**Purpose**:
The study was conducted to evaluate threshold smoothing algorithms to enhance prediction of the rates of visual field (VF) worsening in glaucoma.

**Methods**:
We studied 798 patients with primary open-angle glaucoma and 6 or more years of follow-up who underwent 8 or more VF examinations. Thresholds at each VF location for the first 4 years or first half of the follow-up time (whichever was greater) were smoothed with clusters defined by the nearest neighbor (NN), Garway-Heath, Glaucoma Hemifield Test (GHT), and weighting by the correlation of rates at all other VF locations. Thresholds were regressed with a pointwise exponential regression (PER) model and a pointwise linear regression (PLR) model. Smaller root mean square error (RMSE) values of the differences between the observed and the predicted thresholds at last two follow-ups indicated better model predictions.

**Results**:
The mean (SD) follow-up times for the smoothing and prediction phase were 5.3 (1.5) and 10.5 (3.9) years. The mean RMSE values for the PER and PLR models were unsmoothed data, 6.09 and 6.55; NN, 3.40 and 3.42; Garway-Heath, 3.47 and 3.48; GHT, 3.57 and 3.74; and correlation of rates, 3.59 and 3.64.

**Conclusions**:
Smoothed VF data predicted better than unsmoothed data. Nearest neighbor provided the best predictions; PER also predicted consistently more accurately than PLR. Smoothing algorithms should be used when forecasting VF results with PER or PLR.

**Translational Relevance**:
The application of smoothing algorithms on VF data can improve forecasting in VF points to assist in treatment decisions.

^{1}The ability of clinicians to accurately estimate rates of functional decline with visual fields (VF) is an important basis for making management decisions.

^{2}Because of the confounding effect of variability between VF tests and the inherent lack of external validation, several prediction techniques have been developed.

^{3,4}Visual field indices that consider sensitivity at individual locations are more sensitive to change than global VF indices.

^{5,6}Measurement of glaucoma decay rates helps identify fast progressing patients who may need more aggressive treatment to lessen their chances of visual disability, as opposed to slower progressing patients who may be spared the costs and morbidity of treatment.

^{7}

^{2,8}and measures visual decay rates of all locations of the VF across a wide spectrum of disease severity. Pointwise exponential regression was used to partition VF points into fast and slow components; it was observed that the faster progressing points clustered in a pattern consistent with the anatomy of the retinal nerve fiber layer (RNFL).

^{8}Recent studies demonstrated that VF cluster analysis, as opposed to individual test locations, dampens the effects of longitudinal VF variability,

^{9}facilitates the identification of early glaucomatous damage,

^{9–11}and increases the specificity of glaucoma diagnosis.

^{12}

^{13,14}Spatial filtering, a technique used commonly in digital image processing, can smooth the data and reduce the noise by applying mathematical processes that exploit the spatial relationship between neighboring numeric values.

^{14}As the VF is a numerical matrix, the same rationale may be applied to VF data. With this approach, the measured threshold sensitivity of each test location within the VF is replaced by a “weighted” value, which is estimated with neighboring sensitivity values.

^{15}

^{16,17}Tests were performed with the Humphrey VF analyzer (Carl Zeiss Ophthalmic Systems, Inc., Dublin, CA) with a 24-2 test pattern, size III white stimulus, and with either the full threshold strategy or the ad Swedish Interactive Threshold Algorithm (SITA) Standard strategy. The 24-2 test pattern recorded sensitivities from 54 points of the VF including the physiological blind spot.

^{1}(3) the glaucoma hemi-field test model (GHT),

^{18}and (4) a correlation of rates

^{19}model. The raw sensitivity values (dB) at each VF location for the first 4 years or the first half of the follow-up time (whichever was greater) were weighted individually based on distance influences from each of the other locations for each of the four models.

^{1}defined six VF clusters based on the structure–function correlations between RNFL bundle defects on fundus photographs and VF defects observed in a group of normal-tension glaucoma patients.

^{18}There were five clusters in the superior hemifield and five mirror-image clusters in the inferior hemifield.

^{19}

*d*= distance = 1 (for adjacent VF locations),

*w*= weight = 1/

*d*

^{2},

*n*= number of neighboring VF locations,

*VF*

_{Location}= dB value of VF location being weighted, and

*VF*

_{Neighbor}= dB value of neighboring VF location.

*y*represents threshold sensitivity in dB and

*x*represents follow-up time in years. The variables

*α*and

*β*are parameters estimated by the models, where

*α*is the intercept and

*β*is the regression coefficient.

*X*

_{obs}= average sensitivity (dB) of the final 2 follow-up visits of the observed points,

*X*

_{model}= predicted sensitivity (dB) of the last follow-up of the smoothed points,

*n*= number of visual field points, and

*i*= eye.

^{20}

**Table 1**

**Table 2**

*P*values between the smoothed and unsmoothed differences in sensitivities were

*P*< 0.001. The resultant RMSE values ranked from lowest to highest (dB) are shown in Table 2.

**Figure 1**

**Figure 1**

**Figure 2**

**Figure 2**

*P*< 0.001). An ANOVA with random effects also was used to compare all four smoothing techniques excluding the raw data, and the result also was significant for PER and PLR (

*P*< 0.001). While the means among the four smoothing techniques are significantly different, due to the large sample size, the clinical significance between the smoothing techniques is admittedly marginal.

^{9–11}and others observed that clusters are correlated to the optic nerve head

^{1}and RNFL anatomy.

^{19,21}Clustering of abnormal VF points in an arcuate pattern is more specific for glaucoma rather than if the abnormal points are scattered.

^{12}Requiring progressing points to belong to the same GHT cluster increases the specificity to recognize significant change.

^{22}Traditional progression analysis techniques, such as pointwise linear regression (PLR) or glaucoma probability analysis (GPA), do not nominally require individual progressing points to belong to a specific cluster.

^{19,22,23}Mandava et al.,

^{9}with 11 clusters in a set of 76 Octopus program G1 VFs, reported that VF cluster analysis performed better than global indices (mean defect or MD) for the detection of localized VF progression and had less long-term VF fluctuation compared to pointwise analyses. The clustered MDs had a sensitivity of 90% and a specificity of 93% while the global MD had a sensitivity of 81% and a specificity of 91%. The authors observed that cluster analysis was effective in detecting localized loss and in dampening long-term fluctuation, and pointed out the use of clusters to distinguish normal from glaucomatous as well as stable from deteriorating VFs.

^{19}Various mapping and clustering techniques

^{1,10,21,24–26}have been designed with a variety of algorithms. These techniques also established relationships between functional and structural glaucoma changes and attempted to elucidate this relationship objectively, particularly with regard to VF progression. The use of customized perimetric maps has been reported recently.

^{27}Spatial averaging with the use of such customized maps may provide additional benefits to enhance the accuracy of predicted VF sensitivities, and should be investigated.

^{9}

^{28}The differences in RMSE and absolute dB values between the techniques was small, so that the clinical relevance between the smoothing techniques is limited; still, improvements to VF variability and prediction should be incorporated in clinical research whenever possible.

**E. Morales**, None;

**J.M.S. de Leon**, None;

**N. Abdollahi**, None;

**F. Yu**, None;

**K. Nouri-Mahdavi**, None;

**J. Caprioli**, None

*. 2000; 107: 1809–1815.*

*Ophthalmology**. 2012; 53: 5403–5409.*

*Invest Ophthalmol Vis Sci**. 1988; 106: 619–623.*

*Arch Ophthalmol**. 1999; 117: 1137–1142.*

*Arch Ophthalmol**. 1993; 34: 1907–1916.*

*Invest Ophthalmol Vis Sci**. 1990 ; 31: 512–520.*

*Invest Ophthalmol Vis Sci**. 2008; 145: 191–192.*

*Am J Ophthalmol**. 2011; 52: 4765–4773.*

*Invest Ophthalmol Vis Sci**. 1993; 116: 684–691.*

*Am J Ophthalmol**. 1989; 227: 216–220.*

*Graefes Arch Clin Exp Ophthalmol**. 1991; 109: 1684–1689.*

*Arch Ophthalmol**. 1993; 2: 13–20.*

*J Glaucoma**. 1995; 79: 207–212.*

*Br J Ophthalmol**. 1997; 104: 517–524.*

*Ophthalmology**. 2007; 48: 251–257.*

*Invest Ophthalmol Vis Sci**. 1994; 15: 299–325.*

*Control Clin Trials**. 1998; 105: 1146–1164.*

*Ophthalmology**. 1992; 110: 812–819.*

*Arch Ophthalmol**. 2012; 53: 2390–2394.*

*Invest Ophthalmol Vis Sci**. 2013. Available at: http://www.R-project.org/.*

*R Found Stat Comput Vienna Austria**. 2012; 53: 8396–8404.*

*Invest Ophthalmol Vis Sci**. 2005; 123: 193–199.*

*Arch Ophthalmol**. 1998; 82: 1097–1098.*

*Br J Ophthalmol**. 2008; 49: 3018–3025.*

*Invest Ophthalmol Vis Sci**. 2013; 54: 3289–3296.*

*Invest Ophthalmol Vis Sci**. 2012; 53: 2740–2748.*

*Invest Ophthalmol Vis Sci**. 2015; 122: 1–11.*

*Ophthalmology**. 2012; 53: 224–227.*

*Invest Ophthalmol Vis Sci*