**Purpose.**:
This study was conducted to measure the rate of visual field (VF) decay in glaucoma, to separate faster and slower components of decay, and to predict the rate of VF decay.

**Methods.**:
Patients who had primary glaucoma and 6 or more years of follow-up were included. Thresholds at each VF location were regressed with linear, quadratic, and exponential models. The best model was used to parse the VF into slower and faster rate components. Two independent cohorts (glaucoma [*n* = 87] and cataract [*n* = 38]) were used to determine the technique's ability to distinguish areas of glaucomatous VF changes from those caused by cataract. VF forecasts, derived from the first half of follow-up, were compared with actual VF thresholds at the end of follow-up.

**Results.**:
The mean (±SD) years of follow-up and number of VFs for the main cohort (389 eyes of 309 patients) were 8.2 (±1.1) years and 15.7 (±3.0), respectively. The proportions of best fits were linear 2%, quadratic 1%, and exponential 97%. Proportions of eyes with exponential rates of decay ≥10% for the entire visual field (VF), faster components, and slower components were 20%, 56%, and 4%, respectively. The difference in decay rates between the faster and slower components was greater in the independent glaucoma cohort (19% ± 10%) than in the cataract cohort (5% ± 5%; *P* < 0.001). Test location forecasts significantly correlated with measured values (*r* ^{2} = 0.67; *P* < 0.001).

**Conclusions.**:
This method isolates faster and slower components of VF decay in glaucoma, can identify patients who are fast progressors, and can predict patterns of future VF loss with appropriate confidence intervals. (ClinicalTrials.gov number, NCT00000148.)

^{ 1 }Fast progressors may require suitably aggressive treatment, whereas slow progressors might be spared the expense and morbidity of unnecessary treatments. This topic is particularly important for an aging population with limited resources for medical care. Advancing damage in glaucoma can be measured by structural or functional changes, the latter most often estimated with perimetric measurements. In this article, we address the measurement of rates of damage with standard achromatic automated perimetry. Our goals are to develop a method to reliably measure the rate of functional decline in glaucoma, to use it to identify the fast progressors, and to provide clinically useful forecasts of the disease to help guide treatment. To be useful, the method should perform well across the entire range of disease severity.

^{ 2 }The index is weighted more heavily toward the central VF in proportion to the cortical representation of vision, is normalized to the entire range of VF function, and provides some predictive capability as a linear extrapolation of the index.

^{ 3 }It requires the use of proprietary, stored normative data and assumes a linear rate of worsening. A shortcoming of the global indices in general is the lack of any spatial information with regard to the regions of the VF showing faster progression.

^{ 4 }To test this hypothesis, we have developed a novel method to measure VF decay with a large cohort of glaucoma patients with long-term follow-up. The method identifies VF locations progressing at the fastest rates, provides a method to spatially separate test locations demonstrating slower progression from those showing faster progression, and predicts future VF measurements with appropriate confidence intervals while preserving spatial information.

^{ 5,6 }In this study, patients who had 6 or more years of follow-up and who underwent 12 or more VF examinations were included. VF data were collected according to the AGIS protocol, which required acceptable VF reliability scores.

^{ 7 }VF tests were performed with a visual field analyzer (Humphrey Visual Field Analyzer I; Carl Zeiss Ophthalmic Systems Inc., Dublin, CA) with the 24-2 test pattern, size III white stimulus, and full-threshold strategy. The 24-2 program records sensitivities from 55 locations in the VF, including the physiologic blind spot. All patients gave written informed consent for participation in AGIS, and the study was approved by the individual institutional review boards of the respective clinical centers. The Institutional Review Board of the University of California at Los Angeles approved the present study. All research procedures followed the tenets set forth in the Declaration of Helsinki.

- First-order linear:
*y*=*a*+*bx*; - Second-order linear (quadratic):
*y*=*a*+*bx*+*cx*^{2}; and - First-order exponential:
*y*=*e*^{a}^{+}^{bx}*y*=*a*+*bx*.

*b*in each model. For models 1 and 2,

*b*represents the average annual rate of change (increase or decrease) in

*y*. For model 3,

*b*is the average annual rate of change (increase or decrease) in ln

*y*. Equivalently, for model 3,

*e*represents the ratio of

^{b}*y*in a given year to

*y*in the year before (on the average). In other words,

*e*is interpreted as the average annual rate of decline of

^{b}*y*. The rate of decay is defined as (1 −

*e*).

^{b}^{ 8 }The AIC is defined as 2

*k*− 2ln(L), where

*k*= number of parameters and L = natural log (ln) of the maximum likelihood value. From these results, the selected model (exponential) was used to measure the rate of decay of each test location for the entire VF series for each eye.

*t*-test statistic, and the corresponding

*P*values were adjusted for multiple testing. The null hypothesis was that the mean of the fast group equaled the mean of the slow group. Optimal partitioning was determined by finding the fast subgroup that yielded the minimum

*P*value, with a minimum size of five test locations per cluster. All other locations were assigned to the opposite group. Adjusted

*P*values were used for this multiple testing procedure with the Benjamini-Hochberg correction.

^{ 9 }Each eye provided its own optimal partitioning. The eyes had components of different sizes, but each component consisted of at least five locations. For each eye, the mean decay rate was calculated for each of the partitioned components. Frequency distributions of the faster and slower component rates and their differences were calculated and displayed.

Main Study Sample | Glaucoma (PGL) | Cataract (CAT) | |
---|---|---|---|

Eyes, n | 389 | 87 | 38 |

Patients, n | 309 | 80 | 31 |

Age, y | 64.7 ± 9.6 | 74.7 ± 11.8 | 63.7 ± 15.6 |

Follow-up, y | 8.1 ± 1.1 | 8.3 ± 2.1 | 8.5 ± 3.8 |

Baseline IOP, mm Hg | 15.3 ± 5.0 | 13.2 ± 2.6 | 16.8 ± 5.0 |

Baseline number of medications | 2.8 ± 0.9 | 1.5 ± 1.1 | 0 |

Race, n (%) | |||

White | 174 (44.7) | 63 (72.3) | 35 (92.5) |

Black | 211 (54.2) | 10 (11.5) | 0 (0) |

Other | 4 (1) | 14 (16.2) | 3 (7.5) |

Sex, n (%) | |||

Male | 184 (47.3) | 29 (33) | 19 (50) |

Female | 205 (52.7) | 58 (67) | 19 (50) |

Eye, n (%) | |||

Right | 186 (47.8) | 54 (62) | 21 (55) |

Left | 203 (52.2) | 33 (38) | 17 (45) |

Cataract surgery, n (%) | |||

No | 225 (57.8) | 0 (0) | 38 (100) |

Yes | 164 (42.2) | 87 (100) | 0 (0) |

Number of visual fields | 15.7 ± 3.0 | 11.7 ± 3.9 | 8.6 ± 5.0 |

Initial MD,* dB | −10.9 ± 5.4 | −8.4 ± 6.8 | −0.4 ± 3.5 |

Final MD, dB | −12.9 ± 6.9 | −9.3 ± 7.5 | −2.0 ± 2.3 |

*P*< 0.0001 with D'Agostino's test for skewness; skew = 1.1361).

^{ 10 }

*P*< 0.001).

*P*< 0.01). The faster component would have less effect on the overall changes in MD and would be expected to lie a more horizontal line (slope = 0). For these data, the fitted line for regression of the faster rate component against the percentage of MD change has a slope of 0.19 (

*P*< 0.05).

*n*= 389 for each). A substantial proportion of patients (58%) had a faster VF component, with a half-life of ≤10 years. These patients would be defined by our arbitrary criteria as fast progressors.

*P*< 0.001). The PGL test group, therefore, had a greater average rate for the faster component than did the CAT group, whose average VF decay rate in the faster component was relatively slow.

*n*= 389, for a total of 13,905 comparisons). The correlation between actual and predicted final threshold values was strong (

*r*

^{2}= 0.67 and

*P*< 0.001; Fig. 9). The 10% and 90% confidence intervals were developed for predictions of threshold sensitivity at individual test locations (Fig. 10) and may be considered suggestions for the appearance of nearly best case and worst case future outcomes.

^{ 11 }published recommendations for measuring rates of VF change in glaucoma. Empirical data were used to provide variability estimates of MD. Models were developed to determine the number of tests required over various periods of time to detect change. For example, three tests are required to detect a change in MD of 4 dB over 2 years in an eye with average long-term measurement variability. Regional changes and focal components of damage, to which MD change is not sensitive, are not addressed.

^{ 3 }developed a VF index to calculate glaucoma rates of progression and to predict loss by extrapolation of linear trends. The authors proposed that the index is less affected by cataract and cataract surgery than MD and that the technique can be used to make clinically useful predictions. The VFI is weighted more heavily toward the central VF according to cortical projections of the visual pathway and is normalized for the entire range of perimetric vision. Pattern deviation values are used to select the total deviation values used in the calculation of the index, except when there is advanced VF damage (>20-dB loss), when all total deviation values are used. Predictions of future behavior of the VFI are performed by linear extrapolation. As with other global indices such as MD, no regional information about the VF is available with either the rate measurement or the prediction. VFI has been used recently to measure the relationship between intraocular pressure reduction and rates of progressive VF loss in eyes with optic disc hemorrhage.

^{ 12 }This index showed a beneficial effect on the rate of glaucomatous damage from treatment in patients with disc hemorrhage.

^{ 13 }Disease was classified as progressive or stable based on the slope and statistical significance of the regressions. Rates of progression were in the range of 1 to 5 dB/year, depending on the number of fields, their variability, and the parameter that was used. Different methods of pointwise linear regression were examined by Gardiner and Crabb.

^{ 14 }They concluded that the most sensitive method with which to identify VF progression was a statistically significant linear slope (at the 1% level) of at least −1.0 dB/year. The most specific approach was to confirm change with a “three-omitting” algorithm that used two confirmation fields.

^{ 15 }used the course of VF series over the first 4 years of follow-up to predict 8-year outcomes. The sum of the slopes of individual test locations that regressed over time was used to estimate the probability of subsequent VF worsening with clinically useful accuracy. Crabb et al.

^{ 16 }previously pointed out that predictions of VF progression with pointwise linear regression could be improved by spatial processing (regional averaging). Linear extrapolation of VFI has also been used; predictions based on five initial examinations were found to be a reasonable predictor of future field loss in most patients.

^{ 14 }

^{ 17,18 }In addition, our approach provides the clinician with both slower and faster rates of progression simultaneously so that these can actually be compared and clinical judgment can be applied (Figs. 4, 10). In advanced disease, loss tends to become more diffuse as thresholds approach absolute values over a large area of the VF; the fastest progressing locations will still be detected by the faster rate component with this method.

*r*

^{2}of 0.67, an encouraging correlation that helps validate the technique. However, because the rates of decay spatially cluster in well-defined nerve fiber layer patterns, it may be possible to improve the forecasting model by using the correlation coefficients between the test locations to weight the contributions of the locations in a smoothing procedure. We should also note that the rates of decay are expressed in percentiles with the proposed technique and that comparison of rates must take into account the starting thresholds.

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