A cluster analysis for threshold perimetry

Prediction of visual field progression in glaucoma: existing methods and artificial intelligence

Timely treatment is essential in the management of glaucoma. However, subjective assessment of visual field (VF) progression is not recommended, because it can be unreliable. There are two types of artificial intelligence (AI) strong and weak (machine learning). Weak AIs can perform specific tasks. Linear regression is a method of weak AI. Using linear regression in the real-world clinic has enabled analyzing and predicting VF progression. However, caution is still required when interpreting the results, because whenever the number of VF data sets investigated is small, the predictions can be inaccurate. Several other non-ordinal, or modern AI methods have been constructed to improve prediction accuracy, such as clustering and more modern AI methods of Analysis with Non-Stationary Weibull Error Regression and Spatial Enhancement (ANSWERS), Variational Bayes Linear Regression (VBLR), Kalman Filter and sparse modeling (The least absolute shrinkage and selection operator regression: Lasso). It is also possible to improve the prediction performance using retinal thickness measured with optical coherence tomography by using machine learning methods, such as multitask learning.

Cluster Formation for Analyses of Glaucomatous Visual Field Defects in Central 10-2 Visual Field in Normal Tension Glaucoma Eyes

Purpose

To develop a cluster system to analyze the retinal sensitivity loss of 68 test points in the central 10 degrees of standard automated perimetry (SAP) in eyes with normal tension glaucoma (NTG).

Patients and Methods

Patients with NTG who met the following criteria were included: visual acuity ≥0.7, SAP-derived mean deviation ≥−15 dB, and pattern deviation probability plots with at least one point with a probability of <0.5% and/or two or more contiguous points with a probability of <1% that did not cross the horizontal meridian in the central 12 points of the 24-2 test points. SAP with the Swedish Interactive Threshold Algorithm Standard (SITA-S) 10-2 program (10-2) was performed within 6 months of the SITA-S 24-2. The averaged total deviation (TD) for each of the 68 test points in the 10-2 was calculated. Hierarchical cluster analyses were performed based on the deviation of the TDs of the test points, and a dendrogram was created. The number of clusters was determined following the Sturges’ rule.

Results

One hundred and twenty-six eyes of 126 patients (61.9±11.4 years) were studied. Hierarchical cluster analysis of the TD values statistically obtained a dendrogram that divided the 68 test points into 7 clusters. Of these 7 clusters, 21 points belonging to the clusters in the papillomacular region included cluster 5. Cluster 5 was distributed above and below the horizontal meridian, which does not agree with the course of the retinal nerve fiber layer (RNFL).

Conclusion

The hierarchical cluster analysis of the TD values stratified the 68 test points of the 10-2 into seven clusters. Considering the course of the RNFL, cluster 5 was divided into clusters of 5a and 5b, and consequently eight clusters were considered to be appropriate for detecting glaucomatous visual field defects in the central 10 degrees in NTG eyes.

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

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.

Mapping glaucoma patients' 30-2 and 10-2 visual fields reveals clusters of test points damaged in the 10-2 grid that are not sampled in the sparse 30-2 grid

Purpose

To cluster test points in glaucoma patients' 30-2 and 10-2 visual field (VF) (Humphrey Field Analyzer: HFA, Carl Zeiss Meditec, Dublin, CA) in order to map the different regions damaged by the disease.

Method

This retrospective study included 128 eyes from 128 patients. 142 total deviation (TD) values (74 from the 30-2 VF and 68 from the 10-2 VF) were clustered using the ‘Hierarchical Ordered Partitioning And Collapsing Hybrid – Partitioning Around Medoids’ algorithm. The stability of the identified clusters was evaluated using bootstrapping.

Results

65 sectors were identified in total: 38 sectors were located outside the 10-2 VF whereas 29 sectors were located inside the 10-2 VF (two sectors overlap in both grids). The mapping of many sectors appeared to follow the distribution of retinal nerve fiber bundles. The results of bootstrapping suggested clusters were stable whether they were outside or inside the 10-2 VF.

Conclusion

A considerable number of sectors were identified in the 10-2 VF area, despite the fact that clustering was carried out on all points in both the 30-2 VF and 10-2 VF simultaneously. These findings suggest that glaucomatous central VF deterioration cannot be picked up by the 30-2 test grid alone, because of poor spatial sampling; denser estimation of the central ten degrees, than offered by the 30-2 test grid alone, is needed. It may be beneficial to develop a new VF test grid that combines test points from 30-2 and 10-2 VFs – the results of this study could help to devise this test grid.

Trained artificial neural network for glaucoma diagnosis using visual field data: a comparison with conventional algorithms

PURPOSE

To evaluate and confirm the performance of an artificial neural network (ANN) trained to recognize glaucomatous visual field defects, and compare its diagnostic accuracy with that of other algorithms proposed for the detection of visual field loss.

METHODS

SITA Standard 30-2 visual fields, from 100 glaucoma patients and 116 healthy participants, formed the data set. Our ANN was a previously described fully trained network using scored pattern deviation probability maps as input data. Its diagnostic accuracy was compared to that of the Glaucoma Hemifield Test, the Pattern Standard Deviation index at the P<5% and <1%, and also to a technique based on the recognizing clusters of significantly depressed test points.

RESULTS

The included tests had early to moderate visual field loss (median MD=-6.16 dB). ANN achieved a sensitivity of 93% at a specificity level of 94% with an area under the receiver operating characteristic curve of 0.984. Glaucoma Hemifield Test attained a sensitivity of 92% at 91% specificity. Pattern Standard Deviation, with a cut off level at P<5% had a sensitivity of 89% with a specificity of 93%, whereas at P<1% the sensitivity and specificity was 72% and 97%, respectively. The cluster algorithm yielded a sensitivity of 95% and a specificity of 82%.

CONCLUSIONS

The high diagnostic performance of our ANN based on refined input visual field data was confirmed in this independent sample. Its diagnostic accuracy was slightly to considerably better than that of the compared algorithms. The results indicate the large potential for ANN as an important clinical glaucoma diagnostic tool.

Short wavelength automated perimetry

Short Wavelength Automated Perimetry (SWAP) utilizes a blue stimulus to preferentially stimulate the blue cones and a high luminance yellow background to adapt the green and red cones and to saturate, simultaneously, the activity of the rods. This review describes the theoretical aspects of SWAP, highlights current limitations associated with the technique and discusses potential clinical applications. Compared to white-on-white (W-W) perimetry, SWAP is limited clinically by: greater variability associated with the estimation of threshold, ocular media absorption, increased examination duration and an additional learning effect. Comparative studies of SWAP and W-W perimetry have generally been undertaken on small cohorts of patients. The conclusions are frequently unconvincing due to limitations for SWAP in the delineation of abnormality and of progressive field loss. SWAP is almost certainly able to identify glaucomatous visual field loss in advance of that by W-W perimetry although the incidence of progressive field loss is similar between the two techniques. Increasing evidence suggests that functional abnormality with SWAP is preceded by structural abnormality of the optic nerve head and/or the retinal nerve fibre layer. SWAP appears to be beneficial in the detection of diabetic macular oedema and possibly in some neuro-ophthalmic disorders.

Comparison of methods to detect visual field progression in glaucoma

OBJECTIVE

The purpose of the study is to develop alternative statistical approaches for evaluating the trend of visual field series over time and to compare the results to human observers.

DESIGN

Retrospective analysis of visual field results.

PARTICIPANTS

Eighty-three eyes of 83 patients (phakic or pseudophakic) with open-angle glaucoma and 5 or more eligible fields were included in the study.

INTERVENTION

Three experienced observers independently reviewed the field series to determine stability or progression.

MAIN OUTCOME MEASURES

The following additional methods to determine progression of visual field loss were used: (1) pointwise univariate regression analysis and a glaucoma change analysis; (2) univariate regression analysis on visual field indices mean deviation, corrected loss variance, and glaucoma pattern index; (3) pointwise multivariate regression analysis with fixed effects on panel data; and (4) clusterwise multivariate regression analysis with fixed effects on panel data. The results of different statistical methods were compared by determining the pairwise agreement (Cohen's weighted kappa) between each technique and three experienced observers.

RESULTS

Patients were observed for a mean (+/-standard deviation) of 5.6 (+/-1.4) years. The visual fields of 27 (33%) and 56 (67%) eyes were considered to have progressed or remained stable, respectively, based on agreement of at least 2 of 3 observers. Univariate regression analysis on visual field indices was not useful for detection of visual field progression. Pointwise and clusterwise regression analyses with fixed effects on panel data performed as well as pointwise univariate regression analysis compared with human observers (kappa = 0.52, 0.53, and 0.55, respectively). Both methods showed better agreement with human observers than with glaucoma change analysis (kappa = 0.41).

CONCLUSIONS

A new statistical model, multivariate regression analyses with fixed effects on panel data, is an appropriate method to evaluate the course of visual field series over time and shows reasonable agreement with experienced observers and pointwise univariate regression analysis.

Relative dispersion analysis enhances perimetric sensitivity

Objective identification of minor visual field defects is problematic. A possible solution is to examine spatial correlations by means of relative dispersion analysis, a tool of fractal analysis. We studied patients with glaucoma, previous optic neuritis, chiasmal compression and lesions of the brain hemispheres, using high-pass resolution perimetry. One-hundred visual field records were drawn consecutively for each category and ranked according to severity of defects. Records with scores ranking below the 35th percentile, i.e. those with the smallest field defects, were analysed. Relative dispersion analysis recognized 1.3-2.4 times more abnormal subjects than did pattern standard deviation. A previously described form index was intermediate in sensitivity. Specificity was 96%. Relative dispersion analysis appears to capture a novel aspect of visual field abnormality, with good sensitivity and specificity. The analysis is easily performed.

The Glaucoma Laser Trial (GLT): 6. Treatment group differences in visual field changes. Glaucoma Laser Trial Research Group

PURPOSE

To determine the differences in visual fields during 42 months (3 1/2 years) of follow-up between eyes treated with argon laser trabeculoplasty first and eyes treated with topical medication first in patients with newly diagnosed primary open-angle glaucoma.

METHODS

Visual field examinations were obtained at enrollment, three and six months, and at six-month intervals thereafter during follow-up of 271 patients enrolled in the Glaucoma Laser Trial. Numeric analyses of the examination results, including global indices and patterns of localized changes, as well as masked subjective clinical impression, were used to compare the two treatment groups.

RESULTS

The mean threshold for eyes treated with laser trabeculoplasty first was 0.3 dB better than that for eyes treated with topical medication first averaged over follow-up (95% confidence interval, [-0.1, 0.7]; P = .17). More eyes treated with topical medication first (82 [31%] of 261 eyes) than eyes treated with laser trabeculoplasty first (61 [23%] of 261 eyes) had confirmed localized deterioration at least once during follow-up (P = .02). Improvement was nearly twice as common as deterioration on masked subjective impression in both groups through 30 months (2 1/2 years). Eyes treated with laser trabeculoplasty first were judged to have slightly more improvement and slightly less deterioration than eyes treated with topical medication first.

CONCLUSION

During follow-up, measures of visual field status for eyes treated with laser trabeculoplasty first were slightly better than those for eyes treated with topical medication first. Statistical significance was attained for only some of the differences, and the clinical implications of such small differences are not known.

A cluster and scotoma analysis based on empiric criteria

From a collection of 288 visual fields of glaucomatous or glaucoma suspects, 30 were selected at random and were analyzed by one expert interpreter. Visual field damage varied from nonexistent to severe. The interpreter defined clusters or scotomas subjectively according to adjacency criteria: adjacent test locations which exceeded a critical loss value were grouped as clusters or scotomas. A computer algorithm has been devised which simulates such evaluation methods. In general, a standard setting of several parameters produced a cluster display containing the same number of clusters as determined by the expert interpreter. Another display mode grouped clusters according to polygonal areas of a predetermined size (Voronoi diagram). Due to the broad selection of visual field defects, the specificity of the program with regard to various field decay patterns was small and it should thus be applicable to a broad spectrum of glaucomatous field damage.

Weighting according to location in computer-assisted glaucoma visual field analysis

In recent years several aids for automated interpretation of visual field data have been suggested. We believed that incorporation of thorough knowledge of normal visual field variability would allow improvements in the performance of such aids since more attention would be paid to field results in areas with low physiological variability. Two visual field models for classification of fields in glaucoma based on comparisons of sensitivity values in the upper and lower hemifields and on analysis of test point clusters with diminished sensitivity were compared. Both models were constructed using logistic regression analysis in 101 normal eyes and 101 eyes with glaucoma. The first, more traditional model assumed Gaussian distributions of deviations from age-corrected normal thresholds and constant variability across the field (non-weighted model). The second model took into account empirically determined variability of pointwise threshold results and of cluster volumes in various visual field regions (weighted model). The two models were subsequently tested on an independent material of 163 normal eyes and 76 eyes with glaucoma. The weighted model gave significantly better classification of the fields in both materials. Accounting for physiological threshold variability can offer significant advantages in the construction of perimetric analysis aids for detection of glaucoma.

Spatial analyses of glaucomatous visual fields; a comparison with traditional visual field indices

Interpretation of numeric automated threshold visual field results is often difficult. A large amount of data is obtained for every single field tested. Various approaches to summarize this data have been suggested, most commonly the mean and standard deviation of departures from age-corrected normal threshold values. These visual field indices differ substantially from subjective field interpretation where spatial relationships are important. We have previously devised two methods for automated field interpretation which take spatial information into account--regional up-down comparisons and arcuate cluster analysis. We now studied the merits of using these new spatial methods and compared them to traditional visual field indices for discrimination between normal and glaucomatous field results. Central static 30 degree field results in 101 eyes of 101 normal subjects and 101 eyes of 101 patients with glaucoma were discriminated using logistic regression analysis. The best field classification was obtained with a spatial visual field model combining up-down differences and arcuate clusters. The advantages of the spatial model were confirmed in an independent material of 163 eyes of 163 normal subjects and 76 eyes of 76 patients with glaucoma where eyes with large field defects had been removed. In this material the spatial model gave 87% sensitivity and 83% specificity while the best non-spatial model gave 82% sensitivity and 80% specificity. Visual field interpretation in glaucoma may be significantly enhanced if detection is focused on circumscribed field loss rather than on averages of differential light sensitivities and similar indices which do not take spatial relationships into consideration.

The visual field in chronic open angle glaucoma: the rate of change in different regions of the field

Using automated perimetry the distribution of visual field loss in 40 chronic open angle glaucoma eyes (40 patients) was found to be predominantly in the nasal, supranasal, and superotemporal regions. The rate of change of visual field threshold values in seven regions of the field was measured by trend analysis over 44.9 +/- 17.9 months. Seventeen eyes had a significant rate of field loss in one or more regions of the field with the remaining eyes either showing improvement or stability. Seven of the 17 eyes with significant regional field loss had stable overall fields. The greatest rate of field loss occurred in the temporal and superotemporal regions. The correlation between the mean threshold value of the initial field test and the rate of change of field over time was significant in the temporal region and of borderline significance in the superotemporal region. The relationship was such that the greater the initial threshold value, the greater the subsequent rate of field loss.

Visual field damage in normal-tension and high-tension glaucoma

We studied the ocular characteristics of 40 pairs of normal-tension and high-tension glaucoma patients who matched closely for the extent of field damage, pupil size, and visual acuity. To determine if there were differences in visual field damage between patients with normal-tension and high-tension glaucoma, we studied characteristics of the areas of the patients' visual fields that were undisturbed. We computed the number of normal locations, the number of clustered normal locations, and the size of the largest cluster of normal locations. The results showed that for an equivalent extent of damage, the individuals in the normal-tension group had greater areas with normal sensitivity, hence more localized damage. A comparison of the patient data to control data showed that paired differences were larger when the normal-tension member of a pair had a larger value in any of the parameters. The results support the hypothesis that glaucoma patients with lower intraocular pressures have more localized damage and those with higher intraocular pressures have more diffuse damage.