Global and Pointwise Rates of Decay in Glaucoma Eyes Deteriorating according to Pointwise Event Analysis

Abstract

Purpose.: To estimate rates of change in glaucoma eyes deteriorating according to pointwise event analysis (Guided Progression Analysis, GPA).

Methods.: A total of 274 eyes with six or more reliable visual fields (VF) ≥ 5 years were enrolled (baseline mean deviation [MD]: −4.2 ± 4.5 dB). Pointwise and global rates of decay from linear regression analyses were estimated up to the time of VF deterioration according to GPA or until the last follow-up visit in stable eyes. Relationship of rates of decay with time to worsening and eccentricity and agreement of global and pointwise trend analyses with GPA were explored.

Results.: Seventy eyes (25.5%) worsened according to GPA. A statistically significant global rate of decay (P < 0.05) was observed in 54% (MD) and 62% (visual field index) of deteriorating eyes compared to 22% and 22% in stable eyes (κ = 0.32 vs. 0.37 for agreement with GPA). Rates of decay diminished with longer time to initial worsening and were faster in points within the central 10° of fixation compared to 20° and 30° regions (P = 0.025 and 0.279, respectively). Established criteria for pointwise linear regression (PLR) detected only 31% of locations deteriorating by GPA. Less stringent PLR criteria led to improved agreement with GPA at the expense of higher false detection rate.

Conclusions.: Global and pointwise rates of decay decreased with longer time to VF deterioration. The agreement between pointwise event analysis and global trend analyses was fair. Less stringent criteria for PLR led to improved agreement with GPA at the expense of higher false detection rate.

Introduction

Accurate methods to measure rates of decay in glaucoma are essential to monitor patients and evaluate the efficacy of therapy. Standard achromatic perimetry (SAP) remains the gold standard for measuring the extent of functional damage in glaucoma and for detecting disease worsening over time.^1–3 Several methods have been explored over the last few decades to identify visual field deterioration. ^1–3 These methods are categorized as either “event-based” (such as Guided Progression Analysis or GPA) or “trend-based” analyses (such as pointwise linear regression or PLR). Guided Progression Analysis is software available on the Humphrey Field Analyzer (HFA; Carl Zeiss Meditec, Dublin, CA) to aid clinicians in evaluating visual fields series for stability versus deterioration. The first two reliable visual fields in a series are averaged to create a “baseline” against which future visual fields are compared. Limits of variability have been determined through examination of series of stable glaucoma patients multiple times during a short period of time. ^4–6 A reduction in threshold beyond the 95% confidence interval of variability for a given test location is flagged as potentially abnormal. On the other hand, trend analyses use linear or other forms of regression analyses to estimate rates of change in global indices such as mean deviation (MD) or visual field index (VFI), in visual field clusters, or at individual test locations (PLR). Criteria for PLR have been mostly arbitrary and based on the fact that the average decay rate for the sensitivity at individual test locations has been estimated to be approximately 0.1 dB/y in cross-sectional studies. Based on the magnitude and statistical significance of the slope on regression analysis, visual field deterioration has traditionally been defined as a binary outcome especially for PLR rather than measured as a continuous variable (dB/y). While it has been demonstrated that threshold sensitivities uncorrected for generalized depression of the hill of vision (or total deviation data) are superior to corrected sensitivities for detection of worsening with trend analyses, ^7,8 the current GPA software uses corrected sensitivities or pattern deviation data and has been shown to be reasonably sensitive and specific. ^6,9 Although pointwise event analysis provides clinicians with valuable information regarding possible clinically significant deterioration of the visual field, it does not provide any temporal information (i.e., rates of decay). Significant worsening of the visual field needs to be interpreted within the context of the disease, especially rates of change and the remaining lifetime of the patient. 

The goal of the current study is to estimate global and pointwise rates of decay in glaucomatous eyes worsening according to pointwise event analysis. We hypothesized that the estimated rates of decay decreased with longer time to initial detection of worsening on pointwise event analysis. If so, defining fixed criteria for the magnitude of worsening on global or pointwise trend analyses may lead to reduced likelihood of detection of visual field worsening as follow-up time increases. 

Methods

Study Subjects

Two hundred seventy-four eyes (207 patients) met predetermined inclusion criteria (see below). The Institutional Review Board at the University of California-Los Angeles approved the study, and the tenets of the Declaration of Helsinki were followed. The inclusion criteria were as follows: age > 30 years, baseline best-corrected visual acuity (BCVA) 20/100 or better, follow-up time ≥ 5 years, spherical equivalent less than 8 diopters and astigmatism < 3 diopters, and availability of six or more reliable SITA (Swedish interactive thresholding algorithm)-standard SAP visual fields. Eyes with significant retinal or neurological diseases were excluded. 

Eyes with at least two consecutive, reliable abnormal visual field test results at baseline, demonstrating a pattern standard deviation (PSD) with P < 0.05 and/or Glaucoma Hemifield Test (GHT) flagging “Outside Normal Limits,” were classified as glaucomatous regardless of the appearance of the optic disc. Visual fields not meeting criteria for abnormality were considered normal. Those with suspected glaucoma had suspicious optic discs and/or elevated intraocular pressure (IOP > 21 mm Hg) with normal visual field results at baseline. If both eyes of the same patient were eligible for the study, both were included in the analyses. Each patient was treated at the discretion of the attending ophthalmologist during the follow-up period. The following baseline demographic and clinical data were extracted from the charts: age, sex, race, BCVA, refractive error, lens status, Goldmann IOP measurements, and number of medications. The number of laser and incisional glaucoma surgeries during follow-up was also recorded. 

Visual Field Methods

Standard achromatic perimetry exams (24–2 SITA standard) were exported to a personal computer using PeriData software (version 1.2; PeriData Software GmbH, Hurth, Nordrhein-Westfalen, Germany). Visual field reliability criteria for inclusion in the study were fixation loss and false negative response rate ≤ 25%, and false positive rate ≤ 15%. Gaze tracking was not turned on for any of the perimetry tests. Eyes detected as deteriorating according to GPA criteria (flagged as “Likely Progression” by the HFA) were identified. Guided Progression Analysis uses the Early Manifest Glaucoma Trial (EMGT) criteria to define worsening. ⁶ Presence of three test locations showing deterioration on three consecutive exams is flagged as “Likely Progression” by the GPA. Eyes showing a severe baseline defect where the pattern deviation plot does not display any information, as well as eyes where the follow-up GPA results failed to provide any information because of significant worsening leading to advanced glaucomatous field loss (according to GPA's criteria), were excluded. 

Univariate linear regression analyses were carried out on the global indices MD and VFI to determine rates of change over time. Pointwise linear regression analyses were performed on sensitivity at individual test locations against time. All regression analyses included only exams up to the time of confirmed visual field worsening according to GPA or all available exams for stable eyes. Time to deterioration according to GPA was determined to be when the message “Likely Progression” was displayed. Global and pointwise rates of worsening were compared in deteriorating and stable eyes. Agreement of global and pointwise trend analyses with pointwise event analysis for detection of visual field worsening at individual test locations was investigated. Various cutoff values for the P value with PLR were explored to determine whether changes in criteria for detection of pointwise trends would result in better agreement between trend and event analyses. 

Statistical Analysis

Cohen's Kappa statistic was used to estimate agreement of the categorical variables (binary decisions regarding visual field deterioration or lack thereof). We used appropriate Gaussian and non-Gaussian statistics (paired t-test, Kruskal-Wallis, or Wilcoxon's rank sum test) for comparing numerical data, as required. The cutoff point for statistical significance was set at <0.05. Multiple comparisons performed would potentially increase chances of a type I error, but we felt this would be acceptable given the exploratory nature of this study. The correlation between the two eyes of the same patient was adjusted for where appropriate and feasible. 

Results

Two hundred seventy-four eyes (207 patients) were included in the study. Table 1 describes the baseline characteristics of our study sample in the entire group and according to worsening based on GPA. More than 80% of the study patients were Caucasian, and 93% of the eyes demonstrated evidence of visual field loss at baseline. The average (±SD) baseline MD, number of visual fields, and follow-up time were −4.3 (±4.5) dB, 10.8 (±2.8), and 8.5 (±2.4) years, respectively. The mean logarithm of the minimum angle of resolution (LogMAR) at baseline was 0.14 ± 0.17 (equivalent to average acuity of 20/28) and slightly worsened to 0.19 ± 0.17 (equivalent to average acuity of 20/31) at last follow-up. Seventy eyes (25.5%) of 61 patients deteriorated according to GPA with a median (range) of 3 (3–8) worsening test locations per eye. 

Table 1. 

 

Baseline Demographic and Clinical Characteristics of 274 Eyes of 207 Patients

	Total	Deterioration Based on GPA	Stable Based on GPA	P Value
Number of eyes (patients)	274 (207)	70 (61)	204 (146)
Age, y, average ± SD	76.3 ± 10.5	76.8 ± 10.3	77.1 ± 9.8	0.718*
Sex, male/female	102 (49.3%)/105	30 (49.2%)/31	71 (48.6%)/75	0.424†
Eye laterality, right/left	139/135	29/41	110/94	0.841†
Race, number of patients (%)
White	166 (80.2%)	45 (73.8%)	121 (82.9%)	0.08*
Asian	18 (8.7%)	8 (13.1%)	10 (6.8%)
African American	13 (6.3%)	4 (6.5%)	9 (6.2%)
Hispanic	5 (2.4%)	2 (3.3%)	3 (2.1%)
Middle Eastern	5 (2.4%)	2 (3.3%)	3 (2.1%)
Diagnosis
Glaucoma, eyes	254 (92.7%)	66 (94.3%)	188 (92.1%)	0.71*
Glaucoma suspect, eyes	20 (7.3%)	4 (5.7%)	16 (7.8%)
BCVA, LogMAR	0.14 ± 0.17	0.12 ± 0.13	0.14 ± 0.14	0.627*
Spherical equivalent, average ± SD	−0.18 ± 5.2	−0.20 ± 2.23	− 0.17 ± 5.89	0.321*
IOP at baseline, mm Hg, average ± SD	15.7 ± 5.7	15.5 ± 6.03	15.8 ± 5.6	0.768*
Number of IOP-lowering medications at baseline, average ± SD	1.3 ± 1.2	1.5 ± 1.2	1.3 ± 1.2	0.513*
Baseline mean deviation, dB, average ± SD	−4.2 ± 4.5	−4.5 ± 4.1	−4.1 ± 4.7	0.552*
Baseline PSD, dB, average ± SD	4.5 ± 3.5	4.7 ± 3.2	4.2 ± 4.7	0.453*
Number of visual field exams per eye, average ± SD	10.8 ± 2.8	11.1 ± 2.9	10.6 ± 2.8	0.766*
Visual field follow-up time, y, average ± SD	8.5 ± 2.4	8.4 ± 2.4	8.6 ± 2.4	0.552*

*  Mann-Whitney U test was used for analysis.

†   χ ² test was used for analysis.

Visual field deterioration according to GPA occurred after a median (interquartile range, IQR) of 6.1 (4.1–7.9) years. The median (IQR) absolute change in MD and VFI up to the time of progression in eyes demonstrating worsening according to GPA was −3.1 (−1.6 to −4.8) dB and −8% (−4% to −15%) compared to −0.9 (0.6 to −2.6) dB and −1% (0% to −5%) in stable eyes (P < 0.001; Figs. 1, 2). A statistically significant global slope (P < 0.05) was observed in 54% and 62% of the eyes deteriorating based on pointwise event analyses according to MD and VFI, compared to 22% and 22% in stable eyes (κ = 0.32 vs. 0.37, respectively, for agreement with GPA; Table 2). Among the 70 eyes that worsened according to GPA, no eye demonstrated improvement based on MD and VFI (slope > 0 and P < 0.05). Six (9%) and two (3%) eyes demonstrated improvement with MD and VFI (slope > 0 and P value < 0.05), respectively, among the stable eyes. 

Figure 1. 

 

Distribution of mean deviation rates of change as a function of presence or absence of visual field deterioration on pointwise event analysis (Guided Progression Analysis).

Figure 2. 

 

Distribution of rates of change for visual field index as a function of presence or absence of visual field deterioration on pointwise event analysis (Guided Progression Analysis).

Table 2. 

 

Agreement of Pointwise Event Analysis (Based on GPA on Humphrey Field Analyzer) with Trend Analyses on Global Indices (Mean Deviation and Visual Field Index) for Detection of Glaucoma Progression

	Pointwise Event Analysis (GPA)
	Worsening	Stable	Kappa	95% CI	Agreement
Mean deviation
Worsening	37 (14%)	41 (15%)	0.316	0.189 to 0.424	73%
Stable	33 (12%)	163 (60%)
Visual field index
Worsening	44 (16%)	46 (17%)	0.368	0.249 to 0.487	74%
Stable	26 (10%)	158 (58%)

The magnitude of MD and VFI rates of decay tended to diminish with increasing duration of follow-up in eyes worsening according to GPA regardless of statistical significance (Fig. 3). The agreement between significant MD and VFI rates of decay (defined as slopes with P < 0.05) was fair (observed agreement 74.5% versus expected agreement 57.1%, κ = 0.404; 95% confidence interval [CI]: 0.284–0.524). As shown in Figure 4, the slope for the correlation of VFI versus MD rates of decay was significantly different between stable eyes and eyes deteriorating according to GPA (regression slope = 1.30, 95% CI: −0.95–1.65 for stable eyes versus 3.46, 95% CI: 2.89–4.11 for worsening eyes). Although the correlation of VFI and MD rates of decay was higher in worsening eyes (Spearman's correlation coefficient 0.88 vs. 0.70; P < 0.001 for the difference), the variability between the two indices was higher as evidenced by the higher scatter of points around the line of best fit for deteriorating eyes (P < 0.001 for comparison of residuals for the stable and deteriorating groups). 

Figure 3. 

 

Magnitude of rates of change for mean deviation (A) and visual field index (B) diminished as time to initial detection of visual field deterioration increased. The fitted spline curves demonstrate the trends.

Figure 4. 

 

Correlation of VFI and MD rates of change according to presence or absence of visual field deterioration on pointwise event analysis (Humphrey Field Analyzer's Guided Progression Analysis). It can be seen that the slope for the line of best fit was significantly larger in eyes worsening based on Guided Progression Analysis.

The median pointwise rate of decay at test locations demonstrating evidence of deterioration on GPA was −2.1 dB/y (IQR: −3.6 to −1.0 dB/y) and became smaller with increasing time to event (Spearman's ρ = 0.57; P < 0.001; Fig. 5). The correlation did not change after exclusion of test locations with final threshold of 5 dB or less (Spearman's ρ = 0.603; P < 0.001). Worsening according to established PLR criteria (slope < −1.0 dB/y and P < 0.01) was observed in 84 out of 270 test locations (31%) demonstrating worsening on GPA. No test location among the aforementioned 270 points showed improvement on PLR. This proportion increased to 64% and 81% of test locations when less stringent P cutoff values of <0.05 and <0.1 were used without cutoff levels for the rate of decay. On the other hand, only 3% (104 out of 3513 locations) of stable locations according to GPA met the criteria for worsening on PLR. However, this number increased to 20% and 28% of stable test locations if P value cutoff points of <0.05 and <0.1 were used for pointwise trend analyses without any cutoff points for magnitude of deterioration. We also explored whether eyes flagged as “Likely Progression” during the follow-up period would still be demonstrating evidence of progression at the end of follow-up. Visual field deterioration was initially detected at the final follow-up visit in 13 eyes. Of the remaining 57 eyes, 10 eyes (18%) did not show evidence of worsening according to GPA at the last follow-up visit; 3 eyes (5%) were flagged as possible progression; and the remaining 47 eyes (77%) were considered to be deteriorating. The median number of worsening test locations at last follow-up visit, regardless of the message provided by the HFA, was 4 (range: 0–38). 

Figure 5. 

 

Magnitude of pointwise rates of change as a function of time to initial detection of visual field deterioration at test locations showing worsening on pointwise event analysis (Humphrey Field Analyzer's Guided Progression Analysis). It can be observed that pointwise rates of change diminished significantly as time to initial detection of progression increased. The horizontal dashed line represents the −1.0 dB/y cutoff level usually considered the minimum clinically significant amount of change.

The test locations across the 24–2 visual field were then divided into three groups according to eccentricity (within the central 10°, 20°, and 30° concentric regions, respectively). The corresponding median (IQR) rates of change in the 10°, 20°, and 30° concentric regions were −2.6 (−4.1 to −1.1), −1.7 (−1.0 to −2.9), and −2.0 (−3.6 to −1.4) dB/y (P = 0.047, Kruskal-Wallis test; Fig. 6). The P values for pairwise comparison of rates of decay among the three concentric areas were as follows (Wilcoxon's rank sum test): P = 0.025 for 10° vs. 20° regions; P = 0.279 for 10° vs. 30° regions; and P = 0.072 for 20° vs. 30° regions. The P value cutoff point for statistical significance after Bonferroni correction would be 0.017 given the multiple comparisons performed. 

Figure 6. 

 

Distribution of pointwise rates of change according to eccentricity of test locations in eyes showing deterioration on Guided Progression Analysis.

Discussion

In this longitudinal retrospective study, we investigated global and pointwise rates of change in glaucomatous eyes worsening according to pointwise event analysis (GPA). Event analyses typically do not provide information on rates of damage; therefore, it is important to determine how deterioration on event analysis relates to decay rates according to linear regression analysis, which is commonly used as an appropriate model for estimating rates of change in glaucoma both globally and at individual clusters or test locations. The current GPA software provides clinicians with trend analyses of VFI and MD, and therefore one of the goals of this study was to determine the agreement between GPA and global trend analyses. 

Our results indicate that the agreement between global trend analyses and GPA for detection of glaucoma worsening was only fair (Cohen's κ = 0.316 and 0.368 for agreement with MD and VFI, respectively). The VFI trend analysis demonstrated a somewhat stronger agreement with GPA as compared to MD, although this superior performance was marginal and is of uncertain clinical significance. One would expect VFI to be more consistent with GPA, since both use data derived after correcting for diffuse depression of the hill of vision. ¹⁰ Because of averaging of data across the entire visual field, global indices are not expected to be as sensitive as pointwise criteria for detection of visual field worsening. On the other hand, they do provide clinicians with a summary index based on which the overall visual field status and its trend can be determined. Specifically, visual field indices are less helpful in very early glaucoma because of the wide range of variability in normal individuals and the small effect that early visual field loss has on global indices. This is even more prominent with regard to VFI because of the way it is calculated. ¹¹ Our findings suggest that global indices provide information on disease worsening beyond what is provided by GPA's pointwise event analysis (Table 2). Global indices tend to have less variability than individual test locations, and this may lead to earlier detection of clinically important global trends. Such generalized trends could be filtered out by GPA's algorithm. Given the fact that VFI uses pattern deviation plots to flag abnormal test locations, the generalized trends detected by global indices but missed by GPA are not likely caused by media opacity only. We used a P value cutoff point of 0.05 for defining worsening on global trend analyses, which is similar to the type I error accepted by GPA and has been previously applied to global indices. ^11,12  

Similar to our study, Casas-Llera and colleagues found fair agreement between global indices and GPA with a trend toward better agreement between GPA and VFI compared to MD (κ = 0.52 and 0.48, respectively). ¹³ Medeiros and collaborators recently used Bayesian methods to combine event and trend analyses. ¹⁴ The investigators used the number of locations demonstrating worsening on GPA to calculate the prior probability of visual field deterioration. Trend analysis of VFI over time was used to estimate global rates of decay. The agreement between trend and event analyses was similar to that in our study (κ = 0.42) and increased to 0.68 with the Bayesian approach. This emphasizes the complementary nature of the two approaches for detection of glaucoma worsening. Cho et al. reported that the agreement between MD and VFI was not a function of glaucoma severity. ¹⁵ We found that with increasing rates of decay, the agreement of VFI and MD slopes improved while the variability between the two slopes increased (Fig. 4). Both these findings are likely side effects of the higher range of MD and VFI slopes in the deteriorating group. We expected overall MD rates of worsening to be worse than VFI rates of change because of the potential confounding effect of media opacity. However, the slope of the VFI versus MD scatter plot for worsening eyes (3.45) is not quite consistent with our hypothesis. The main clinical implication is that the MD and VFI rates of decay may not be interchangeable in eyes with faster rates of deterioration. 

Pointwise and global rates of worsening demonstrated a strong relationship with time to deterioration in our study (Figs. 4, 5). In other words, eyes that showed worsening earlier during follow-up demonstrated faster rates of decay compared to eyes worsening later during the follow-up period. Although this would be expected, other explanations need to be considered. Rates of decay could decrease because of mathematical factors since with longer follow-up, the denominator (i.e., follow-up time) increases and can lead to seemingly lower rates of progression, especially if rates of progression are not quite linear. To explore this, we plotted rates of progression in stable eyes over the initial 10 years of follow-up to avoid the confounding issue of treatment (data not shown). We found that even in stable eyes, where treatment effect is likely minimal, the rates of decay tended to decrease over time. To rule out the potential confounding caused by a floor effect, we reevaluated the pointwise scatter plots after excluding test locations with final threshold of 5 dB or lower. The results were similar, suggesting that the floor effect was not a major contributor to the change in rates observed with longer follow-up time. This slowing of rates of decay over time is not commonly appreciated, and the clinical implications with regard to PLR are important to note. Traditionally, PLR criteria have consisted of definitions for the magnitude of change as well as cutoff levels for the P value for the difference from a slope of zero. A slope or rate of deterioration ≤ −1 dB/y is a commonly used criterion for the magnitude of change with PLR. ^16,17 However, as evident on Figure 5, a significant number of test locations worsening according to GPA have a lower rate of change than this cutoff criterion (dashed line on Fig. 5). We believe this is one of the reasons the agreement between pointwise trend and event analyses has been found to be only fair. ¹⁸ When less stringent criteria for the P values were used for definition of change with PLR without any cutoff points for the magnitude of decay, the agreement between the two methods improved significantly, from 31% to 64% to 81%. Based on this, it could be construed that the currently used criteria for PLR may be too stringent, especially in eyes with slower rates of decay, where worsening is detected on GPA only after a longer period of follow-up. However, using less stringent criteria also led to a higher proportion of worsening at test locations deemed to be stable on GPA. Although there is no gold standard for visual field worsening, the EMGT criteria are considered one of the more sensitive techniques among available methods for detection of glaucoma worsening. ^9,19 Therefore, the higher proportion of test locations worsening according to PLR in the stable group when less stringent criteria are used likely represents false detection. Using global indices for estimating rates of change with no cutoff criteria for the magnitude of worsening seems reasonable and more intuitive clinically. Information from highly correlated test locations, such as those belonging to the same visual field cluster, are not currently integrated in a rational way in either event or trend analyses; such an approach may improve the performance of both techniques and their agreement. ²⁰  

An interesting finding of our study was that the rates of deterioration were highest within 10° of fixation. Peripheral visual field test locations demonstrate higher cross-sectional variability and are expected to have larger longitudinal variability because of the lower threshold sensitivity. ^4,5 Therefore, we expected to find larger slopes of change for peripheral test locations worsening on GPA as compared to more central test locations. Rates of decay, however, also depend on the natural course of the disease and the mix of any given cohort with regard to risk factors for faster visual field deterioration or factors affecting central versus peripheral visual field worsening. ²¹ It should be noted that the differences found among various regions were of borderline significance given the multiple comparisons performed. 

The results of our study need to be considered in the context of the selected study sample and methods. The GPA software does not provide any information with regard to worsening in eyes that have severe baseline field loss or for series of visual fields where deterioration leads to profound visual field loss (typically MD worse than −15 dB). ²² Therefore, our study sample represents a group of glaucoma suspects and eyes with early to moderate glaucomatous visual field loss, in which worsening, if any, was not very fast or did not lead to profound visual loss. 

In summary, we found that the agreement between GPA's pointwise event analysis and global trend analysis was only fair when either MD or VFI was used. Global and pointwise rates of decay tended to diminish with longer follow-up time. Agreement between PLR and GPA improved with less stringent criteria for definition of visual field worsening with PLR, but only at the expense of an increased false detection rate for glaucoma deterioration in seemingly stable eyes. Pointwise rates of decay were fastest within the central 10° of the visual field. 

Footnotes

 Supported in part by an unrestricted departmental grant from Research to Prevent Blindness.

Footnotes

 Disclosure: N. Nassiri, None; S. Moghimi, None; A.L. Coleman, None; S.K. Law, None; J. Caprioli, Allergan (C); K. Nouri-Mahdavi, Allergan (C)