Enhancement of Visual Field Predictions with Pointwise Exponential Regression (PER) and Pointwise Linear Regression (PLR)

Efficacy of Smoothing Algorithms to Enhance Detection of Visual Field Progression in Glaucoma

Purpose

To evaluate and compare the effectiveness of nearest neighbor (NN)- and variational autoencoder (VAE)-smoothing algorithms to reduce variability and enhance the performance of glaucoma visual field (VF) progression models.

Design

Longitudinal cohort study.

Subjects

7150 eyes (4232 patients), with ≥ 5 years of follow-up and ≥ 6 visits.

Methods

Vsual field thresholds were smoothed with the NN and VAE algorithms. The mean total deviation (mTD) and VF index rates, pointwise linear regression (PLR), permutation of PLR (PoPLR), and the glaucoma rate index were applied to the unsmoothed and smoothed data.

Main Outcome Measures

The proportion of progressing eyes and the conversion to progression were compared between the smoothed and unsmoothed data. A simulation series of noiseless VFs with various patterns of glaucoma damage was used to evaluate the specificity of the smoothing models.

Results

The mean values of age and follow-up time were 62.8 (standard deviation: 12.6) years and 10.4 (standard deviation: 4.7) years, respectively. The proportion of progression was significantly higher for the NN and VAE smoothed data compared with the unsmoothed data. VF progression occurred significantly earlier with both smoothed data compared with unsmoothed data based on mTD rates, PLR, and PoPLR methods. The ability to detect the progressing eyes was similar for the unsmoothed and smoothed data in the simulation data.

Conclusions

Smoothing VF data with NN and VAE algorithms improves the signal-to-noise ratio for detection of change, results in earlier detection of VF progression, and could help monitor glaucoma progression more effectively in the clinical setting.

Financial Disclosures

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Pointwise and Region-Wise Course of Visual Field Loss in Patients With Glaucoma

Purpose

Accurate assessment of visual field (VF) trend may help clinicians devise the optimum treatment regimen. This study was conducted to investigate the behavior of VF sequences using pointwise and region-wise linear, exponential, and sigmoid regression models.

Materials and Methods

In a retrospective cohort study, 277 eyes of 139 patients with glaucoma who had been followed for at least 7 years were investigated. Linear, exponential, and sigmoid regression models were fitted for each VF test location and Glaucoma Hemifield Test (GHT) region to model the trend of VF loss. The model with the lowest root mean square error (RMSE) was selected as the best fit.

Results

The mean age (standard deviation [SD]) of the patients was 59.9 years (9.8) with a mean follow-up time of 9.3 (0.7) years. The exponential regression had the best fit based on pointwise and region-wise approaches in 39.3% and 38.1% of eyes, respectively. The results showed a better performance based on sigmoid regression in patients with initial VF sensitivity threshold greater than 22 dB (71.6% in pointwise and 62.2% in region-wise approaches). The overall RMSE of the region-wise regression model was lower than the overall RMSE of the pointwise model.

Conclusions

In the current study, nonlinear regression models showed a better fit compared to the linear regression models in tracking VF loss behavior. Moreover, findings suggest region-wise analysis may provide a more appropriate approach for assessing VF deterioration.

Translational Relevance

Findings may confirm a nonlinear progression of VF deterioration in patients with glaucoma.

The Usefulness of Assessing Glaucoma Progression With Postprocessed Visual Field Data

Purpose

Data postprocessing with statistical techniques that are less sensitive to noise can be used to reduce variability in visual field (VF) series. We evaluated the detection of glaucoma progression with postprocessed VF data generated with the dynamic structure–function (DSF) model and MM-estimation robust regression (MRR).

Method

The study included 118 glaucoma eyes with at least 15 visits selected from the Rotterdam dataset. The DSF and MRR models were each applied to observed mean deviation (MD) values from the first three visits (V_1–3) to predict the MD at V_4. MD at V₅ was predicted with data from V_1–4 and so on until the MD at V₉ was predicted, creating two additional datasets: DSF-predicted and MRR-predicted. Simple linear regression was performed to assess progression at the ninth visit. Sensitivity was evaluated by adjusting for false-positive rates estimated from patients with stable glaucoma and by using longer follow-up series (12th and 15th visits) as a surrogate for progression.

Results

For specificities of 80% to 100%, the DSF-predicted dataset had greater sensitivity than the observed and MRR-predicted dataset when positive rates were normalized with corresponding false-positive estimates. The DSF-predicted and observed datasets had similar sensitivity when the surrogate reference standard was applied.

Conclusions

Without compromising specificity, the use of DSF-predicted measurements to identify progression resulted in a better or similar sensitivity compared to using existing VF data.

Translational Relevance

The DSF model could be applied to postprocess existing visual field data, which could then be evaluated to identify patients at risk of progression.

Rate of visual field decay in glaucomatous eyes with acquired pits of the optic nerve

BACKGROUND

To evaluate the relationship between the presence of an acquired pit of the optic nerve (APON) and the rate of visual field (VF) decay in primary open-angle glaucoma (POAG).

METHODS

Consecutive patients with POAG were screened for APON by three glaucoma specialists. A control group of POAG eyes without APON were matched with the APON group for factors such as age, gender, baseline intraocular pressure and baseline mean deviation (MD). The pointwise rate of change (PRC) was used for pointwise comparisons between the two groups. MD rate, Visual Field Index (VFI) rate and Glaucoma Rate Index (GRI) were used for global rate comparisons. We compared the proportions of eyes progressing in the groups with event-based guided progression analysis (GPA), MD, VFI and GRI criteria.

RESULTS

Mean (SD) PRC was faster in the APON group -1.00 (±2.57) %/year compared with the control group -0.25 (±2.19) %/year; p<0.001. MD rate (-0.22 (±0.27) dB/year vs 0.03 (±0.41) dB/year; p=0.009), VFI rate (-0.81 (±0.86) %/year vs -0.05 (±1.0) %/year; p=0.04) and GRI (-12.27 (±16.27) vs -3.75 (±10.6); p=0.052) were all faster in the APON group compared with controls. The proportion of progressing eyes with GPA, MD, VFI and GRI was not significantly different between the two groups (p>0.1).

CONCLUSIONS

The presence of APON in patients with POAG is associated with focal, fast rates of VF decay. Identification of patients with APON should alert clinicians to the possibility of a fast rate of functional progression and to consider appropriately aggressive treatment of their glaucoma.

Pointwise Methods to Measure Long-term Visual Field Progression in Glaucoma

Importance

Rates of visual field (VF) progression vary among patients with glaucoma. Knowing the rate of progression of individual patients would allow appropriately aggressive therapy for patients with high rates of visual loss and protect those with low rates from unnecessary therapy.

Objective

To compare 3 pointwise methods of estimating the rate of VF progression in glaucoma.

Design, Setting, and Participants

This retrospective, observational cohort study included 729 eyes of 567 consecutive patients with primary open-angle glaucoma who had at least 6 reliable VFs and at least 3 years of follow-up. One hundred seventy-six patients (257 eyes) were treated at a tertiary glaucoma center; in addition, data were collected from 391 participants (472 eyes) in the Advanced Glaucoma Intervention Study. Data were collected from May 1988 to November 2004 and analyzed from October 2018 to February 2019.

Exposures

Estimates of VF progression were measured with guided progression analysis (GPA), pointwise linear regression (PLR), and the glaucoma rate index (GRI). A subgroup analysis was performed in a subset of patients with likely VF progression and likely VF stability.

Main Outcomes and Measures

Proportion of VF series detected as progressing, estimates of false-positive proportions, time to detect progression, and agreement among measures.

Results

Among the 567 patients included in the analysis, mean (SD) age was 65.6 (9.7) years, 300 (52.9%) were female, and 295 (52.0%) were white. The median baseline mean deviation was -6.7 (interquartile range [IQR], -11.6 to -3.5) dB; the median follow-up time, 8.9 (IQR, 7.3-10.4) years. The proportion of eyes labeled as progressing was 27.7% according to the GPA, 33.5% according to the PLR, and 52.9% according to the GRI; pairwise differences for GRI vs PLR were 20% (95% CI, 17%-23%); for GRI vs GPA, 25% (95% CI, 22%-29%); and for PLR vs GPA, 6% (95% CI, 3%-9%; P < .001 for all comparisons, McNemar test). The shortest median time to progression was with the GRI (8.8 [IQR, 2.4-10.5 years), compared with the GPA and PLR (both >16 years). The hazard ratio of VF progression for GRI vs PLR (reference) was 11.3 (95% CI, 9.2-13.7); for GRI vs GPA (reference), 18.1 (95% CI, 14.5-22.6); and for PLR vs GPA (reference), 1.5 (95% CI, 1.3-1.9; P < .001 for all comparisons, Cox proportional hazards regression). These results held in the subgroup with likely progression; the proportions of progressing eyes were 73.7% (115 of 156) for GPA, 81.4% (127 of 156) for PLR, and 92.9% (145 of 156) for GRI. Pairwise difference for GRI vs PLR was 11.5% (95% CI, 7.4%-17.6%; P < .001, McNemar test); for GRI vs GPA, 19.2% (95% CI, 12.6%-26.4%; P < .001, McNemar test); and for PLR vs GPA, 7.7% (95% CI, 0.3%-15.7%; P = .08, McNemar test).

Conclusions and Relevance

These results suggest GRI can detect long-term VF progression in glaucoma earlier than PLR or GPA. Validation with prospective designs may strengthen the generalizability and value of this method.

Risk Factors for Fast Visual Field Progression in Glaucoma

PURPOSE

To identify baseline and longitudinal risk factors for fast visual field (VF) decay in patients with open-angle glaucoma.

DESIGN

Retrospective cohort study.

METHODS

Patients with open-angle glaucoma with ≥6 VFs and ≥4 years of follow-up were included. VF decay rates were measured with the following methods: mean deviation (MD) rate, VF index (VFI) rate, and the Glaucoma Rate Index (GRI). The relationship between VF rates and clinical variables were investigated with linear mixed models. Logistic regression analysis was performed to determine which factors were associated with fast progression.

RESULTS

A total of 1317 eyes of 745 patients with a mean (± SD) age of 63.3 (±10.9) years and a median (interquartile range) MD -2.4 (-0.7 to -5.6) dB at baseline were analyzed. The median (interquartile range) number of VFs was 12 (9 to 16), and mean follow-up duration was 11.5 (±3.7) years. Older age (P < .001), higher peak intraocular pressure (IOP) (P < .001), and glaucoma surgery during the study period (P < .001) were associated with faster rates of progression regardless of the method used. Worse baseline MD was associated with MD rate (P = .02), but neither with VFI rate (P = .37) nor GRI (P = .31); whereas pseudoexfoliative glaucoma was associated with faster rates of progression with MD (P = .008) and VFI (P = .01) rates, but not with GRI. Higher peak IOPs (P = .005) was a significant predictor for fast progression.

CONCLUSION

In this cohort, older age, peak IOP, pseudoexfoliative glaucoma, and baseline MD were associated with the rate of glaucomatous VF worsening. Fast progressors had a higher peak IOP than non-fast progressors. The identification and appropriately aggressive treatment of fast progressors would reduce visual disability from glaucoma.

Cataract Surgery and Rate of Visual Field Progression in Primary Open-Angle Glaucoma

PURPOSE

To test the hypothesis that cataract surgery slows the apparent rate of visual field (VF) decay in primary open-angle glaucoma patients compared with rates measured during cataract progression.

DESIGN

Retrospective cohort study.

METHODS

Consecutive open-angle glaucoma patients who underwent cataract surgery and who had ≥4 VFs and ≥3 years of follow-up before and after surgery were retrospectively reviewed. Mean deviation (MD) rate, visual field index (VFI) rate, pointwise linear regression (PLR), pointwise rate of change (PRC), and the Glaucoma Rate Index (GRI) were compared before and after cataract surgery.

RESULTS

A total of 134 eyes of 99 patients were included. Median (interquartile range) follow-up was 6.5 (4.7-8.1) and 5.3 (4.0-7.3) years before and after cataract surgery, respectively. All intraocular pressure (IOP) parameters (mean IOP, standard deviation of IOP, and peak IOP) significantly improved (P < .001) after cataract surgery. All VF indices indicated an accelerated VF decay rate after cataract surgery: MD rate (-0.18 ± 0.40 dB/year vs -0.40 ± 0.62 dB/year, P < .001), VFI rate (-0.44% ± 1.09%/year vs -1.19% ± 1.85%/year, P < .001), GRI (-5.5 ± 10.8 vs -13.5 ± 21.5; P < .001), and PRC (-0.62% ± 2.47%/year before and -1.35% ± 3.71%/year after surgery; P < .001) and PLR (-0.20 ± 0.82 dB/year before and -0.42 ± 1.16 dB/year after surgery; P < .001) for all VF locations. Worse baseline MD and postoperative peak IOP were significantly associated with the postoperative VF decay rate and the change in the decay rate after cataract surgery.

CONCLUSION

Although all IOP parameters improved after cataract surgery, VFs continued to progress. Cataract surgery does not slow the apparent rate of glaucomatous VF decay as compared to rates measured during the progression of the cataract.

A Method to Measure the Rate of Glaucomatous Visual Field Change

Purpose

To develop a method to measure the rate of glaucomatous visual field (VF) deterioration and to identify fast progressors.

Methods

Retrospective, longitudinal, observational study of 8486 eyes of 4610 glaucomatous patients with ≥6 VFs and ≥3 years of follow-up. A Glaucoma Rate Index (GRI) was calculated. VF locations were partitioned into exponential decay or exponential improvement models. A pointwise rate of change (PRC) was estimated with an exponential fit and expressed as the percent/year change of the age- and location-matched normal perimetric range, presented as a spatially conserved VF map. PRCs were summed and normalized with boundary rates set by simulated decaying and improving VF series on a scale of -100 to +100, respectively.

Results

A total of 89,704 VF examinations with 425,039 test location series was used. Median follow-up and number of VFs/eye were 9.7 years and 9 VFs, respectively. Initial and final mean deviations (±SD) were -4.2 (±5.2) and -5.7 (±6.4) dB. The proportions of test locations designated as decayed, improved, and unchanged were 13%, 4%, and 83%, respectively. Mean PRCs for decay, improvement, and no change were -3.7 (±4.7)%/y, 2.5 (±2.6)%/y, and -0.5 (±2.1)%/y, respectively. The number of eyes with negative and positive GRIs was 5802 (68%) and 2390 eyes (28%), respectively. The proportion of eyes defined as fast progressors was 6.8%.

Conclusions

GRI provides a robust measure of glaucomatous VF change, operates without discontinuity over the entire perimetric range, and can be used to identify fast progressors.

Translational Relevance

This study describes a novel method that can help the clinician to determine VF progression.