Detection of progression of glaucomatous visual field damage using the point-wise method with the binomial test

Understanding and identifying visual field progression

Detecting deterioration of visual field sensitivity measurements is important for the diagnosis and management of glaucoma. This review surveys the current methods for assessing progression that are implemented in clinical devices, which have been used in clinical trials, alongside more recent advances proposed in the literature. Advice is also offered to clinicians on what they can do to improve the collection of perimetric data to help analytical progression methods more accurately predict change. This advice includes a discussion of how frequently visual field testing should be undertaken, with a view towards future developments, such as digital healthcare outside the standard clinical setting and more personalised approaches to perimetry.

Investigating the clinical validity of the guided progression analysis definition with 10-2 visual field in retinitis pigmentosa

PURPOSE

To investigate the clinical validity of the Guided Progression Analysis definition (GPAD) and cluster-based definition (CBD) with the Humphrey Field Analyzer (HFA) 10-2 test in retinitis pigmentosa (RP).

METHODS

Ten non-progressive RP visual fields (VFs) (HFA 10-2 test) were simulated for each of 10 VFs of 111 eyes (10 simulations × 10 VF sequencies × 111 eyes = 111,000 VFs; Dataset 1). Using these simulated VFs, the specificity of GPAD for the detection of progression was determined. Using this dataset, similar analyses were conducted for the CBD, in which the HFA 10-2 test was divided into four quadrants. Subsequently, the Hybrid Definition was designed by combining the GPAD and CBD; various conditions of the GPAD and CBD were altered to approach a specificity of 95.0%. Subsequently, actual HFA 10-2 tests of 116 RP eyes (10 VFs each) were collected (Dataset 2), and true positive rate, true negative rate, false positive rate, and the time required to detect VF progression were evaluated and compared across the GPAD, CBD, and Hybrid Definition.

RESULTS

Specificity values were 95.4% and 98.5% for GPAD and CBD, respectively. There were no significant differences in true positive rate, true negative rate, and false positive rate between the GPAD, CBD, and Hybrid Definition. The GPAD and Hybrid Definition detected progression significantly earlier than the CBD (at 4.5, 5.0, and 4.5 years, respectively).

CONCLUSIONS

The GPAD and the optimized Hybrid Definition exhibited similar ability for the detection of progression, with the specificity reaching 95.4%.

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.

Detecting Progression of Retinitis Pigmentosa Using the Binomial Pointwise Linear Regression Method

Purpose

A method of evaluating central visual field (VF) progression in eyes with retinitis pigmentosa (RP) has still to be established. We previously reported the potential merit of applying a binomial test to pointwise linear regression (binomial PLR) in glaucoma progression. In the current study, we investigated the usefulness of binomial PLR in eyes with RP.

Methods

A series of 10 VFs (VF 1–10, Humphrey field analyzer, 10-2 test) from 196 eyes of 103 patients with RP were collected retrospectively. The PLR was performed by regressing the total deviation of all test points with the complete series of 10 VFs. The accuracy (positive predictive value, negative predictive value, and false-positive rate) and the time required to detect VF progression with shorter VF series (from VF 1–5 to VF 1–9) were compared across the binomial PLR, a permutation analysis of PLR (PoPLR), and a mean deviation (MD) trend analysis.

Results

In evaluating VF progression, the binomial PLR was comparable with the PoPLR and MD trend analyses in its positive predictive value (0.55 to 0.95), negative predictive value (0.67 to 0.92), and false-positive rate (0.01 to 0.05). The binomial PLR required significantly less time to detect VF progression (5.0 ± 2.0 years) than the PoPLR and MD trend analyses (P < 0.01, P < 0.001, respectively).

Conclusions

The application of a binomial PLR achieved reliable and earlier detection of central VF progression in eyes with RP.

Translational Relevance

A binomial PLR was useful in assessing VF progression in RP.

Variability and Power to Detect Progression of Different Visual Field Patterns

PURPOSE

To compare the variability and ability to detect visual field (VF) progression of 24-2, central 12 locations of the 24-2 and 10-2 VF tests in eyes with abnormal VFs.

DESIGN

Retrospective, multisite cohort.

PARTICIPANTS

A total of 52 806 24-2 and 11 966 10-2 VF tests from 7307 eyes from the Glaucoma Research Network database were analyzed. Only eyes with ≥ 5 visits and ≥ 2 years of follow-up were included.

METHODS

Linear regression models were used to calculate the rates of mean deviation (MD) change (slopes), whereas their residuals were used to assess variability across the entire MD range. Computer simulations (n = 10 000) based on real MD residuals of our sample were performed to estimate power to detect significant progression (P < 5%) at various rates of MD change.

MAIN OUTCOME MEASURES

Time required to detect progression.

RESULTS

For all 3 patterns, the MD variability was highest within the -5 to -20 decibel (dB) range and consistently lower with the 10-2 compared with 24-2 or central 24-2. Overall, time to detect confirmed significant progression at 80% power was the lowest with 10-2 VF, with a decrease of 14.6% to 18.5% when compared with 24-2 and a decrease of 22.9% to 26.5% when compared with central 24-2.

CONCLUSIONS

Time to detect central VF progression was reduced with 10-2 MD compared with 24-2 and C24-2 MD in glaucoma eyes in this large dataset, in part because 10-2 tests had lower variability. These findings contribute to current evidence of the potential value of 10-2 testing in the clinical management of patients with glaucoma and in clinical trial design.

Predicting eyes at risk for rapid glaucoma progression based on an initial visual field test using machine learning

OBJECTIVE

To assess whether machine learning algorithms (MLA) can predict eyes that will undergo rapid glaucoma progression based on an initial visual field (VF) test.

DESIGN

Retrospective analysis of longitudinal data.

SUBJECTS

175,786 VFs (22,925 initial VFs) from 14,217 patients who completed ≥5 reliable VFs at academic glaucoma centers were included.

METHODS

Summary measures and reliability metrics from the initial VF and age were used to train MLA designed to predict the likelihood of rapid progression. Additionally, the neural network model was trained with point-wise threshold data in addition to summary measures, reliability metrics and age. 80% of eyes were used for a training set and 20% were used as a test set. MLA test set performance was assessed using the area under the receiver operating curve (AUC). Performance of models trained on initial VF data alone was compared to performance of models trained on data from the first two VFs.

MAIN OUTCOME MEASURES

Accuracy in predicting future rapid progression defined as MD worsening more than 1 dB/year.

RESULTS

1,968 eyes (8.6%) underwent rapid progression. The support vector machine model (AUC 0.72 [95% CI 0.70-0.75]) most accurately predicted rapid progression when trained on initial VF data. Artificial neural network, random forest, logistic regression and naïve Bayes classifiers produced AUC of 0.72, 0.70, 0.69, 0.68 respectively. Models trained on data from the first two VFs performed no better than top models trained on the initial VF alone. Based on the odds ratio (OR) from logistic regression and variable importance plots from the random forest model, older age (OR: 1.41 per 10 year increment [95% CI: 1.34 to 1.08]) and higher pattern standard deviation (OR: 1.31 per 5-dB increment [95% CI: 1.18 to 1.46]) were the variables in the initial VF most strongly associated with rapid progression.

CONCLUSIONS

MLA can be used to predict eyes at risk for rapid progression with modest accuracy based on an initial VF test. Incorporating additional clinical data to the current model may offer opportunities to predict patients most likely to rapidly progress with even greater accuracy.

Investigating the clinical usefulness of definitions of progression with 10-2 visual field

BACKGROUND/AIM

To investigate the clinical validity of the Guided Progression Analysis definition (GPAD) and cluster-based definition (CBD) with the Humphrey Field Analyzer 10-2 test in diagnosing glaucomatous visual field (VF) progression, and to introduce a novel definition with optimised specificity by combining the 'any-location' and 'cluster-based' approaches (hybrid definition).

METHODS

64 400 stable glaucomatous VFs were simulated from 664 pairs of 10-2 tests (10 sets × 10 VF series × 664 eyes; data set 1). Using these simulated VFs, the specificity to detect progression and the effects of changing the parameters (number of test locations or consecutive VF tests, and percentile cut-off values) were investigated. The hybrid definition was designed as the combination where the specificity was closest to 95.0%. Subsequently, another 5000 actual glaucomatous 10-2 tests from 500 eyes (10 VFs each) were collected (data set 2), and their accuracy (sensitivity, specificity and false positive rate) and the time needed to detect VF progression were evaluated.

RESULTS

The specificity values calculated using data set 1 with GPAD and CBD were 99.6% and 99.8%. Using data set 2, the hybrid definition had a higher sensitivity than GPAD and CBD, without detriment to the specificity or false positive rate. The hybrid definition also detected progression significantly earlier than GPAD and CBD (at 3.1 years vs 4.2 years and 4.1 years, respectively).

CONCLUSIONS

GPAD and CBD had specificities of 99.6% and 99.8%, respectively. A novel hybrid definition (with a specificity of 95.5%) had higher sensitivity and enabled earlier detection of progression.

The usefulness of the Deep Learning method of variational autoencoder to reduce measurement noise in glaucomatous visual fields

The aim of the study was to investigate the usefulness of processing visual field (VF) using a variational autoencoder (VAE). The training data consisted of 82,433 VFs from 16,836 eyes. Testing dataset 1 consisted of test-retest VFs from 104 eyes with open angle glaucoma. Testing dataset 2 was series of 10 VFs from 638 eyes with open angle glaucoma. A VAE model to reconstruct VF was developed using the training dataset. VFs in the testing dataset 1 were then reconstructed using the trained VAE and the mean total deviation (mTD) was calculated (mTDVAE). In testing dataset 2, the mTD value of the tenth VF was predicted using shorter series of VFs. A similar calculation was carried out using a weighted linear regression where the weights were equal to the absolute difference between mTD and mTDVAE. In testing dataset 1, there was a significant relationship between the difference between mTD and mTDVAE from the first VF and the difference between mTD in the first and second VFs. In testing dataset 2, mean squared prediction errors with the weighted mTD trend analysis were significantly smaller than those form the unweighted mTD trend analysis.

Validating the efficacy of the binomial pointwise linear regression method to detect glaucoma progression with multicentral database

BACKGROUND/AIM

We previously reported the benefit of applying binomial pointwise linear regression (PLR: binomial PLR) to detect 10-2 glaucomatous visual field (VF) progression. The purpose of the current study was to validate the usefulness of the binomial PLR to detect glaucomatous VF progression in the central 24°.

METHODS

Series of 15 VFs (Humphrey Field Analyzer 24-2 SITA-standard) from 341 eyes of 233 patients, obtained over 7.9±2.1 years (mean±SD), were investigated. PLR was performed by regressing the total deviation of all test points. VF progression was determined from the VF test points analyses using the binomial test (one side, p<0.025). The time needed to detect VF progression was compared across the binomial PLR, permutation analysis of PLR (PoPLR) and mean total deviation (mTD) trend analysis.

RESULTS

The binomial PLR was comparable with PoPLR and mTD trend analyses in the positive predictive value (0.18-0.87), the negative predictive value (0.89-0.95) and the false positive rate (0.057-0.35) to evaluate glaucomatous VF progression. The time to classify progression with binomial PLR (5.8±2.8 years) was significantly shorter than those with mTD trend analysis (6.7±2.8 years) and PoPLR (6.6±2.7 years).

CONCLUSIONS

The binomial PLR method, which detected glaucomatous VF progression in the central 24° significantly earlier than PoPLR and mTD trend analyses, shows promise for improving our ability to detect visual field progression for clinical management of glaucoma and in clinical trials of new glaucoma therapies.

Forecasting future Humphrey Visual Fields using deep learning

Purpose

To determine if deep learning networks could be trained to forecast future 24–2 Humphrey Visual Fields (HVFs).

Methods

All data points from consecutive 24–2 HVFs from 1998 to 2018 were extracted from a university database. Ten-fold cross validation with a held out test set was used to develop the three main phases of model development: model architecture selection, dataset combination selection, and time-interval model training with transfer learning, to train a deep learning artificial neural network capable of generating a point-wise visual field prediction. The point-wise mean absolute error (PMAE) and difference in Mean Deviation (MD) between predicted and actual future HVF were calculated.

Results

More than 1.7 million perimetry points were extracted to the hundredth decibel from 32,443 24–2 HVFs. The best performing model with 20 million trainable parameters, CascadeNet-5, was selected. The overall point-wise PMAE for the test set was 2.47 dB (95% CI: 2.45 dB to 2.48 dB), and deep learning showed a statistically significant improvement over linear models. The 100 fully trained models successfully predicted future HVFs in glaucomatous eyes up to 5.5 years in the future with a correlation of 0.92 between the MD of predicted and actual future HVF and an average difference of 0.41 dB.

Conclusions

Using unfiltered real-world datasets, deep learning networks show the ability to not only learn spatio-temporal HVF changes but also to generate predictions for future HVFs up to 5.5 years, given only a single HVF.

Early Detection of Glaucomatous Visual Field Progression Using Pointwise Linear Regression With Binomial Test in the Central 10 Degrees

PURPOSE

We previously reported that it was beneficial to apply binomial pointwise linear regression (PLR) to detect 24-2 glaucomatous visual field (VF) progression, compared to mean deviation (MD) trend analysis and permutation analysis of PLR (PoPLR). The purpose of the current study was to validate the usefulness of the binomial PLR method to detect VF progression in the central 10 degrees in glaucoma patients.

DESIGN

Reliability assessment.

METHODS

A series of 15 VFs (Humphrey Field Analyzer 10-2 SITA-standard) from 97 eyes in 69 primary open-angle glaucoma patients, obtained over 8.5 ± 1.3 years (mean ± SD), were investigated. PLR was performed by regressing the total deviation of all test points on the series of 15 VFs. VF progression was determined from the analyses of VF test points using the binomial test (1-sided, P < .025). The time needed to detect VF progression was also investigated. The results were compared with PoPLR and MD trend analyses.

RESULTS

The binomial PLR was comparable to PoPLR and MD trend analyses in the positive predictive value (0.19 to 0.80), the negative predictive value (0.86 to 1.0), and the false positive rate (0.0 to 0.13) to evaluate glaucomatous VF progression. The time needed to detect VF progression (4.2 ± 1.8 years) was significantly shorter with the binomial PLR method compared with PoPLR and MD trend analysis (P = .04, P = .012, respectively).

CONCLUSIONS

The binomial PLR method detected glaucomatous VF progression in the central 10 degrees significantly earlier than PoPLR and MD trend analyses.

Investigating the usefulness of a cluster-based trend analysis to detect visual field progression in patients with open-angle glaucoma

BACKGROUND/AIMS

To investigate the usefulness of the Octopus (Haag-Streit) EyeSuite's cluster trend analysis in glaucoma.

METHODS

Ten visual fields (VFs) with the Humphrey Field Analyzer (Carl Zeiss Meditec), spanning 7.7 years on average were obtained from 728 eyes of 475 primary open angle glaucoma patients. Mean total deviation (mTD) trend analysis and EyeSuite's cluster trend analysis were performed on various series of VFs (from 1st to 10th: VF1-10 to 6th to 10th: VF6-10). The results of the cluster-based trend analysis, based on different lengths of VF series, were compared against mTD trend analysis.

RESULT

Cluster-based trend analysis and mTD trend analysis results were significantly associated in all clusters and with all lengths of VF series. Between 21.2% and 45.9% (depending on VF series length and location) of clusters were deemed to progress when the mTD trend analysis suggested no progression. On the other hand, 4.8% of eyes were observed to progress using the mTD trend analysis when cluster trend analysis suggested no progression in any two (or more) clusters.

CONCLUSION

Whole field trend analysis can miss local VF progression. Cluster trend analysis appears as robust as mTD trend analysis and useful to assess both sectorial and whole field progression. Cluster-based trend analyses, in particular the definition of two or more progressing cluster, may help clinicians to detect glaucomatous progression in a timelier manner than using a whole field trend analysis, without significantly compromising specificity.

Unsupervised Gaussian Mixture-Model With Expectation Maximization for Detecting Glaucomatous Progression in Standard Automated Perimetry Visual Fields

Purpose

To validate Gaussian mixture-model with expectation maximization (GEM) and variational Bayesian independent component analysis mixture-models (VIM) for detecting glaucomatous progression along visual field (VF) defect patterns (GEM–progression of patterns (POP) and VIM-POP). To compare GEM-POP and VIM-POP with other methods.

Methods

GEM and VIM models separated cross-sectional abnormal VFs from 859 eyes and normal VFs from 1117 eyes into abnormal and normal clusters. Clusters were decomposed into independent axes. The confidence limit (CL) of stability was established for each axis with a set of 84 stable eyes. Sensitivity for detecting progression was assessed in a sample of 83 eyes with known progressive glaucomatous optic neuropathy (PGON). Eyes were classified as progressed if any defect pattern progressed beyond the CL of stability. Performance of GEM-POP and VIM-POP was compared to point-wise linear regression (PLR), permutation analysis of PLR (PoPLR), and linear regression (LR) of mean deviation (MD), and visual field index (VFI).

Results

Sensitivity and specificity for detecting glaucomatous VFs were 89.9% and 93.8%, respectively, for GEM and 93.0% and 97.0%, respectively, for VIM. Receiver operating characteristic (ROC) curve areas for classifying progressed eyes were 0.82 for VIM-POP, 0.86 for GEM-POP, 0.81 for PoPLR, 0.69 for LR of MD, and 0.76 for LR of VFI.

Conclusions

GEM-POP was significantly more sensitive to PGON than PoPLR and linear regression of MD and VFI in our sample, while providing localized progression information.

Translational Relevance

Detection of glaucomatous progression can be improved by assessing longitudinal changes in localized patterns of glaucomatous defect identified by unsupervised machine learning.