Evaluating Visual Field Progression in Advanced Glaucoma Using Trend Analysis of Targeted Mean Total Deviation

Abstract

Purpose:

Trend analysis of visual field (VF) global indices may underestimate the rate of progression in severe glaucoma due to the influence of test points without detectable sensitivity. To test this hypothesis, we compared the rates of change of VF global indices with and without exclusion of undetectable points at various disease stages.

Methods:

Six hundred and forty-eight eyes of 366 glaucoma patients with 8 or more reliable 30–2 standard automated perimetry over more than 2 years were enrolled. We calculated targeted mean total deviation (TMTD) by averaging total deviation except points which were consistently undetectable in 3 baseline tests. Eyes were classified as early (≥ −6 dB), moderate (− 6 dB to −12 dB), advanced (−12 dB to −20 dB), and severe (< −20 dB) based on baseline mean deviation (MD). The rates of change of MD and TMTD in each stage were statistically compared

Results:

Mean age ± standard deviation at baseline was 56.9 ± 11.9 years. The MD slope (−0.34 dB/year) in severe glaucoma was significantly slower than TMTD slope (−0.42 dB/year, P=0.028) and was slower than MD slopes in the other stages. Difference between MD slopes and TMTD slopes was most prominent in eyes with MD values less than −25 dB (P=0.002).

Conclusions:

Undetectable locations in eyes with severe glaucoma may lead to an underestimate of the rates of VF progression. Trend analysis of TMTD rather than global indices offers a practical and simple approach for alleviating underestimation of VF progression in severe glaucoma.

Glaucoma is a progressive optic neuropathy characterized by structural changes in the optic nerve head and accompanying visual field (VF) damage.¹ As glaucomatous optic neuropathy is irreversible, the main goal of glaucoma treatment is to slow the deterioration of visual function to maintain the patients’ quality of life. To achieve that goal, identification of eyes with VF deterioration at a rate that threatens the patient’s visual function compared with their longevity is critical.² Trend analyses of global indices such as mean deviation (MD) and visual field index (VFI) are among the most commonly used methods for estimating the rates of VF progression (slopes).^3–6

In advanced glaucoma where there is considerable risk of developing visual disability, estimation of the rate of progression is of vital importance.⁷ However, trend analysis of global indices may underestimate the rate of progression in advanced glaucoma due to the influence of test points without detectable sensitivity (blind locations). Previous research has shown that there are a large number of test locations that are reproducibly undetectable in advanced glaucoma.⁸ Because MD slope is an average rate of VF decline from all VF test locations including both undetectable and detectable locations, this value should be smaller than the rates of only detectable locations. In support of this notion, Rao et al. reported that the rate of change in visual field index becomes slower in a very advanced stage because of a floor effect and emphasized the necessity of developing an alternative for quantifying VF progression in advanced-stage glaucoma.⁹

In this study, we sought to evaluate the impact of continuously undetectable points on the estimates of global visual field progression. To achieve this goal, we developed targeted mean total deviation (TMTD), an average of total deviation values that excludes undetectable locations. We compared the values of TMTD slopes to those of standard MD slopes in each severity stage defined by initial MD values.

Materials and Methods

In this retrospective, longitudinal, single-center cohort study, we enrolled consecutive glaucoma patients who were examined with standard automated perimetry (SAP) at Osaka University Hospital. The study was conducted in compliance with the institutional review board (IRB) of Osaka University Hospital. The IRB waived the need for written informed consent because of the retrospective and non-invasive nature of the study. The study followed the tenets of the Declaration of Helsinki.

A patient list of SAP was reviewed for selecting glaucoma patients who were examined from January 2004 to February 2020 at Osaka University Hospital. Then we reviewed the charts of the possible participants to determine the eligibility for the study. Participants were selected based on the following criteria: 1) at least 8 reliable SAP tests acquired with the Humphrey Field Analyzer (HFA; Carl Zeiss Meditec) with the 30–2 test pattern using Swedish interactive thresholding algorithm standard over at least 2 years; age 20 to 80 years at the baseline test; having a diagnosis of primary open-angle glaucoma (POAG) including normal tension glaucoma (NTG), primary angle closure glaucoma (PACG), or exfoliation glaucoma (XFG). For inclusion, VF tests were required to have fixation losses <20%, and false positive responses<15%. Glaucoma was defined as the presence of glaucomatous optic neuropathy based on photograph review by 2 independent glaucoma specialists at baseline.

Participants were divided into four subgroups based on baseline MD values: early (MD ≥ −6 dB), moderate (−6 dB > MD ≥ −12 dB), advanced (−12 dB > MD ≥ −20 dB), severe (−20 dB >MD).

Targeted mean total deviation (TMTD)

Targeted mean total deviation (TMTD) was calculated as the average of the total deviation values after excluding locations that were consistently undetected (i.e., had a threshold sensitivity value of <0dB). To calculate TMTD, we first defined undetected locations in each eye as points that consistently had <0 dB threshold sensitivity on the first three VF examinations (Figure 1). This is because locations that were consistently undetectable in 3 consecutive tests showed undetectable thresholds in 88% of subsequent tests in a previous report.⁸ TMTD values in each test were calculated by averaging the remaining deviation values. We then performed ordinary least-squares (OLS) linear regression analysis of TMTD to calculate the rate of change per year (TMTD slope) for each eye. The first VF test for each eye was excluded when calculating the TMTD slope.

Figure 1:

Calculation of TMTD slopes. First, blind locations were defined in each eye as locations consistently showed <0 dB threshold values throughout the 3 baseline tests (left panel). Then, TMTD values were calculated in each follow-up test as the mean of total deviation values after removing the baseline blind locations (top right). Finally, linear regression analysis of TMTD values against time (year) was performed in each eye to obtain TMTD slope values (bottom right).

Statistical Analysis

Descriptive statistics such as mean, median, standard deviation, and range were calculated for clinical factors including age, MD, PSD, number of tests, duration of follow-up, initial IOP, number of blind locations, MD slope, and TMTD slope to visualize the distribution of these variables in all participants as well as in each subgroup. Correlation analyses between MD slope and TMTD slope were performed to look at the inter-relationship of these slope metrics. Correlation between number of blind locations and initial MD was also analyzed. As the influence of undetectable locations on underestimation of MD slope should be most prominent in severe glaucoma, we extensively investigated the relationship between MD slope, TMTD slope, and baseline MD values in each eye in severe glaucoma.

All statistical analyses were performed using the statistical computing language R (The R Foundation for Statistical Computing, Vienna, Austria).

Results

Baseline Characteristics

Six hundred and forty-eight eyes of 366 glaucoma patients satisfied the inclusion criteria. Mean age ± standard deviation at baseline was 56.9 ± 11.9 years. Total number of VF tests was 8323. The average number of VF examinations per eye was 12.8 (range, 8–29), with median follow-up of 8.6 years. Two-hundred and ninety-eight eyes were classified as early (MD ≥ −6 dB), 174 eyes were moderate (−6 dB > MD ≥ - 12 dB), 142 eyes were advanced (−12 dB > MD ≥ −20 dB), and 34 eyes were severe (−20 dB > MD). Baseline characteristics of the participants are presented in Table 1.

Table 1:

Baseline characteristics

	Early	Moderate	Advanced	Severe	Total	P-value
Number of Eyes	298	174	142	34	298
Number of Subjects	169	99	82	16	366
Age (year)	55.2 ± 12.7	57.9 ± 10.2	59.3 ± 11.7	56.7 ± 12.8	56.9 ± 11.9	0.080
Gender (female / male)*	160 / 138	100 / 74	72 / 70	16 / 18	190 / 176	0.6431
Baseline MD (dB)	−2.43 ± 2.13	−8.9 ± 1.73	−15.49 ± 2.12	−23.8 ± 2.97	−8.15 ± 6.64	< 0.001
Number of tests	12.8 ± 4.6	13.1 ± 4.6	13.0 ± 4.8	12.4 ± 4.3	12.0 ± 3.8	0.2416
Duration of follow-up (years)	9.5 ± 2.7	8.5 ± 3.1	7.7 ± 3.1	7.3 ± 2.6	8.7 ± 3.0	< 0.001

IOP: intraocular pressure; MD: mean deviation

^*Gender was counted in by-eye basis in each stage, and by-subject basis in the total group. Because some participants had different stages between eyes.

TMTD slope, MD slope, and VF severity

Overall, TMTD slope was significantly correlated with MD slope (Figure 2, P < 0.001). Table 2 shows the distribution of TMTD slope and MD slope in each stage defined by the severity of glaucomatous VF loss. MD slope showed small but significantly smaller (more negative) values than TMTD in total participants and in early and moderate stages (0.04, 0.06, and 0.05, respectively). There was no significant difference between MD slope and TMTD slope in advanced glaucoma. MD slope was significantly larger (less negative) than TMTD slope only in severe glaucoma, and the difference was much larger than any other stage (0.16). One-way analysis of variance showed significant difference in both MD slope (P=0.001) and TMTD slope (P<0.001) among stages. Tukey test showed that MD slope was significantly slower in severe glaucoma than moderate glaucoma (P=0.0349), but no significant difference was found between early and moderate, early and advanced, early and severe, moderate and advanced, and advanced and severe glaucoma (P=0.076, 0.566, 0.416, 0.823, and 0.139, respectively). TMTD slope was significantly slower in early glaucoma than moderate and advanced glaucoma (P=0.034 and 0.019, respectively), but no difference was detected between early and severe, moderate and advanced, moderate and severe, and advanced and severe glaucoma (P=0.981, 0.987, 0.741, and 0.631, respectively). (Figure 3)

Figure 2:

Scatterplot illustrating the relationship between TMTD slope and MD slope. TMTD slope was significantly correlated with MD slope (P <0.001).

Table 2:

MD slope and TMTD slope in each stage

	MD slope	TMTD slope	P-value
Early	−0.45 ± 0.43	−0.39 ± 0.46	<0.001*
Moderate	−0.55 ± 0.41	−0.5 ± 0.41	0.002*
Advanced	−0.51 ± 0.42	−0.52 ± 0.42	0.440
Severe	−0.34 ± 0.46	−0.42 ± 0.44	0.028*
Total	−0.49 ± 0.44	−0.45 ± 0.44	<0.001*

Tables show mean ± standard deviation values.

MD: mean deviation; TMTD: targeted mean total deviation

Figure 3:

Boxplots showing the distribution of TMTD slope and MD slope in four VF stages. MD slope (white) was significantly smaller (more negative, or faster) in early and moderate glaucoma than TMTD slope (grey, P <0.001, and P=0.002, respectively), but it was significantly larger (less negative, or slower) than TMTD in severe glaucoma (P=0.028).

Figure 4 shows the scatterplot of the relationship between difference in slopes (TMTD slope minus MD slope) versus baseline MD. Investigating the relationship between MD slopes, TMTD slopes, and baseline MD values in each case of severe glaucoma, we found that underestimation of MD slope was especially pronounced in eyes with baseline MD values less than −25 dB. All of 9 eyes with baseline MD values < −25 dB showed MD slopes larger (less negative) than TMTD slopes. Average TMTD slope (−0.243 ± 0.340 dB/year) was significantly smaller than average MD slope (0.07 ± 0.331 dB/year) in these eyes (P=0.002). Six eyes (66.7%) showed positive MD slopes, half of which (3 eyes) showed negative TMTD slopes. In contrast, there was no significant difference between TMTD slope (−0.486 ± 0.448 db/year) and MD slope (−0.483 ± 0.461 dB/year) in eyes with baseline MD values between −20 dB and −25 dB (P=0.920). Only 2 eyes (0.1%) in this stage showed positive MD slope, both of which also showed positive TMTD slope values. These results clearly showed that underestimation of MD slope was most prominent in eyes with baseline MD values less than −25 dB.

Figure 4:

Scatterplot illustrating the relationship between slope difference (TMTD slope minus MD slope) and baseline MD. Difference was most prominent in eyes with MD values less than −25 dB

Number of blind locations

Total and mean ± standard deviation (SD) number of blind locations was 5274 and 8.14 ± 11.1 in the whole participants. Total and mean ± SD number of blind locations in each stage was 347 and 1.2 ± 1.1 in early, 1137 and 6.5 ± 5.9 in moderate, 2477 and 17.4 ± 8.2 in advanced, and 1313 and 38.6 ± 11.6 in severe glaucoma, respectively (Figure 5). This means that more than half of the test points were blind from the beginning and therefore had no room for further progression in severe glaucoma (MD <−20 dB). Number of blind locations and its variability increased as glaucoma stage advanced, and the correlation between number of blind locations and baseline MD value was statistically significant (P<0.001).

Figure 5:

Scatterplot illustrating the relationship between number of blind locations (locations that consistently showed <0 dB threshold throughout 3 baseline tests) and baseline MD. Number of blind locations as baseline MD worsened (P<0.001).

We investigated the percentage of blind (< 0dB) threshold sensitivity in follow-up tests at blind locations (that showed undetectable responses in baseline tests); 93.9% (48,706 of total 51,884 threshold values) of follow-up tests showed consistently undetected thresholds.

Discussion

In this study, we compared the estimated rates of VF change before (MD) and after (TMTD) removing continuously undetectable locations in eyes at various stages of glaucoma. The MD slope was significantly slower than the TMTD slope in severe glaucoma, particularly in eyes with baseline MD values less than −25 dB. More than half of the test points were consistently undetectable in severe glaucoma.

Overall, TMTD rate of change strongly correlated with MD rate of change. When both slope values were compared in each severity stage, MD rate of change was significantly slower than TMTD rate of change in severe glaucoma. This suggests the underestimation of progression by MD slope in severe glaucoma. On the other hand, MD slope was significantly faster than TMTD slope in early and moderate glaucoma. Small but significant difference between TMTD rate of change and MD rate of change in earlier stages possibly results from the difference that MD is more heavily weighted in central locations while TMTD is not. MD values after excluding blind locations (targeted MD) may be better than TMTD values for directly quantifying the influence of blind locations on MD slope calculation. However, it was impossible for us to calculate targeted MD values because the calculation formula for MD, especially weights on central field locations, is not publicly available. Used in several earlier studies to estimate the rate of VF progression, mean total deviation appears to be a reasonable surrogate for MD.^10–12

The number of undetectable locations increased as MD decreased (worsened), and more than half of locations were already undetected in baseline tests in severe glaucoma. These results support our hypothesis that the lower rate of MD slopes in severe glaucoma is caused by the presence of consistently undetectable, and thus non-progressive locations. This also suggests that trend analyses of conventional global indices may not be optimal for estimating the rate of VF progression in severe glaucoma. It is challenging to confirm the accuracy of TMTD slopes in severe glaucoma because there is no established reference standard to be compared in this stage. However, it seems clear that conventional MD slope that shows positive slopes in 67% of cases with MD values less than −25 dB is not appropriate for estimating the rates of progression in these eyes, and TMTD slopes may be a promising alternative.

We defined undetectable locations as points that consistently showed <0 dB threshold throughout 3 baseline tests. This is based on a previous report that the median probability to observe < 0 dB again in locations that showed <0 dB threshold in 3 consecutive tests was 88%.⁸ We investigated the threshold values of blind locations in all follow-up tests to confirm the validity of this definition. We found that 93.9% of the threshold values obtained in follow-up examinations at locations that consistently showed <0 dB threshold in 3 baseline tests were <0 dB. These findings extended those of Junoy Montolio et al., confirming that locations that showed blind responses in 3 consecutive tests were highly likely to repeat blind responses throughout the follow-up tests. However, if 6.1% positive responses acquired in follow-up tests at undetectable locations reflect improvement of visual field sensitivity, it may not be appropriate to exclude these locations from trend analysis. Although it seems more reasonable to regard those positive responses as variability rather than improvement considering the low probability of positive responses and the irreversible nature of the disease, the optimal cut-off for defining undetected locations warrants further research. We excluded initial tests from regression analysis in this study. We confirmed that excluding 1 or 2 baseline tests did not significantly affect the resultant TMTD slopes in this study (data not shown), but the optimal number of baseline tests to be excluded also needs further investigation.

The relationship between baseline VF severity and the risk of VF progression remains controversial. Some studies reported that better baseline VF increased the risk of subsequent VF progression.^13,14 However, there also are conflicting studies that showed just the opposite relationship,^11,15–17 and even studies that reported no significant association between baseline VF severity and the risk of progression.¹⁸ There are many factors that may help explain the disagreement between studies such as differences in participant population, treatment, and scales to measure VF sensitivity.¹⁹ The results of the current study suggest that apparent slowing of MD slope in severe glaucoma due to blind locations may be another confounding factor that complicates the association between baseline severity and progression of VF.

In late-stage glaucoma, estimating the rate of VF progression is of vital importance, but especially challenging.⁷ Estimating the rate of changes in OCT parameters is also challenging in late stage because of so-called floor effect.^20–23 Therefore, reliable methods for evaluating the progression of severe glaucoma are needed. One reason for the difficulty in VF progression analysis in severe glaucoma may be attributable to low reproducibility,^24,25 and algorithms that remove locations with low reliability have been proposed but are not widely available in clinical practice.^26,27 Trend analysis of TMTD is another possible strategy for VF progression analysis in late-stage glaucoma. The advantage of TMTD slope may be that it can be obtained by simply removing blind locations from readily available SAP tests without the need for any additional device. However, it is notable that the average TMTD slope in the severe glaucoma eyes is shallower than at earlier disease stages, albeit not statistically significant. This suggests the possibility that our method lessens but does not eliminate the underestimation. As there is no established reference standard for VF progression analysis in severe glaucoma, further longitudinal study is warranted to confirm whether trend analysis of TMTD accurately evaluate the rate of progression. Future development of a thresholding algorithm that remove consistently undetectable locations in preceding tests could contribute not only to minimizing underestimation of progression in severe glaucoma but also to reducing test time.²⁸

Other methods, such as exponential regression,²⁹ pointwise linear regression (PLR) and cluster trend analysis (CTA) may be used for estimating the rate of visual field deterioration in severe glaucoma. PLR provides estimates of the rate of change for each VF location.^30–32 Although PLR has been reported to be more sensitive to focal glaucomatous progression than global indices, there are several shortcomings. There has been no consensus on what threshold should be adopted to define progression with PLR.³³ More importantly, it is well known that fulfilling a standard criteria for progression at just one VF location without any confirmation criteria may cause high false positive rate because of substantial variability at individual locations and increased risk of statistical type I error by performing multiple tests at many locations.^32,33 Therefore, various methods for confirmation requiring spatial or temporal consistency have been proposed for PLR.³⁴ However, these methods may not perform equally well in severe glaucoma with many blind locations. Regression analyses of the mean sensitivity by sectors or clusters (CTA) have been reported to provide a better combination of sensitivity and specificity than global trend analyses or PLR.^31,32,35 However, CTA also may cause underestimation of the rates of visual field progression in severe glaucoma when many locations in each cluster are undetectable from baseline. In summary, both PLR and CTA also are potentially influenced by undetectable locations in severe glaucoma, and no method has been established to adjust for the underestimation for either PLR or CTA.

Several limitations of this study should be pointed out such as the inclusion of only Japanese population, retrospective nature of the study, and relatively small number of patients with severe glaucoma.

In conclusion, the current study demonstrated that MD rate of progression is lower in severe glaucoma compared to earlier stages, and this apparent reduction of progression rates becomes smaller by removing consistently undetected VF locations. When using trend analysis of global indices in severe glaucoma, particularly in eyes with MD values less than −25 dB, the possibility of underestimation should be taken into account. Trend analysis of TMTD offers a practical and simple approach for alleviating underestimation of VF progression in severe glaucoma.