensitivity or MD of VF clusters; and in a pointwise manner to individual test locations. Pointwise approaches have the advantage of being more sensitive to localized loss and retain the clinically important spatial representation of the VF. An experienced examiner can add specificity to the VF assessment by accounting for the spatial relationships of change.

The purpose of this study is to compare the performance of 3 pointwise methods for detection of glaucoma progression. Two of these approaches, guided progression analysis (GPA) and pointwise linear regression (PLR), are well known and frequently used in clinical and research environments. The third approach, the glaucoma rate index (GRI), has been recently described.^12,13

This study followed the tenets of the Declaration of Helsinki for research on human subjects,¹⁴ was approved by the UCLA Human Research Protection Program without requiring informed consent, and adhered to Health Insurance Portability and Accountability Act compliance regulations. This retrospective cohort study involved no more than minimal risk to the participants and did not adversely affect their rights and welfare. In addition, this study was not a clinical investigation subject to US Food and Drug Administration regulations. Considering these conditions, the UCLA institutional review board guidelines did not require an informed consent to be obtained from the participants of this study. All patient data used in the study were deidentified and labeled with a code that only the investigators of this study could access. This study followed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) reporting guideline.

Data were collected from May 1988 to November 2004. Patients with primary open-angle glaucoma belonging to either of 2 cohorts were included: 257 eyes of 176 patients treated at the Glaucoma Division, Stein Eye Institute, UCLA (this group of patients is a subset of a cohort of 253 patients selected for a different comparison of methods described by Kim et al¹⁵), and 472 eyes of 391 patients from the Advanced Glaucoma Intervention Study (AGIS). The AGIS study design and methods have been described in detail previously.⁵

All patients had 6 or more reliable VFs and a minimum follow-up of 3 years. The VFs were considered reliable if they had less than 15% false-positive rates and less than 30% fixation losses and false-negative rates according to previous criteria.¹⁵ Tests were performed with the Humphrey Visual Field Analyzer (Carl Zeiss Ophthalmic Systems, Inc) with a 24-2 test pattern and size III white stimulus. Full-threshold strategy was used in the AGIS cohort, and the Swedish Interactive Thresholding Algorithm standard strategy was used in the UCLA cohort.

Each VF series was analyzed with the following methods. First, GPA (software available on the Humphrey Visual Field Analyzer) involved a pointwise event-based analysis of VF progression. Pointwise mean pattern deviation values were calculated from 2 baseline VFs and were compared with those obtained at each subsequent VF test. Significant change at 2-sided P < .05 at a given location was considered pointwise progression. Confirmed worsening of a given location on 1, 2, or 3 consecutive examinations was documented. If progression of the same 3 or more locations on 3 or more consecutive examinations was measured, the series was labeled as progressing (criteria established by the Early Manifest Glaucoma Trial³). Locations marked with an X on the GPA printout have low threshold baseline values that prevent meaningful comparison, making them unsuitable for further analysis. In addition, when a substantial number of X locations is present in a severely depressed VF, the GPA software does not generate a global result. Those VFs were excluded from this analysis.

Second, PLR of the threshold sensitivity over time was performed, and the rate of change was expressed in decibels per year. A rate of change of at least −1.0 dB/y and 2-sided P < .01 defined a single location as decaying; the entire VF series was labeled as progressing if at least 3 locations met the above requirements.¹⁶ Locations having a threshold sensitivity value of 0 dB in 2 of the first 3 examinations were excluded.

Third, we used the GRI, a recently described trend-based method to measure VF progression that demonstrated good sensitivity and compared favorably to other methods.^12,13 Briefly, a monotone increasing or decreasing pointwise exponential regression was applied if a pointwise series in the VF was categorized as improving or decreasing, respectively. After pointwise exponential regression was calculated, the pointwise rate of change was expressed as the proportional change per year of the entire perimetric range corrected for age and location. An overall rate index was generated by summing all statistically significant pointwise rate of change values (details in eMethods in the Supplement), which were then normalized from a maximum rate of decay (−100) to a maximum rate of improvement (+100); a GRI value of −6 or less defines progression.¹² Test locations at which 2 of the first 3 tests had a sensitivity value of 0 dB were excluded.

Comparisons of results between methods were limited by the lack of a criterion standard for the detection of true progression. To establish a common reference for comparisons among the 3 methods of this study, we applied a method known for its high specificity,^13,17,18 the AGIS scoring system, to the entire database. As previously detailed,⁵ each VF was assigned a score based on the number, depth, and spatial distribution of depressed locations (details in the eMethods in the Supplement). Eyes progressing according to the AGIS score were defined as a reference group with likely progression that could be used to find a surrogate measurement of sensitivity.

Similar to the approach for the group with likely progression, we applied a method with high sensitivity,^13,19 permutation analyses of pointwise linear regression (PoPLR),²⁰ to the entire cohort to generate a subgroup of likely stable eyes. The PoPLR algorithm used data from each individual patient to establish significance of progression (details in the eMethods in the Supplement). We used the reported high positive rate of PoPLR to establish a reference group with low false-negative findings as a surrogate measurement of specificity, which we reported as an estimated false-positive proportion (FPP).

Data were analyzed from October 2018 to February 2019. All statistical analyses were performed with the open-source programming language R, version 3.4.3 (R Project for Statistical Computing).²¹ Proportions of eyes and locations labeled as progressing according to each method were calculated, and their overlap was identified with a Venn diagram. The McNemar test was used to compare pairwise sensitivities for detection of progression. Pairwise agreements of methods were estimated with the Cohen κ statistic, and 95% CIs were reported. The κ values were classified as slight (0-0.2), fair (>0.2-0.4), moderate (>0.4-0.6), substantial (>0.6-0.8), and almost perfect (>0.8-1.0) agreement levels.²² Time to detection of progression was estimated with Kaplan-Meier curves, and differences were evaluated with the Cox proportional hazards regression model, which used a shared frailty approach to account for nonindependence of fellow eyes; hazard ratios (HRs) and 95% CIs were reported.

We also investigated the detection of progression for each method, time to detect progression, and agreement between methods in the entire database as a function of baseline VF severity status in a post hoc analysis; according to the baseline MD, eyes were categorized into mild (>−6 dB), moderate (≤−6 to≥−12 dB), and severe (<−12 dB) VF loss.²³

We included 729 eyes of 567 patients for analysis, of whom 295 (52%.0) were white, 300 (52.9%) were female, and 267 (47.1%) were male. Mean (SD) age was 65.6 (9.7) years. Median follow-up was 8.9 (interquartile range [IQR], 7.3-10.4) years, and median number of VFs obtained was 14 (IQR, 12-17). Median baseline MD (the mean of the first 2 VFs in a sequence) was −6.7 (IQR, −11.6 to −3.5). Demographic and clinical data for the entire cohort and the subgroups with likely progressors and likely stability are reported in Table 1. A total of 4410 VFs were part of this analysis; 79 VF examinations in which GPA could not generate a result were excluded.

As shown in Figure 1A, the detection rate for VF progression in the entire cohort was highest for GRI (52.9%), followed by PLR (33.5%) and GPA (27.7%). Pairwise differences for PLR vs GPA were 6% [95% CI, 3%-9%]; for GRI vs GPA, 25% [95% CI, 22%-29%]; and for GRI vs PLR, 20% [95% CI, 17%-23%]; P < .001 for all comparisons, McNemar test). According to Kaplan-Meier analysis, the GRI had a median time to detect progression of 8.8 (IQR, 2.4-10.5) years, shorter than the time for the other 2 methods (HR for PLR vs GPA [reference], 1.5 [95% CI, 1.3-1.9]; HR for GRI vs GPA [reference], 18.1 [95% CI, 14.5-22.6]; HR for GRI vs PLR [reference], 11.3 [95% CI, 9.2-13.7]; P < .001 for all comparisons using Cox proportional hazards regression with mixed-effects model) (Figure 2A). The median times for PLR and GPA (>16 years) could not be generated because the proportion of patients detected as progressing by either method was less than 50% during the entire follow-up (Figure 2A).

Pairwise agreement of each VF series was similar within the moderate range for all comparisons. The κ values for detection of progression were 0.59 (95% CI, 0.54-0.64) between GRI and PLR, 0.56 (95% CI, 0.49-0.62) between PLR and GPA, and 0.43 (95% CI, 0.37-0.48) between GRI and GPA.

The number of eyes with mild glaucoma was 270; moderate glaucoma, 252; and severe glaucoma, 207. For all severities, GRI remained the method with the highest detection of progression (range, 50.0%-55.1%), whereas agreement on detection between methods was better in the group with mild damage (κ range, 0.58-0.59 vs 0.38-0.63 for moderate and 0.28-0.57 for severe damage); complete results are shown in Table 2. At each severity level, GRI had shorter times than PLR or GPA, because median times could not be generated for these 2 methods. For GRI, a longer time to detect progression was seen in the mild group (median, 17.2 [IQR, 2.7 to >18.8] years) compared with the moderate (4.9 [IQR, 2.6-14.8] years) and severe (median, 5.0 [IQR, 2.1-7.6] years) groups (eFigure 1 in the Supplement). The Venn diagram depicted in eFigure 2 in the Supplement shows that of 405 eyes found to be progressing by any method, 152 eyes (37.5%) progressed according to all methods, 113 (27.9%) were detected only by GRI, 14 (2.0%) only by GPA, and 2 (0.3%) only by PLR.

A total of 37 908 test locations of 729 eyes were evaluated. The numbers of excluded locations based on GPA and GRI criteria were similar at 2895 (7.6%) and 3455 (9.1%), respectively, whereas 846 locations (2.2%) were excluded by both methods.

Pointwise decay proportions were 23% for GRI, 9% for PLR, and 6% for GPA criteria. The percentage of decaying locations represented in spatially conserved plots according to each criterion are shown in Figure 3.

Of the 729 eyes in the entire cohort, 156 progressed according to the AGIS scoring system and were considered to have likely progression. In this group, 145 (92.9%) of eyes were considered to have progression according to GRI, 127 (81.4%) according to PLR, and 115 (73.7%) according to GPA (pairwise differences for PLR vs GPA, 7.7% [95% CI, 0.3%-15.7%; P = .08, McNemar test]; for GRI vs GPA, 19.2% [95% CI, 12.6%-26.4%; P < .001, McNemar test]; for GRI vs PLR, 11.5% [95% CI, 7.4%-17.6%; P < .001, McNemar test]) (Figure 1B). Median time to progression was fastest for GRI (2.5 [IQR, 1.9-3.7] years), followed by PLR (4.7 [IQR, 3.1-7.9] years) and GPA (6.0 [IQR, 3.8-8.9] years) (HR for PLR vs GPA [reference], 1.4 [95% CI, 1.1-1.9; P = .02 using Cox proportional hazards regression with mixed-effects model]; HR for GRI vs GPA [reference], 10.3 [95% CI, 7.6-14.1; P < .001 using Cox proportional hazards regression with mixed-effects model]; HR for GRI vs GPA [reference], 7.2 [95% CI, 5.3-9.6; P < .001 using Cox proportional hazards regression with mixed-effects model]) (Figure 2B). The Venn diagram (eFigure 2 in the Supplement) shows that of 148 eyes found to be progressing by any method, 101 (68.2%) progressed according to all methods, 7 (4.7%) were detected only by GRI, 3 eyes (2.0%) were detected only by GPA, and no eyes were detected as progressing only by PLR criteria.

Of the entire group of eyes, 176 were considered stable according to the PoPLR algorithm (Figure 1C). Very low estimated FPPs were found for all methods (Figure 1), with 2.2% for GPA and 0.6% for both PLR and GRI (pairwise differences for PLR vs GPA, 1.7% [95% CI, 0.5%-4.9%; P = .25, McNemar test]; for GRI vs GPA, 1.7% [95% CI, 1.1%-5.2%; P = .38, McNemar test]; GRI vs PLR, 0 [95% CI, −2.7 to 2.7; P > .99, McNemar test]).

We compared 3 pointwise methods to detect glaucoma progression: GPA, PLR, and GRI. Our results suggest the GRI has a high detection rate and can identify disease deterioration earlier than PLR or GPA. These results held in a subset of patients with likely progression based on an external criterion. In a subset of patients with likely stable disease, all methods had low estimated FPPs. When a stratified analysis was performed based on severity, both trend-based outcomes remained consistent among severity groups; GPA had lower detection rates than PLR and GRI in eyes with severe damage.

A common limitation of comparative studies in this field is addressing sensitivity and specificity without an external (criterion standard) reference. To overcome this problem, researchers have used several approaches. Clinician judgment, which is a common approach in clinical practice, has been used as the reference standard in some studies; however, it is time consuming and cumbersome, and its reliability is suspect.²⁴ Other approaches include short-term test-retest data and computer simulation models.^17,25 We used a different approach in this study to provide an estimate of sensitivity and specificity. By selecting eyes with progression according to a well-known external method that has shown consistently high specificity (the AGIS scoring system),^17,18 we defined a subgroup with likely progression. Detection of progression in this group of eyes may be regarded as a surrogate for the sensitivity of each method evaluated. The results in this group were consistent with the findings in the entire cohort, with GRI demonstrating the highest detection rate.

For the group with likely stable disease, we chose the PoPLR method, which has been reported to exhibit a high sensitivity.^13,19,20 In this group considered to have likely stability, we found low estimated FPPs, which indicates a high surrogate specificity for all 3 methods tested.

Although event-based methods offer a binary outcome that is determined by exceeding test-retest variability between initial and final values, trend-based methods use all the data available and define progression based on rates of change. Hence, the latter methods are more sensitive to small and gradual localized changes,^26,27 with the caveat of more VF tests required to attain reasonably reproducible trends.²⁸ Previous studies that included comparisons between the GPA and the PLR^19,29 have reported higher detection rates but longer times to detect progression with the former vs the latter; however, based on a clustered VF paradigm used in the UK Glaucoma Treatment Study,²⁹ it has been proposed that trend-based methods may have increased power to detect progression during short follow-up.³⁰

The moderate agreement between methods in this study is consistent with previous reports in the literature.^17,31,32 Our results show higher κ values between trend-based methods when compared with the event-based approach. Nouri-Mahdavi et al³³ reported modest spatial agreement of about one-third of the locations found to be progressing separately by PLR and glaucoma change probability. eFigure 3 in the Supplement shows a typical example of the discrepancy in the spatial correlation of decaying locations in an eye in the likely progression group in which change was detected with GRI but not with GPA.

In our stratified analysis based on severity, no substantial changes in detection rates or agreement among the 3 categories of glaucoma damage was observed with GRI or PLR. The proportion of progressing eyes with GPA and agreement with PLR and GRI declined in the moderate and severe groups. This finding has been reported before. Tanna et al³⁴ compared GPA with clinician assessment of VFs with a subset analysis based on severity. Agreement was higher in eyes with early moderate damage (κ = 0.55) compared with eyes with the worst VF (κ = 0.36). This outcome is likely related to a limitation of the GPA software wherein no result is provided by the software in badly damaged VFs (usually MD of<−15 dB). Time to detect progression stratified by severity showed that the baseline MD level is profoundly associated with these results with longer times in the mild group compared with moderate and severe groups (eFigure 1 in the Supplement).

Progression of the glaucomatous VF has been shown to exhibit a nonlinear trend.^35,36 Pathak et al³⁷ demonstrated that an exponential fit improved prediction of VF data compared with a linear one. In agreement with these observations, previous work found that nonlinear models display superior fits for VF data: Otarola et al³⁸ showed that the long-term pattern of perimetric decay is better represented with the asymptotic trends of nonlinear models, and Caprioli et al³⁹ reported a method to measure regional VF decay rates with pointwise exponential regressions of threshold sensitivity. The GRI uses an exponential function to measure rates of change, and our results show that the GRI has a higher detection rate, measures progression earlier, and has similarly low FPP, compared with PLR. Although PLR and GPA accept all VF data, the GRI method incorporates removal of outliers and a statistical barrier for significant change based on the 95% CI band (eMethods in the Supplement).

Limitations of this study include the retrospective design and irregular intervals of VF testing (in the UCLA group). Intrinsic differences in the Swedish Interactive Thresholding Algorithm and full-threshold strategies result in progression outcomes that may not be equivalent with the methods compared herein.⁴⁰ Other limitations are a function of the algorithms described; for instance, in this analysis we selected only 1 set of criteria for progression with GPA (used in the Early Manifest Glaucoma Trial) and with PLR of the various combinations reported in the literature based on number of locations or the significance value of the slope.¹⁷ Given the anatomical arrangement of the retinal nerve fibers with a corresponding representation on the VF, the addition of spatial information improves detection of real change in the VF.^25,41 We included patients with a wide range of disease severity and long-term follow-up to improve the clinical relevance and applicability of our results. The reported very low sensitivity (11%-22%³³) of the AGIS score restricts identification of most patients with true-positive findings but allows us to obtain a subset in which we can have a high likelihood of progression.

Our study compared outcomes and agreement of pointwise methods to assess glaucoma progression. The trend-based GRI had the highest sensitivity to detect progression and exhibited the shortest time to detection while maintaining a low estimated false-positive rate. Significant differences were seen depending on baseline severity. These results suggest GRI can detect long-term VF progression in glaucoma earlier than PLR or GPA. Additional validation in prospective designs could strengthen the generalizability and value of this innovative technique to model longitudinal VF measurements.

Accepted for Publication: February 12, 2020.

Corresponding Author: Joseph Caprioli, MD, Glaucoma Division, Jules Stein Eye Institute, David Geffen School of Medicine, UCLA, 100 Stein Plaza, Los Angeles, CA 90095 (caprioli@jsei.ucla.edu).

Published Online: April 2, 2020. doi:10.1001/jamaophthalmol.2020.0647

Author Contributions: Drs Salazar and Caprioli had full access to all the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.

Concept and design: Salazar, Rabiolo, Lin, Caprioli.

Acquisition, analysis, or interpretation of data: Salazar, Morales, Rabiolo, Capistrano, Lin, Afifi, Yu, Nouri-Mahdavi.

Drafting of the manuscript: Salazar, Morales, Lin, Caprioli.

Critical revision of the manuscript for important intellectual content: Salazar, Morales, Rabiolo, Capistrano, Afifi, Yu, Nouri-Mahdavi, Caprioli.

Statistical analysis: Salazar, Morales, Capistrano, Lin, Afifi, Yu, Caprioli.

Obtained funding: Caprioli.

Administrative, technical, or material support: Salazar, Capistrano, Lin, Caprioli.

Supervision: Lin, Nouri-Mahdavi, Caprioli.

Conflict of Interest Disclosures: Dr Nouri-Mahdavi reported receiving personal fees from Aerie Pharmaceuticals, Inc, and Heidelberg Engineering, Inc, outside the submitted work. Dr Caprioli reported receiving grants from Aerie Pharmaceuticals, Inc, Alcon, Allergan, Inc, Glaukos Corporation, New World Medical, Inc, RPB, Simms/Mann Family Foundation, and Payden Fund during the conduct of the study. No other disclosures were reported.

Funding/Support: This study was supported by RPB, the Simms/Mann Family Foundation, and grant K23 5K23EY022659 from the National Institutes of Health.

Role of the Funder/Sponsor: The sponsors had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

Meeting Presentation: This paper was presented as a poster at the 91st Annual Meeting of the Association for Research in Vision and Ophthalmology; April 29, 2019; Vancouver, British Columbia, Canada.