Mathematical and optimal clustering of test points of the central 30-degree visual field of glaucoma

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.

Development and validation of a visual field cluster in retinitis pigmentosa

The aim was to establish and evaluate a new clustering method for visual field (VF) test points to predict future VF in retinitis pigmentosa. A Humphrey Field Analyzer 10-2 test was clustered using total deviation values from 858 VFs. We stratified 68 test points into 24 sectors. Then, mean absolute error (MAE) of the sector-wise regression with them (S1) was evaluated using 196 eyes with 10 VF sequences and compared to pointwise linear regression (PLR), mean sensitivity of total area (MS) and also another sector-wise regression basing on VF mapping for glaucoma (29 sectors; S2). MAE with S1 were smaller than with PLR when between the first-third and first-seventh VFs were used. MAE with the method were significantly smaller than those of S2 when between the first-sixth and first-ninth VFs were used. The MAE of MS was smaller than those with S1 only when first to 3rd and first to 4th VFs were used; however, the prediction accuracy became far larger than any other methods when larger number of VFs were used. More accurate prediction was achieved using this new sector-wise regression than with PLR. In addition, the obtained cluster was more useful than that for glaucoma to predict progression.

Functional assessment of glaucoma: Uncovering progression

Clinicians who manage glaucoma patients carefully monitor the visual field to determine if treatments are effective or interventions are needed. Visual field tests may reflect disease progression or variability among examinations. We describe the approaches and perimetric tests used to evaluate glaucomatous visual field progression and factors that are important for identifying progression. These include stimulus size, which area of the visual field to assess (central versus peripheral), and the testing frequency, evaluating which is important to detect change early while minimizing patient testing burden. We also review the different statistical methods developed to identify change. These include trend- and event-based analyses, parametric and nonparametric tests, population-based versus individualized approaches, as well as pointwise and global analyses. We hope this information will prove useful and important to enhance the management of glaucoma patients. Overall, analysis procedures based on series of at least 5 to 6 examinations that require confirmation and persistence of changes, that are guided by the pattern and shape of the glaucomatous visual field deficits, and that are consistent with structural defects provide the best clinical performance.

Usefulness of axonal tract-dependent OCT macular sectors for evaluating structural change in normal-tension glaucoma

Purpose

To identify sectors of the optical coherence tomography (OCT) macular map that could be used to effectively assess structural progression in patients with normal-tension glaucoma (NTG).

Methods

This study examined 117 eyes of 117 NTG patients to establish axonal tract-dependent macular sectors, and also examined a separate group of 122 eyes of 81 NTG patients to evaluate the ability of these sectors to reveal glaucoma progression. Longitudinal data, including macular maps from at least 5 OCT examinations performed over at least 2 years, was available for all patients in this group. Circumpapillary retinal nerve fiber layer thickness (cpRNFLT), temporal clockwise sector scans (from 7 to 11 o’clock), macular retinal nerve fiber layer thickness (mRNFLT), and macular ganglion cell layer plus inner plexiform layer thickness (mGCIPLT) were measured with spectral-domain OCT (3D OCT-2000, TOPCON). The axonal tract-dependent macular sectors were identified by calculating Spearman’s rank correlation coefficient for each point on a grid overlaid on the macular map and cpRNFLT in each clockwise scan sector. Trend and event analyses for the slope of progression in each sector and macular map were performed. Visual field progression in the macula was defined by the presence of more than 2 progressive test points in the 16 central test points of the Humphrey field analyzer SITA standard 24–2 program, evaluated with Progressor software.

Results

The slope of progression in the entire macular area was -0.22 ± 0.58 μm/year for mRNFLT and -0.35 ± 0.52 μm/year for mGCIPLT. The fastest-progressing mRNFLT sector (-1.00 ± 0.84 μm/year, p < 0.001) and mGCIPLT sector (-1.16 ± 0.63 μm/year, p < 0.001) progressed significantly faster than the overall macula. Classifying patients according to visual field progression showed that baseline mRNFLT in the inferior hemifield, 7 and 8 o’clock sectors, as well as baseline mGCIPLT in the overall macular map, inferior hemifield, and 8 o’clock sector, were significantly lower in progressors (22 eyes) than non-progressors (100 eyes). There were significant differences in mRNFLT slope in 8 o’clock sector and in the fastest progressing sector in progressors and non-progressors, but mGCIPLT did not differ, even in the fastest-progressing sector. Event analysis showed that progression occurred most frequently in inferior mRNFLT and superior mGCIPLT in this study.

Conclusion

Axonal tract-dependent OCT macular sectors could effectively reveal structural change in patients with NTG. Furthermore, mRNFLT slope was consistent with visual field progression. This method promises to open new avenues for the OCT-based evaluation of glaucoma progression.

Evaluating Silent Reading Performance with an Eye Tracking System in Patients with Glaucoma

Objective

To investigate the relationship between silent reading performance and visual field defects in patients with glaucoma using an eye tracking system.

Methods

Fifty glaucoma patients (Group G; mean age, 52.2 years, standard deviation: 11.4 years) and 20 normal controls (Group N; mean age, 46.9 years; standard deviation: 17.2 years) were included in the study. All participants in Group G had early to advanced glaucomatous visual field defects but better than 20/20 visual acuity in both eyes. Participants silently read Japanese articles written horizontally while the eye tracking system monitored and calculated reading duration per 100 characters, number of fixations per 100 characters, and mean fixation duration, which were compared with mean deviation and visual field index values from Humphrey visual field testing (24–2 and 10–2 Swedish interactive threshold algorithm standard) of the right versus left eye and the better versus worse eye.

Results

There was a statistically significant difference between Groups G and N in mean fixation duration (G, 233.4 msec; N, 215.7 msec; P = 0.010). Within Group G, significant correlations were observed between reading duration and 24–2 right mean deviation (r_s = -0.280, P = 0.049), 24–2 right visual field index (r_s = -0.306, P = 0.030), 24–2 worse visual field index (r_s = -0.304, P = 0.032), and 10–2 worse mean deviation (r_s = -0.326, P = 0.025). Significant correlations were observed between mean fixation duration and 10–2 left mean deviation (r_s = -0.294, P = 0.045) and 10–2 worse mean deviation (r_s = -0.306, P = 0.037), respectively.

Conclusions

The severity of visual field defects may influence some aspects of reading performance. At least concerning silent reading, the visual field of the worse eye is an essential element of smoothness of reading.

Clinical relevance of cluster analysis in phenotyping allergic rhinitis in a real-life study

BACKGROUND

Disease stratification, using phenotypic characterization performed either by hypothesis- or data-driven methods, was developed to improve clinical decisions. However, cluster analysis has not been used for allergic rhinitis.

OBJECTIVE

To define clusters in allergic rhinitis and to compare them with ARIA (Allergic Rhinitis and Its Impact on Asthma), a hypothesis-driven approach.

METHODS

A French observational prospective multicenter study (EVEIL: Echelle visuelle analogique dans la rhinite allergique) was carried out on 990 patients consulting general practitioners for allergic rhinitis and treated as per clinical practice. In this study, changes in symptom scores, visual analogue scales and quality of life were measured at baseline and after 14 days of treatment. A post hoc analysis was performed to identify clusters of patients with allergic rhinitis – using Ward's hierarchical method – and to define their clinical relevance at baseline and after 14 days of treatment. The cluster approach was compared to the ARIA approach.

RESULTS

Patients were clustered into 4 phenotypes which partly followed the ARIA classes. These phenotypes differed in their disease severity including symptoms and quality of life. Physicians in real-life practice prescribed medication regardless of the phenotype and severity, with the exception of patients with ocular symptoms. Prescribed treatments were comparable in hypothesis- and data-driven analyses. The prevalence of uncontrolled patients during treatment was similar in the 4 clusters, but was significantly different according to the ARIA classes.

CONCLUSION

Cluster analysis using demographic and clinical parameters only does not appear to add relevant information for disease stratification in allergic rhinitis.

Contributing factors for progression of visual field loss in normal-tension glaucoma patients with medical treatment

PURPOSE

To investigate the prognostic factors responsible for the progression of visual field defects (VFDs) in patients with normal-tension glaucoma (NTG) treated with topical antiglaucoma medications.

PATIENTS AND METHODS

A total of 92 eyes in 92 NTG patients treated with only topical antiglaucoma medications for ≥ 5 years were retrospectively analyzed. To identify subfield-based prognostic factors, the central 30-degree visual field (Humphrey Field Analyzer) was divided into 6 subfields: upper and lower arcuate, paracentral, and cecocentral subfields. Factors related to subfield-based progression (age, refraction, mean intraocular pressure (IOP), IOP variability, central corneal thickness, and disc hemorrhage) were evaluated using a linear mixed model.

RESULTS

Ninety-two eyes in 92 NTG patients were included in this study. The mean observation period was 7.7 ± 2.7 (5.0 to 15.5) years, and the estimated rate of change in the mean deviation value was -0.16 ± 0.31 dB/y (P<0.001). A subfield-based linear mixed model analysis of the time course of changes in the mean of total deviation identified a greater extent of myopia as a significant positive prognostic factor for VFD progression in the upper paracentral area (P=0.016). The mean IOP, central corneal thickness, disc hemorrhage, age, and IOP variation showed no significant contribution in any of the subfields.

CONCLUSIONS

The extent of myopia was found to be a significant positive prognostic factor for VFD progression in the upper paracentral subfield for non-high-myopic NTG eyes with an average IOP of 14.2 mm Hg under topical antiglaucoma medication.

Visual field loss in patients with normal-tension glaucoma under topical nipradilol or timolol: subgroup and subfield analyses of the nipradilol-timolol study

PURPOSE

To estimate the deterioration rates of visual field loss in Japanese normal-tension glaucoma (NTG) patients under either topical nipradilol or timolol, and to explore intergroup differences in the treatment results.

METHODS

A total of 146 NTG patients with mild to moderate damage were randomized to either nipradilol or timolol and followed for 3 years with a periodic comprehensive ophthalmological visual field examination (30-2 Humphrey perimeter program) every 6 months (the Nipradilol-Timolol Study). The time course of mean deviation (MD), the average total deviation (TD(mean)) in four subfields, and the corrected pattern standard deviation (CPSD) were compared between the two groups using regression analysis with a linear mixed effect model.

RESULTS

The estimated slope for MD (dB/year) was -0.03 in the nipradilol and -0.05 in the timolol group (P > 0.4). In both groups, TD(mean) in the superior-central subfield and CPSD showed significant changes (-0.3 and 0.2-0.3, P <or= 0.001). In the patients with early visual field loss or those younger than 40 years, deterioration of some visual field parameters tended to be slower in the nipradilol group than in the timolol group.

CONCLUSION

During 3 years of monotherapy with either nipradilol or timolol in NTG patients, only TD(mean) in the superior-central subfield and the CPSD changed significantly without any intergroup differences.

Assessing visual field clustering schemes using machine learning classifiers in standard perimetry

PURPOSE

To compare machine learning classifiers trained on three clustering schemes to determine whether distinguishing healthy eyes from those with glaucomatous optic neuropathy (GON) can be optimized by training with clustered data.

METHODS

Two machine learning classifiers-quadratic discriminant analysis (QDA) and support vector machines with Gaussian kernel (SVMg)-were trained separately using standard perimetry data from the Diagnostic Innovations in Glaucoma Study (DIGS), clustered using three clustering schemes on a training data set (123 eyes/123 glaucoma patients with GON; 135 eyes/135 normal control subjects). Trained classifiers were then applied to an independent data set containing 69 eyes of 69 glaucoma patients with early visual field loss and 83 eyes of 83 normal control subjects. Two control conditions were included: unclustered data and a random assignment of locations to clusters.

RESULTS

Areas under the receiver operating characteristic (ROC) curve ranged from 0.85 (SVMg, thresholds clustered by Glaucoma Hemifield Test sectors) to 0.92 (QDA, thresholds clustered by Garway-Heath mapping) for the training data set. Use of clustered data showed no significant optimization of sensitivity over use of unclustered data, and no single clustering method resulted in significantly higher performance in the independent data set. Sensitivities tended to be higher with QDA than with SVMg, regardless of specificity cutoff and clustering

METHOD

CONCLUSIONS

QDA performed better with the early glaucoma data set than did the SVMg. Clustering may be advantageous when data-dimension reduction is needed-for example, when combining field results with other high-dimensional data (e.g., structural imaging data)-but it is not necessary for visual field data alone.

No Apparent Association Between Ocular Perfusion Pressure and Visual Field Damage in Normal-Tension Glaucoma Patients

PURPOSE

To investigate the correlation of ocular perfusion pressure (OPP) with general and localized visual field damage in normal-tension glaucoma (NTG) patients.

METHODS

Correlations between OPP, blood pressure, age, intraocular pressure, refractive error, and extent of visual field damage in the eye with the worst mean deviation (MD) were investigated retrospectively in 94 eyes of 94 NTG patients. Visual fields were analyzed statistically with respect to 15 sectors between two age-matched groups of subjects with high or low OPP.

RESULTS

Significant positive correlations were found between OPP and age (P < 0.001), blood pressure and age (P < 0.05), and MD and refractive error (P < 0.01). OPP had no significant correlation with MD or mean sensitivity in the visual field in any of the visual field sectors.

CONCLUSION

OPP and systemic blood pressure have no evident effect on the extent or pattern of visual field damage in NTG.

Relationship between visual field loss and contrast threshold elevation in glaucoma

BACKGROUND

There is a considerable body of literature which indicates that contrast thresholds for the detection of sinusoidal grating patterns are abnormally high in glaucoma, though just how these elevations are related to the location of visual field loss remains unknown. Our aim, therefore, has been to determine the relationship between contrast threshold elevation and visual field loss in corresponding regions of the peripheral visual field in glaucoma patients.

METHODS

Contrast thresholds were measured in arcuate regions of the superior, inferior, nasal and temporal visual field in response to laser interference fringes presented in the Maxwellian view. The display consisted of vertical green stationary laser interference fringes of spatial frequency 1.0 c deg(-1) which appeared in a rotatable viewing area in the form of a truncated quadrant extending from 10 to 20 degrees from fixation which was marked with a central fixation light. Results were obtained from 36 normal control subjects in order to provide a normal reference for 21 glaucoma patients and 5 OHT (ocular hypertensive) patients for whom full clinical data, including Friedmann visual fields, had been obtained.

RESULTS

Abnormally high contrast thresholds were identified in 20 out of 21 glaucoma patients and in 2 out of 5 OHT patients when compared with the 95% upper prediction limit for normal values from one eye of the 36 normal age-matched control subjects. Additionally, inter-ocular differences in contrast threshold were also abnormally high in 18 out of 20 glaucoma patients who had vision in both eyes compared with the 95% upper prediction limit. Correspondence between abnormally high contrast thresholds and visual field loss in the truncated quadrants was significant in 5 patients, borderline in 4 patients and absent in 9 patients.

CONCLUSION

While the glaucoma patients tested in our study invariably had abnormally high contrast thresholds in one or more of the truncated quadrants in at least one eye, reasonable correspondence with the location of the visual field loss only occurred in half the patients studied. Hence, while contrast threshold elevations are indicative of glaucomatous damage to vision, they are providing a different assessment of visual function from conventional visual field tests.