**Purpose.**:
This study was conducted to validate a recently described technique for measuring the rates of visual field (VF) decay in glaucoma.

**Methods.**:
A pointwise exponential regression (PER) model was used to calculate average rates of faster and slower deteriorating VF components, and that of the entire VF. Rapid progressors had a faster component rate of >25%/year. Mean deviation (MD) and visual field index (VFI) forecasts were calculated by (1) extrapolation of linear regression of MD and VFI, and (2) calculation de novo from the PER-predicted final thresholds.

**Results.**:
The mean (± SD) years of follow-up and number of VFs were 9.2 (± 2.7) and 13.7 (± 5.8), respectively. The median rates of the decay were −0.1 and 3.6 (%/year) for the slower and the faster components, respectively. The “rapid progressors” (32% of eyes) had a mean decay rate of 52.2%/year. In comparison with actual values, the average absolute difference and the mean squared error for MD forecasts with linear extrapolation of indices were 3.58 dB and 31.91 dB^{2}, and with the de novo recalculation from PER predictions were 2.95 dB and 17.49 dB^{2}, respectively. Similar results were obtained for VFI forecasts. Comparisons of the prediction errors for both the MD and VFI favored the PER forecasts (*P* < 0.001).

**Conclusions.**:
PER for measuring rates of VF decay is a robust indicator of rates across a wide range of disease severity and can predict future global indices accurately. The identification of “rapid progressors” identifies high-risk patients for appropriate treatment.

^{ 1 }By identifying patients with faster rates of visual field decay and with appropriately early intervention, long-term visual function can be preserved and limited resources applied appropriately to optimize patient outcomes.

^{ 2 }but a clinically useful assessment of the rate of worsening remains a challenge. Given the discrepancy among clinicians in the interpretation of VFs,

^{ 3,4 }a great deal of interest has been generated in the “perfect tool” for an objective assessment of VF decay. Current methods either are event-based or trend-based, and involve analysis of serial VFs. Unfortunately, no available gold standards are devoid of limitations, either in terms of accounting for confounding factors, or having a limited range of operation.

^{ 5 }

^{ 6 }We identified patients at potentially highest risk of deterioration by analyzing single locations in serial VFs and assessed their individual rates of decay. As such, individual locations were assigned as having a fast or slow rate of decay, while preserving the spatial distribution in the analysis. In our study, we used PER to validate the technique in a group of patients with less severe glaucomatous VF loss compared to the previously described group of patients,

^{ 6 }and to detect the technique's accuracy in predicting future values of the mean deviation (MD) and VF index (VFI) by using individually regressed thresholds compared to linear extrapolation of the indices.

^{ 6 }In accordance with the tenets set forth in the Declaration of Helsinki, the individual Institutional Review Board of UCLA approved the study.

^{ 6 }Each VF location was regressed exponentially against time and a regression coefficient (equivalent to rate) was obtained. The mathematical model used in these calculations was $ y = e a + b x $. The 54 locations were ranked according to the rate of decay and partitioned into two groups (faster and slower). For each partitioning, a

*t*-test was performed and the corresponding

*P*values were adjusted for multiple testing. The Benjamini-Hochberg correction was used to find the optimal

*P*value to maximize the difference between the faster and slower groups by minimizing the

*P*value between component rates.

^{ 7 }A minimum of 5 test locations was required in either the slow or fast groups. Global rates of decay then were obtained from the mean of all the test locations, and the mean fast and slow components. The fast component then was analyzed for any potential subdivisions within the group. The rates of change in these components then were compared to the rates of change in the MD.

^{ 8,9 }and VFI are in the public domain.To estimate the normal age-matched threshold for each location, the difference between the observed thresholds and total deviation values for each decile age group was used. This was repeated for at least 10 patients and an average of “normal” was obtained for each location for every decile of age. The SDs and the weighting system used in the MD calculation for each 10-year age group were obtained from a previous publication by Heijl.

^{ 10 }The estimated normal values for individual locations for each decile age group together with the SDs then were inserted into the known formulae. When compared to actual known values, there was a high level of correlation with a random sample of our estimates using the above methods (MD

*r*= 0.996, VFI

^{2}*r*= 0.991)

^{2}^{ 8 }

^{ 6 }The VF test strategies for the UCLA group included SITA standard (88%), full threshold (12%), and SITA fast (3%). The characteristics and demographic data for the two groups are given in Table 1. The UCLA group consisted of patients with less severe glaucoma (initial MD −5.5 ± 5.5, final MD −6.7 ± 7.3 dB) compared to the AGIS group (initial MD −10.9 ± 5.4, final MD −12.9 ± 6.9 dB), as shown as frequency distributions in Figure 1.

**Figure 1.**

**Figure 1.**

**Table 1.**

**Table 1.**

UCLA | AGIS | |

Eyes, n | 409 | 389 |

Patients, n | 279 | 309 |

Age, y | 75 ± 11.0 | 64.7 ± 9.6 |

Follow-up, y | 9.2 ± 2.7 | 8.1 ± 1.1 |

Baseline IOP, mm Hg | 15.3 ± 5.1 | 15.3 ± 5.0 |

Baseline number medications | 2.0 ± 1.0 | 2.8 ± 0.9 |

Eye, n (%) | ||

Right | 297 (72.6) | 186 (47.8) |

Left | 112 (27.4) | 203 (52.2) |

Number of VFs | 13.7 ± 5.8 | 15.7 ± 3.0 |

Initial MD* (dB) | −5.5 ± 5.5 | −10.9 ± 5.4 |

Final MD *(dB) | - 6.7 ± 7.3 | −12.9 ± 6.9 |

*P*< 0.0001), with the division at the 25%/year decay rate. It consists of a group with a mean decay of 3.3%/year (SD ±5.4%), and a second more rapidly deteriorating group with a mean decay of 52.2%/year (SD ±13.8%) as shown in Figure 3B. The latter group consisted of 32% of the eyes. The rate of the decay in the faster component was independent of the MD rate of decay, whereas there was a linear relationship between the slower component and the MD (Fig. 4).

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

*n*= 798 for the purposes of making MD and VFI forecasts. Figure 5 shows the relationship between the predicted MD and VFI with the Statpac and the PER model on a frequency distribution (binary classifier) curve. Of the two curves on each graph, the one to the upper left represents the technique with the better predictive potential, that is the smallest difference from the actual value. In both cases of MD and the VFI forecasts, the de novo calculation of the indices from PER regression of individual threshold values was closer to the actual values compared to the linear regression of the indices themselves. Comparisons between the two methods of MD and VFI predictions are summarized in Table 2. The de novo calculations with PER of individual thresholds are more consistent (smaller mean squared error) with smaller prediction errors (smaller average absolute differences), and when the areas under the frequency distribution prediction errors (using PER versus linear regression) are compared, they are significantly different (

*P*< 0.001)

**Figure 5.**

**Figure 5.**

**Table 2.**

^{ 6 }With the PER technique in the UCLA patients, we demonstrated that the rates of VF decay for individual eyes can be divided into faster and slower components. The faster component appears to be divided into two groups with a subgroup demonstrating a more rapid VF loss and this subgroup is identified as “rapid progressors.” Furthermore the faster component appears to be independent of changes in the rate of MD in contrast to the slower component with which it has a strong linear relationship (Fig. 4). As with its relationship to the MD, the faster component also appears to be independent of VFI as shown by an example in Figure 6. This suggests that test locations can be identified where local glaucomatous deterioration is occurring, independent of diffuse VF loss, which are more likely to be caused by conditions, such as media opacities and aging. In this study, by combining groups of patients with both severe (AGIS data) and the less severe (UCLA patients) glaucoma groups, we also demonstrated that the PER of threshold sensitivities can be applied across a wide range of VF severity, allowing differentiation of the rates of decay into fast and slow components, and hence enabling us to make predictions on regional rates of decay while preserving the spatial information provided by the VF.

**Figure 6.**

**Figure 6.**

^{ 5 }Trend-based analyses, on the other hand, have the potential to provide estimates of the rates of VF decay. There is little consistency among various investigators on the criteria set for the detection of VF progression.

^{ 9–13 }Analysis of global indices has the advantage of providing a single figure and, therefore, a quick guide for the clinician when analyzing serial VFs of an individual patient, but at the expense of losing spatial information. Point-wise linear regression of individual threshold sensitivities (regional trend based analysis) provides an estimate of VF worsening,

^{ 14,15 }and this technique is available currently as software for clinical use (PROGRESSOR; Medisoft Ltd., Leeds, UK). Decay is said to be clinically significant when the rate of deterioration is at least −1.0 dB/year and the statistical significance of the linear slope is

*P*< 0.01. With these criteria for progression, Nouri-Mahdavi et al. found PLR to be at least comparable to the AGIS criteria for detection of longitudinal VF progression.

^{ 16 }By comparing several methods, Gardiner et al. found that a “three omitting” technique leads to an increase in the specificity of PLR.

^{ 17 }

^{ 18 }Final VFI for 100 patients with an average follow-up of 8.2 years and 11 VF examinations was predicted by linear regression of 5 initial tests. They found the technique to be a reliable predictor of future VF loss. Of patients 70% had a predicted final VFI within ± 10% of the estimated final VFI (particularly in patients with abnormal initial VF tests), with a correlation coefficient of 0.84 between predicted and estimated VFI. While this technique is useful in most cases, it may not be applicable reliably across the entire range of VF due to the way the VFI is calculated. While the effect of confounders (e.g., cataracts) is reduced by the use of pattern deviation probability maps to calculate VFI, the authors acknowledge that in advanced cases where even the 85th percentile most sensitive test point has been affected, such maps no longer can be used, and the reliability of VFI is reduced beyond a cut off of −20dB, where the index is derived from the total deviation plots.

^{ 14 }Artes et al. recently compared the properties of VFI and MD in a 204 eyes with a range of MD from −2 to −10dB, and found them to be closely related (

*r*= 0.88,

*P*< 0.001), and concluded that VFI may have reduced sensitivity to changes in early glaucoma damage due to the ceiling effect cause by pattern deviation maps.

^{ 19 }

^{ 18 }We also used the technique to predict MD as a further validation measure, and found that in the case of VFI and MD, de novo recalculations from PER of individual threshold sensitivities were statistically significantly closer to actual values (

*P*< 0.001) than simple linear regression of both of these global indices.

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