**Purpose**:
Cluster trend analysis detects glaucomatous deterioration within predefined subsets (clusters) of visual field locations. However, it may miss small defects straddling boundaries between the clusters. This study assesses whether simultaneously using a second set of clusters, overlapping the first, could improve progression detection.

**Methods**:
Deterioration in eyes with or at risk of glaucomatous visual field loss was “detected” by mean deviation (MD) on the first visit at which the *P* value from linear regression over time was below the fifth percentile of its permutation distribution. Similarly, *P* values were calculated for each of 10 predefined nonoverlapping clusters of locations, or 21 overlapping clusters; deterioration was “detected” when the *N*th-smallest *P* value was below the fifth percentile of its permutation distribution, for different *N*. Times to detect deterioration were compared using survival models.

**Results**:
Biannual series of ≥5 visual fields (mean = 14) were available for 420 eyes of 213 participants. Deterioration of 33% of eyes was detected earliest using *N* = 1 overlapping cluster in 3.3 years (95% confidence interval 2.7–4.6 years); or *N* = 2 nonoverlapping clusters in 3.3 years (2.7–5.0) (comparison *P* = 0.654). There was also no significant difference in the probability that deterioration would be confirmed (92.8% vs. 94.4%, *P* = 0.289). Both overlapping and nonoverlapping clusters detected deterioration significantly sooner than MD (4.5 years, *P* ≤ 0.001).

**Conclusions**:
After equalizing specificity, overlapping clusters of locations did not significantly reduce the time to detect deterioration compared with nonoverlapping clusters.

**Translational Relevance**:
Cluster trend analyses detected deterioration sooner than global analyses even when defects straddled cluster borders.

^{1}Treatment decisions can then be made on the basis of whether functional loss is progressing rapidly enough to be a severe threat to the patient's quality of life.

^{2}However, the best way to use visual field data to assess progression remains unclear. In particular, there is disagreement on the extent to which global indices should be relied on, such as mean deviation (MD)

^{3}or the visual field index (VFI)

^{4}

^{,}

^{5}when using the Humphrey Field Analyzer (HFA; Carl Zeiss Meditec Inc., Dublin, CA, USA). A recent survey of UK ophthalmologists reported that “Strong agreement consensus was achieved that visual field stability should be assessed by trend analysis or by summary measures of VFI/MD progression.”

^{6}By contrast, the World Glaucoma Association's consensus on Progression of Glaucoma states that “Both local and global metrics are needed for assessment of progression.”

^{7}

^{8}As a reasonable middle ground between those two conflicting priorities, we suggested looking at the rate of change within 10 predefined nonoverlapping subsets (“clusters”) of visual field locations, as implemented in the cluster trend analysis that forms part of the EyeSuite software developed for the Octopus perimeter (Haag-Streit Inc., Bern, Switzerland).

^{9}

^{10}Only tests with ≤15% false positives and ≤33% fixation losses were used for the primary analysis. Because fixation losses are frequently the result of inaccurate mapping of the blind spot at the start of the test rather than true unreliability due to unstable fixation, a secondary analysis was performed using tests with ≤15% false positives but without any criterion for fixation losses. For this study, only eyes with series of at least five reliable tests by these criteria were included in the analysis.

^{8}Total deviation values for each location were used instead of raw sensitivities to account for the effect of normal aging; therefore in the absence of disease progression each cluster would be expected to show zero change over time. We have previously shown that “censoring” sensitivities below 15 dB and setting them equal to 15 dB improves reliability and, hence, the ability to detect change; therefore the total deviation values for any such locations were set to equal the total deviation value for a sensitivity of 15dB.

^{11}

^{,}

^{12}For the overlapping clusters analysis, these 10 clusters were supplemented by an additional eleven clusters, as shown by the red lines in Figure 1B. These additional clusters were selected based on the average angle at which nerve fiber bundles from each location enter the optic nerve head, according to the map of Garway-Heath et al.

^{13}; and such that each cluster contained at least two locations. The clusters include locations whose average angle of entry is 20° to 60°; 60° to 80°; 80° to 100°; 100° to 120°; 120° to 180°; 180° to 240°; 240° to 260°; 260° to 280°; 280° to 290°; 290° to 340°; and 340° to 20°. Therefore there are a total of 21 overlapping clusters, shown in Figure 1C. Note that the two clusters temporal of the blind spot are counted twice in the overlapping clusters analysis to ensure that any defects in this underrepresented region of the visual field will still be detected.

^{14}rather than using the same

*P*value cutoff for both overlapping and nonoverlapping cluster analyses.

^{8}The method for detecting deterioration was based on the published permutation analyses of pointwise linear regression approach

^{14}and implemented in R statistical programming language (version 3.5.0).

^{15}For a series of

*V*visual fields, where

*V*≥ 5, the “observed” significance of the rate of change was defined as the

*P*value from an ordinary least squares regression over time. Next, a permutation distribution for this

*P*value was derived. The values of MD for visits 1-

*V*were reordered, and these reordered MD values were regressed against the original test dates. For

*V*= 5, this was done for all 120 possible reorderings of the five visits; for

*V*> 5, 475 randomly chosen reorderings were used to avoid excessive computation time.

*Deterioration*in MD was “detected” at the first visit

*V*for which the observed significance was below the fifth percentile of the permutation distribution. Therefore this criterion has a specificity of 95% and, based on a binomial distribution 475 reorderings, gives a confidence interval for this specificity of ±1%.

*P*value for the rate of change is less than 5%. However, it makes fewer distributional assumptions, particularly concerning homoscedasticity. More importantly, it can more easily be extended to cluster analyses, as detailed in the next section, to ensure consistency between the analysis types.

^{14}

*V*, and the associated

*P*value for the rate of change was recorded. This gives a set of 10

*P*values when using nonoverlapping clusters and 21

*P*values when using overlapping clusters. These were sorted from smallest to largest. As before, the visits in the series were then reordered, either using all possible reorderings for

*V*= 5 or 475 random reorderings for

*V*> 5. For a given number of clusters

*N*, deterioration was “detected” on the first visit

*V*for which the

*N*th-smallest observed

*P*value was below the fifth percentile of the

*N*th-smallest

*P*values from all reorderings. Note that the

*N*th-smallest

*P*value will not always be from the same cluster in each reordering; instead the

*P*values are sorted from smallest to largest for each individual reordering before deriving the fifth percentile for each

*N*. This analysis ensures that the specificity is exactly equal to 95% for each technique, allowing a fair comparison between the times to detect deterioration.

*V*at which the

*N*th-smallest observed

*P*value was below the fifth percentile of the

*N*th-smallest

*P*values from all reorderings, for both visits the series 1 through

*V*and the series 1 through (

*V*+1). The date of detection is defined as being visit

*V*, not visit

*V*+1. It was not necessary for the

*N*th-smallest

*P*value to come from the same sector for both time points. The probability that “confirmed deterioration” was detected on the same date that “deterioration” was detected can then be taken as a metric of the robustness of a particular analysis.

^{16}

^{,}

^{17}

^{18}Differences between the survival curves were assessed using a stratified Cox proportional hazards model,

^{19}with strata identifying fellow eyes of the same individual. Including strata is equivalent to using generalized estimating equations (GEE) in a linear model to adjust for intereye correlations.

^{20}Subanalyses were performed within the subset of eyes that were abnormal at the start of their series, defined as either abnormal pattern standard deviation (

*P*< 5%) or a glaucoma hemifield test result of either “abnormal” or “borderline”; and within the subset of eyes that did not meet those criteria and so would be considered normal at the start of their series. GEE logistic regressions were used to determine whether the probability that deterioration would be subsequently confirmed differed between criteria.

*P*values comparing the time to detect deterioration between each pair of these criteria based on stratified Cox proportional hazards models; and in italics the equivalent

*P*values comparing the time to detect confirmed deterioration. Cluster trend analysis, using either one or two nonoverlapping clusters, or using one to three overlapping clusters, detected deterioration significantly sooner than MD. The criteria that detected deterioration soonest were using one nonoverlapping cluster, or one or two overlapping clusters; these three criteria were not significantly different from each other for detecting either deterioration or confirmed deterioration. There were also no significant differences among these three criteria in the probability that deterioration would be confirmed (

*P*= 0.910 for one nonoverlapping vs. one overlapping, by logistic GEE regression;

*P*= 0.229 for one nonoverlapping vs. two overlapping; and

*P*= 0.197 for one nonoverlapping vs. two nonoverlapping). Figure 2 shows Kaplan-Meier survival curves comparing the time to detect deterioration by these three criteria, and by MD.

*P*= 0.043), but none of the other comparisons between the three cluster criteria were statistically significant (all

*P*> 0.05).

*P*≤ 0.001), but as in the primary analysis the overlapping cluster criteria were not significantly sooner than the nonoverlapping cluster criterion (

*P*= 0.394 for one overlapping cluster vs. one nonoverlapping cluster;

*P*= 0.095 for two overlapping clusters vs. one nonoverlapping cluster).

*P*value based on a series of seven visits and, hence, was the sector that would trigger “detection” by visit seven when

*N*= 1, among the 107 eyes for which deterioration would be detected by this visit using nonoverlapping clusters (Fig. 4A) and among the 116 eyes for which deterioration would be detected using overlapping clusters (Figs. 4B and 4C).

*P*< 5%” to “at least one of 21 overlapping clusters has

*P*< 5%” would naturally increase sensitivity while decreasing specificity for detecting deterioration, especially when the ten non-overlapping clusters form a subset of the 21 overlapping clusters. To avoid this problem, we used permutation analysis to equalize specificity between criteria and between series lengths. After equalizing specificity, we found that using overlapping clusters of locations did not significantly reduce the time to detect deterioration compared with nonoverlapping clusters. We thus conclude that the identified caveat with the previous results, concerning defects straddling cluster borders, does not in fact significantly reduce the utility of the cluster trend analysis technique.

^{21}

^{–}

^{25}but it is less disease specific because it can also be caused by other factors such as cataract.

^{4}

^{,}

^{26}

^{,}

^{27}Therefore it is natural to suppose that diagnostic measures of glaucomatous progression would be better based on localized rather than global analyses. However, global analyses also have advantages. Because they are based on information from multiple locations, global indexes are considerably less variable than pointwise sensitivities, and so any deterioration that is detected is more likely to be confirmed on subsequent retesting,

^{8}reducing the need for as many confirmatory follow-up visits.

^{28}The likelihood of confirmation is also enhanced by using trend analyses rather than event analyses, for which as many as half of clinical trial endpoints may not be confirmed upon retest.

^{16}Cluster trend analysis

^{9}appears to represent a good compromise between these two priorities, providing rapid detection of subsequently confirmed progression without excessive false-positive determinations.

^{8}

^{9}is simpler to visually represent and, hence, quicker to understand and so may be preferred for clinical use.

^{8}The poorer performance of MD could be related to the lower number of test locations in central versus peripheral regions, which is only partly compensated for by the increased weighting given to those central locations; but it seems more likely that it is because glaucomatous progression consists of not just generalized but also localized deterioration which a global average is poorly suited to detecting. Cluster trend analysis does appear to provide a useful tool for clinical care; indeed it could be a useful addition to the analysis software available for other commercial perimeters.

^{29}Participants in this study had either clinically diagnosed or suspected glaucoma, and so it would be expected that the average rate of deterioration would be faster than in a healthy population. Despite this, deterioration was detected in fewer than half of the cohort even after an average of eight years. This partly reflects the relatively early functional loss, if any, of many eyes in the study (not least because both eyes were included even if only one eye would be considered glaucomatous clinically). It also reflects the fact that the participants were not only being clinically managed, but were also interested and dedicated enough to participate in a long-term study, and as such could be expected to have higher medication adherence than a more general population of glaucoma patients.

^{30}

^{,}

^{31}However it also reflects the fact that intertest variability makes it difficult to detect disease progression by functional testing alone.

^{32}

^{–}

^{36}

^{37}

^{–}

^{39}Among eyes for which deterioration was detected by the end of their series using one non-overlapping cluster, the average time until detection was 2.8 years. Given that a minimum of five visual fields was required, which would cover a period of approximately two years, analysis tools may be approaching the point at which any further improvements in the time to detect progression will become less clinically significant. There is still room for improvement in data analysis, but there may be greater benefits to be obtained by developing new testing methods that can reduce test variability to the point where a reliable measurement of the rate of change can be obtained using only four or fewer visits.

^{40}With a longer intertest interval, the amount of deterioration that has occurred relative to the test-retest variability would be higher, and so estimates of the rate of change should become more reliable.

^{36}This would be expected to have greater impact on cluster analyses than on global analyses such as mean deviation, where the large number of pointwise deviation values being included in the weighted average means that measurement noise is already greatly reduced. We would therefore conjecture that the benefits of cluster analyses over global indexes would be greater with less frequent testing. However, this has not yet been tested. A further caveat is that the participants in this study are highly experienced with automated perimetry, because of the time they have been in the study; averaging information from a large number of locations may be more beneficial in less-experienced patients who might be expected to give more variable test results.

^{41}

^{,}

^{42}

^{13}This topographic map is known to vary between individuals.

^{43}This variability should not greatly affect the clusters, which are based on the relative proximity of axons as they enter the optic nerve head rather than the exact position at which this happens. The possible exception to this would be along the temporal raphe, because the most temporal visual field locations could map to either hemifield of the disc.

^{44}Although we cannot discount the possibility that customized structure-function mapping could improve the utility of cluster analyses, it is notable in Figure 4 that the clusters bordering (and potentially encompassing) the raphe were no less likely to detect deterioration than more superior or inferior clusters.

^{45}

^{,}

^{46}However, it should be noted that there were eyes for which the strongest signal of deterioration came from central locations, particularly in the superior hemifield. This is in agreement with the recent work of Hood and colleagues,

^{47}

^{,}

^{48}showing that central visual field loss commonly occurs in glaucoma, even though it is often missed due to the low number of field locations within this region in the 24-2 test grid relative to the density of retinal ganglion cells.

**S.K. Gardiner,**None;

**S.L. Mansberger,**None

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