A variance-equalizing transformation for the analysis of visual fields

A VARIANCE-EQUALIZING TRANSFORMATION FOR THE ANALYSIS OF VISUAL FIELDS

HONG GU,1 PAUL H. ARTES,2 DAVID C. HAMILTON1 and BALWANTRAY C. CHAUHAN2

1Departments of Mathematics & Statistics and 2Ophthalmology, Dalhousie University, Halifax, Canada

Abstract

Background

The variability of threshold estimates increases when visual field sensitivity is reduced, but, owing to the limited dynamic range of automated perimetry, decreases again when visual field defects advance towards absolute loss. The strong, non-monotonic relationship between sensitivity and variability makes it difficult: a. to estimate trends over time and their significance; and b. to quantify differences in variability between patients with different levels of visual field loss. The purpose of this work was to develop a transformation to equalize the variability of threshold estimates across the scale of conventional perimetry.

Methods

The relationship between sensitivity and variability was characterized by a gamma-like function in longitudinal visual field data from 108 patients with glaucoma and 113 normal controls. This function, in turn, was used to find the appropriate variance-stabilizing transformation for the measurement scale (dB). Test/retest intervals (fifth and 95th percentiles of retest threshold estimates, stratified by baseline sensitivity) were subsequently derived on the transformed scale.

Results

The function fitted to the sensitivity-variability relationship had similar parameters for controls and patients with glaucoma, reaching its maximum at approximately 10 dB. The transformation of the scale by the integral of this function nearly eliminated the relationship between sensitivity and the variability of threshold estimates and led to approximately uniform test/retest intervals across the entire dynamic range. The transformed scale may increase the power of trendand event-type analyses for the detection of visual field progression.

Address for correspondence: Paul H. Artes, PhD, Department of Ophthalmology, QEII Health Sciences Centre, Centennial Building, VG Site, 1278 Tower Rd, Halifax, Nova Scotia B3H 2Y5, Canada. Email: paul_h_artes@yahoo.co.uk

Perimetry Update 2002/2003, p. 29

Proceedings of the XVth International Perimetric Society Meeting, Stratford-upon-Avon, England, June 26–29, 2002

edited by David B. Henson and Michael Wall

© 2004 Kugler Publications, The Hague, The Netherlands

A NEW SPATIAL FILTER FOR VISUAL FIELD DATA

Testing and evaluation

D.P. CRABB,1 S.K. GARDINER,1 F.W. FITZKE,2 and R.A. HITCHINGS3

1Nottingham Trent University, Nottingham; 2Institute of Ophthalmology, London; 3Moorfields Eye Hospital, London; UK

Abstract

Purpose

To demonstrate how a new spatial filter could be used on visual field data to improve the diagnosis of visual field progression.

Methods

Firstly, 5000 noisy visual field series (consisting of five years worth of annual tests) were simulated for a stable field. Next, 5000 noisy visual field series (of five years) based on each of ten different artificial localized defects (consisting of one or more points deteriorating at 2 dB/year, and the two points at either end of the defect deteriorating at 1 dB/year) were simulated. The probabilities of each point from each series being flagged as progressing by point-wise linear regression were measured. An unrealistic nonglaucomatous defect, perpendicular to the expected shape, was tested in the same way.

Results

For a stable field, the proportion of points flagged as progressing (all of which are false-positives) was 0.59% for the raw data, improving to 0.04% after filtering. Out of the localized defects tested, the new filter increased the proportion of progressing points successfully detected in all ten cases (on average from 19.6 to 33.3%), while the gaussian filter reduced this proportion in three of the cases (and gave an average of only 22.6%). The proportions of points detected from the unrealistic defect fell after filtering the raw data (from 19.7 to 10.0%), whereas gaussian filtering increased this proportion to 30.0%.

Conclusions

The new spatial filter decreases the number of false-positives when detecting progression by reducing the level of noise present. The new filter behaves and discriminates quite differently to the gaussian filter in that it significantly increases the probability of detecting true deteriorating points (even in localized defects), and it also reduces the chances of flagging unrealistic, non-glaucomatous defects. The filter could provide a useful tool for improving visual field measurements.1

References

1.Gardiner SK, Crabb DP, Fitzke FW, Hitchings RA: Reducing noise in suspected glaucomatous visual fields by using a new spatial filter. Vision Res 2004 (in press)

Address for correspondence: David Crabb, PhD, School of Science, Nottingham Trent University, Clifton Campus, Nottingham, NG11 8NS, UK. Email: david.crabb@ntu.ac.uk

Perimetry Update 2002/2003, p. 31

Proceedings of the XVth International Perimetric Society Meeting, Stratford-upon-Avon, England, June 26–29, 2002

edited by David B. Henson and Michael Wall

© 2004 Kugler Publications, The Hague, The Netherlands

A NEW SPATIAL FILTER FOR VISUAL FIELD DATA

Derivation and reducing noise

S.K. GARDINER,1 D.P. CRABB,1 F.W. FITZKE2 and R.A. HITCHINGS3

1Nottingham Trent University, Nottingham; 2Institute of Ophthalmology, London; 3Moorfields Eye Hospital, London; UK

Abstract

Background

Simple spatial filtering (gaussian filtering) of visual field data after perimetric examination for glaucoma has been shown to reduce noise in the measurements, but it may ‘blur’ defects and scotomas of interest.

Purpose

To develop a new spatial filter for reducing noise in visual field data which takes into account the physiological structure of the eye.

Methods

From a uniquely large retrospective database of 98,000 visual fields from patients at a glaucoma clinic, obtained with Humphrey perimetry, the covariances between sensitivities at different points in the eye were obtained. Series of regressions on these covariances were used to produce a map, detailing how to predict the sensitivity of a point from the sensitivities elsewhere in the field. The filtered value at that point is then a combination of this predicted value and the raw sensitivity measured during the test, where the raw value is given more weight at points that were found to be less predictable (based in part on the correlations between the raw and predicted values). This leads to a unique filter for each location in the field. To test the filter, the correlation between sensitivity and time was found for fields 3 to 20 of each sufficiently long series in the database, before and after filtering.

Results

Details of the map were found to conform to the expected structure of the retinal nerve fiber layer. Filtering significantly increased the correlation between sensitivity and time; the proportion of the series that had a correlation >0.5 doubled with filtering. This indicates that the values are less noisy after filtering, as they are more consistent over time.

Conclusion

The new filter appears to reduce the noise present in visual field readings.1

References

1.Gardiner SK, Crabb DP, Fitzke FW, Hitchings RA: Reducing noise in suspected glaucomatous visual fields by using a new spatial filter. Vision Res 2004 (in press)

Address for correspondence: David Crabb, MD, Faculty of Science, Nottingham Trent University, Clifton Campus, Nottingham, NG11 8NS, UK. Email: david.crabb@ntu.ac.uk

Perimetry Update 2002/2003, p. 33

Proceedings of the XVth International Perimetric Society Meeting, Stratford-upon-Avon, England, June 26–29, 2002

edited by David B. Henson and Michael Wall

© 2004 Kugler Publications, The Hague, The Netherlands