**Purpose.**:
To explore whether pointwise rates of visual field progression group together in patterns consistent with retinal nerve fiber layer (RNFL) bundles.

**Methods.**:
Three hundred eighty-nine eyes of 309 patients from the Advanced Glaucoma Intervention Study with ≥6 years of follow-up and ≥12 reliable visual field exams were selected. Linear and exponential regression models were used to estimate pointwise rates of change over time. Clustering of pointwise rates of progression was investigated with hierarchical cluster analysis using Pearson's correlation coefficients as distance measure and an average linkage scheme for building the hierarchy with cutoff value of *r* > 0.7.

**Results.**:
The average mean deviation (±SD) was −10.9 (±5.4). The average (±SD) follow-up time and number of visual field exams were 8.1 (±1.1) years and 15.7 (±3.0), respectively. Pointwise rates of progression across the visual field grouped into clusters consistent with anatomic patterns of RNFL bundles with both linear (10 clusters) and exponential (six clusters) regression models. One hundred forty-four (37%) eyes progressed according to the two-omitting pointwise linear regression model.

**Conclusions.**:
Pointwise rates of change in glaucoma patients cluster into regions consistent with RNFL bundle patterns. This finding validates the clinical significance of such pointwise rates. The correlations among pointwise rates of change can be used for spatial filtering purposes, facilitating detection or prediction of glaucoma progression.

^{ 1 }Such correlations are a function of test location eccentricities, especially in normal visual fields, or the relationship of test locations with respect to specific nerve fiber bundle patterns, which is more likely in fields with abnormal test locations. The correlation among test locations tends to follow the pattern of the retinal nerve fiber layer (RNFL) bundles. It has been shown that clustering of abnormal locations in an arcuate pattern can better discriminate between glaucoma patients and normal subjects compared with when the abnormal points are not grouped together.

^{ 2 }The cross-sectional correlation of visual field test locations is also the basis for the Glaucoma Hemifield Test (GHT) originally described by Asman and Heijl.

^{ 3 }Other visual field clustering schemes have been explored over time to define groups of related points across the visual field.

^{ 1,4,5 }In some definitions of early visual field loss, clustering of test locations is required to establish presence of early glaucomatous damage.

^{ 5 }

^{ 6 }In addition, determining the statistical significance of pointwise rates of progression is complicated by the high number of regression analyses carried out on individual test locations in a field series. Linear regression analysis of average threshold sensitivity in visual field clusters has therefore been explored to address this issue.

^{ 7 }Determination of the statistical significance of pointwise rates of progression is further complicated by the correlated nature of sequential data. One assumption of linear regression is that the error term is independent from visit to visit, which may not be necessarily correct. There is no hard evidence in the literature regarding the strengths and topography of correlations of pointwise rates of progression. Current progression criteria such as pointwise linear regression (PLR) or guided progression analysis (GPA) do not require change to occur in points belonging to the same cluster. It has been shown that requiring progressing points to belong to the same GHT cluster increases PLR's specificity.

^{ 8 }

**.**

^{ 9 }All patients gave written informed consent for participation in AGIS. The Institutional Review Board of the University of California at Los Angeles approved this study of the AGIS data, and all procedures followed the tenets set forth in the Declaration of Helsinki.

^{ 10 }We used both models to describe clustering of pointwise rates of progression. In the aforementioned study, an exponential model best described progression at individual test locations across the visual field.

*y*=

*a*+

*bx*

*a*= intercept (baseline threshold here), and

*b*= regression coefficient expressing change as dB/year.

*y*=

*e*

^{a}^{+bx }, or equivalently,

*ln*(

*y*) =

*a*+

*bx*.

*e*= base of the natural logarithm,

*ln*= natural logarithm,

*a*= intercept, and

*b*= regression coefficient.

*b*in both models. For an exponential model,

*b*is the average annual rate of change in

*ln*(

*y*). The quantity (100

*b*) can be interpreted as the percentage loss per year as in exponential decay.

^{ 11 }An agglomerative hierarchical cluster analysis is a “bottom up” approach of cluster analysis, in which each test location starts in its own cluster. In order to decide which test locations should be combined into one cluster, the hierarchical clustering starts by finding the similarity between every pair of test locations. We used Pearson's correlation coefficient as the measure of similarity between every pair, and pairs of test locations with the highest similarity (correlation coefficient) were merged up one level as a single cluster. Next, the similarity between every pair of clusters was calculated, and pairs of clusters with the highest similarity were merged up another level as a new single cluster. The similarity between any two clusters was the mean correlation of all pairwise correlations between all elements within each cluster (also called average linkage clustering). This process was repeated until the similarity between remaining pairs of clusters was too far apart to be merged (distance criterion), defined as 0.7 or above for the mean correlation within all clusters. A tree-like diagram (dendrogram) illustrates the similarity of rates for test locations and was mapped with a color-coded scheme (Fig. 1). The agglomerative hierarchical cluster analysis was performed using MATLAB Version R2009b (MathWorks, Inc., Natick, MA; see Appendix).

**Figure 1.**

**Figure 1.**

^{ 12 }It is considered a conservative approach to PLR with high specificity. In summary, a linear regression analysis of threshold sensitivity at each test location is performed against time, once after excluding the last available threshold and a second time after excluding the threshold before the last available one. The foveal and blind spot test locations (i.e., locations 15 degrees temporal and 3 degrees above and below the horizontal midline) were excluded from analyses. Test locations demonstrating a significant change on both regression analyses were considered to be worsening (slope ≤ −1.0 dB/year along with

*P*≤ 0.01) or improving (slope ≥ 1.0 dB/year along with

*P*≤ 0.01). Eyes in which the number of worsening test locations exceeded the improving points by 3 or more were considered to be worsening at the end of follow-up.

*r*≥ 0.7) was set with the linear model. Ten individual clusters were defined by the hierarchical clustering approach, when linear rates of change were used. Based on the two-omitting PLR method, 144 (37.0%) eyes progressed at the end of the follow-up period.

**Table 1.**

**Table 1.**

Characteristics | |

Number of eyes/patients | 389/309 |

Age (years, mean ± SD) | 64.7 ± 9.5 |

Follow-up (years, mean ± SD) | 8.1 ± 1.1 |

Baseline IOP (mm Hg, mean ± SD) | 15.3 ± 4.9 |

Baseline number medications (mean ± SD) | 2.8 ± 0.9 |

Race | |

White | 44.7% |

Black | 54.2% |

Other | 1% |

Sex | |

Male | 47.3% |

Female | 52.7% |

Eye laterality | |

Right | 47.8% |

Left | 52.2% |

Cataract surgery | |

No | 57.8% |

Yes | 42.2% |

Number of visual fields (mean ± SD) | 15.7 ± 3.0 |

Initial MD (dB, mean ± SD) | −10.9 ± 5.4 |

Final MD (dB, mean ± SD) | −12.9 ± 6.9 |

**Figure 2.**

**Figure 2.**

**.**We found that longitudinal perimetric rates of change grouped into clusters that were consistent with RNFL bundle patterns. This was true for both linear and exponential models. Although the clusters derived from exponential and linear models were not expected to exactly match, they were quite similar.

^{ 1,}

^{ 13–15 }Wirtschafter et al. defined the boundary lines of the visual field clusters by overlaying illustrations of the primate RNFL onto a scaled visual field map.

^{ 13 }Similarly, the Glaucoma Hemifield clusters were originally based on the superimposition of RNFL bundle patterns and the 74 test locations belonging to the 30-2 testing strategy of the HFA.

^{ 3 }Garway-Heath and coworkers defined visual field clusters based on the structure–function correlations between RNFL bundle defects on fundus photographs and visual field defects observed in a group of normal-tension glaucoma patients.

^{ 15 }Mandava et al.

^{ 1 }defined visual field clusters using the cross-sectional correlation of threshold sensitivities at individual test locations on Octopus visual fields in normal and stable glaucomatous eyes. The visual field clusters based on exponential rates of progression in this study closely resemble those reported by Garway-Heath et al.

^{ 15 }The correlation of rates of progression and distribution of clusters across the visual field would be expected to vary as a function of glaucomatous damage at baseline. Despite a potentially high correlation between any pair of test locations, the correlation would be observed only if the baseline threshold sensitivity in either test location was high enough to allow detection of any change. However, as can be seen comparing the clusters derived from linear and exponential regressions, general patterns emerge that are consistent with the scheme of clusters derived from cross-sectional correlation of structure and function in glaucoma. It is reassuring to observe that rates of progression follow a pattern of correlation similar to the RNFL bundle trajectories. This suggests that the rates of progression as measured with regression analyses reflect a biological phenomenon.

^{ 16–19 }We speculate that the correlation coefficients derived from the current study might be better suited for such spatial filtering compared with the cross-sectional weighting schemes used in prior studies. Gaussian and non-Gaussian filters are mostly based on information from neighboring points, while the correlation of visual field test locations normally goes beyond immediately adjacent points. This is the focus of an ongoing investigation by the authors.

^{ 7 }or according to Glaucoma Hemifield Test clusters, which are based on RNFL bundle anatomic patterns.

^{ 20,21 }Further study is needed to determine whether clusters derived from correlation of longitudinal rates of progression, as found in this study, would improve the sensitivity of such cluster-based trend analyses. One challenging and unsolved issue in pointwise regression analyses has been the inherent correlation among test locations across the visual field. Given the fact that the correlation among clusters is lower than the correlation among individual test locations, linear and nonlinear mixed models with random slopes for such longitudinally defined clusters might result in increased sensitivity and specificity for detection of glaucoma progression. Mandava and colleagues found that clusters performed better than global indices for detection of localized glaucomatous loss and that the long-term fluctuation was lower in clusters compared with individual test locations.

^{ 1 }

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