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Spatial and Temporal Processing of Threshold Data for Detection of Progressive Glaucomatous Visual Field Loss
Paul G. D. Spry, PhD;
Chris A. Johnson, PhD;
Alex B. Bates;
Andrew Turpin, PhD;
Balwantray C. Chauhan, PhD
Arch Ophthalmol. 2002;120:173-180.
ABSTRACT
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Objective To evaluate the effect of spatial and temporal filtering of threshold
visual field data on the ability of pointwise linear regression (PLR) to detect
progressive glaucomatous visual field loss.
Methods Longitudinal visual field data (Full-Threshold Program 30-2 test point
pattern) were simulated using a computer model of glaucomatous visual field
progression. This approach permitted construction of a "gold standard" because
matching visual field data without variability could be generated and analyzed.
Four clustered progressive defects were produced, consisting of 2, 3, 9, and
18 locations, respectively, each with progression rates of -1 and -2.5
dB/y. Pointwise linear regression was used to identify progressive test locations
(criterion for progression of statistically significant slope of  -1
dB/y, P<.05). Each visual field series was analyzed
after the following 3 procedures: (1) no filtering (unprocessed data), (2)
Gaussian spatial possessing (3 x 3 grid), and (3) temporal processing
(2 field moving average). The effect of spatial and temporal processing on
PLR discriminatory power for progression detection was quantified by comparison
with the gold standard.
Results Spatial processing reduced PLR sensitivity to levels below that achieved
for analysis of unprocessed data for small progressive defects (9 locations)
or at the low true progression rate (-1 dB/y). Under these conditions,
spatial processing caused small PLR specificity improvement. Spatial processing
only improved PLR sensitivity above unprocessed levels when progressive defects
were large and changing rapidly (progression rate of -2.5 dB/y). Temporal
processing gave consistent PLR improvement in sensitivity for all defect sizes
and true progression rates. Pointwise linear regression sensitivity gain provided
by temporal processing allowed progression to be detected 2 to 3 visual fields
earlier than for analysis of raw data. Specificity dropped slightly as a result
of temporal processing but remained at 89% or above for all conditions studied.
Conclusions Gaussian spatial processing reduces PLR discriminatory power with low
true progression rates or small progressive defect sizes and, therefore, is
of limited use for detection of progressive visual field loss. Temporal processing
improves the sensitivity of PLR and reduces the number of tests required to
detect progressive loss with minimal loss of specificity.
Clinical Relevance Image processing techniques can be applied to threshold visual field
data to enhance sensitivity or specificity of PLR for the determination of
progressive change. This investigation demonstrates that temporal processing
may assist with the detection of significant progressive visual field loss
with fewer test results than unprocessed data.
INTRODUCTION
THRESHOLD VISUAL field analysis represents an essential component of
the full ocular examination in glaucoma and related ocular pathologic abnormalities.
Visual field assessment assists clinicians in detecting the onset of initial
visual function loss and monitoring existing areas of sensitivity loss. Evaluation
of visual function with threshold visual field analysis provides quantitative
measures of both the spatial arrangement and magnitude of sensitivity loss
present within the area examined. However, the visual field is not a stable
quantity and measurements of threshold sensitivity can vary physiologically
over relatively short periods (minutes) or over more lengthy periods (days).
This variability (or "noise") occurs in all individuals and is caused by a
variety of factors including patient response fluctuations1
and cyclic alterations of sensitivity. Variability is also dependent on the
thresholding algorithm2-4
and has been shown to become greater in areas of pathologically reduced sensitivity.1, 5-8
The presence of variability makes identification of test locations with
progressive visual loss difficult by masking the progressive change especially
at gradual rates of sensitivity decline. Accordingly, many multicenter clinical
trials in glaucoma have found that a large number of visual fields are needed
to accurately distinguish true visual field progression from intertest variability.
A variety of statistical approaches may be used to extract information on
progressive loss (signal) from variability (noise), including trend analyses
such as linear regression of threshold sensitivity at each test location.
It has been suggested that pointwise linear regression (PLR) is advantageous
because it may be able to detect low progression rates.9
However, previous reports have suggested that at least 8 annual test visual
field results are required to detect gradually progressive test locations
using this technique.10-11 Although
more frequent testing can reduce the interval for identification of true progressive
locations, this approach to reducing detection time requires more clinical
resources and is also subject to diminishing returns.12
Ideally, it would be clinically advantageous to identify progressive loss
with fewer test results.
Image processing has been used within computer science to extract information
by reducing noise from matrices of digital information.13
This processing involves computational manipulation of the original data values
with a predefined mathematical "process" or filter. Within vision science,
spatial processing (or filtering) has been applied to the grid-based patterns
of threshold visual field test results. This technique smoothes the visual
field surface by replacing each original threshold with a weighted neighborhood
average, thereby reducing the local noise produced by variability. Spatial
processing of perimetric threshold sensitivity values using a Gaussian filter
has been reported to be useful for quantification of local spatial variability,14 improvement of the predictive performance of future
threshold values using PLR,15 and reduction
of test-retest threshold variability in glaucoma.16
The latter 2 of these findings has prompted the suggestion that spatial processing
of data prior to analysis for detection of change could boost the progression
(signal)-variability (noise) ratio and, therefore, may enhance the ability
to detect visual field change. It is also reasonable to suggest that because
visual field variability occurs over time, temporal threshold averaging (temporal
processing) may also be beneficial. This study evaluates and compares the
effects of 2 methods of processing threshold visual field data—spatial
and temporal processing—for the detection of progressive visual field
loss using PLR.
MATERIALS AND METHODS
Longitudinal glaucomatous visual field data (Full-Threshold Program
30-2 test point pattern) were simulated using a previously described model
that incorporates many aspects of visual field behavior.11
This model simulates sets of full-threshold visual fields between predefined
initial and final tests. Simulation permits control of many variables that
affect threshold sensitivity including short- and long-term fluctuations and,
therefore, allows construction of a "gold standard" because data may be simulated
from the same initial and final tests without variability.
Three sizes of progressive hemifield defects were generated by simulation;
small (2 and 3 horizontally adjacent test locations), medium (9 locations
arranged in a 3 x 3square), and large (18 clustered locations in an
arcuate pattern). The spatial arrangements of these defects are shown in Figure 1. Two true rates of progression were
used for each size of progressive defect, with each test location within the
progressive area changing at -1 dB/y and -2.5 dB/y.
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Figure 1. Four sizes of progressive defect
(2, 3, 9, and 18 test locations [shaded areas]) were used for generation of
progressive visual field series.
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Each simulated visual field set had 2 dB of short-term fluctuation and
1 dB of long-term fluctuation, typical values in patients with glaucoma who
have early damage assessed with a 4-2 staircase strategy.17
Each simulated set consisted of 10 serial visual fields, equivalent to 10
years of annual testing. In this study, 20 simulation iterations were performed
for each progressive defect.
Each visual field set was analyzed after (1) no processing (raw threshold
data), (2) processing with a previously described Gaussian spatial filter,15-16 and (3) processing with a 2-field
temporal filter (moving average). Gaussian spatial processing was performed
using a 3 x 3 grid, as shown in Figure
2A. Each filter cell contains a different weight configured such
that the grid forms a Gaussian profile from any angle. The filter is centered
on a test location, and thresholds underlying each filter cell are multiplied
by the appropriate weight. The sum of these weighted threshold products is
divided by the sum of the filter weights to produce a spatially processed
threshold value that replaces the original central grid value. Spatial processing
was performed at each test location by moving the filter across all points
in the visual field. Where the grid extends over the edge of the visual field,
only occupied cells are included in processing.
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Figure 2. A, Schematic depicts the principle
of spatial filtering for a single test location. This procedure was in accord
with that described by Fitzke et al9, 16
and Crabb et al.18 B, Schematic depicts the
principle of temporal processing, whereby a moving average of 2 sequential
visual field test results is calculated. N indicates
the visit number; boldface value, original threshold.
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Temporal processing consisted of replacing the threshold at each location
by the average threshold at the same location from the current and single
immediately preceding test. This is equivalent to the moving average of 2
test results. Temporal processing dictates that the first field in the test
set may not be processed because no prior threshold values are available.
An example of temporal processing at a single test location is shown in Figure 2B.
Unprocessed, spatially processed, and temporally processed sets were
subsequently analyzed separately using PLR analysis to identify progressive
test locations. Progressive test locations were defined; those with statistically
significant regression line slopes were equal to -1 dB/y (P<.05) or worse. This criterion for progression was based on use
in previous studies of progressive
visual field loss.9, 19-21
The ability of PLR to detect progressive test locations (sensitivity)
and nonprogressive test locations (specificity) was quantified for each sequential
field by comparison with gold standard data for unprocessed, spatially processed,
or temporally processed threshold data for each progressive defect and true
rate of progression. The gold standard consisted of visual field set generated
using the same progressive defects but without glaucomatous levels of variability.
This was performed for each field in each simulation iteration. Average sensitivity
and specificity were calculated for each condition.
RESULTS
SENSITIVITY
The effect of spatial processing on sensitivity was found to depend
on both the number of progressive test locations and true rate of progression.
With small progressive defects (2 or 3 progressive test locations), spatial
processing (Figure 3, circles) caused
a reduction in the sensitivity of PLR to detect progressive test locations
compared with unprocessed data (squares). As shown in Figure 3A through Figure 3D,
this effect was found at both of the true rates of progression evaluated in
this study (-1 dB/y and -2.5 dB/y), although a larger reduction
in sensitivity was found for the lowest true progression rate (-1 dB/y).
For this low true progression rate, the reduction in sensitivity produced
by spatial filtering increased when more fields were used within the regression
analysis and when analysis was based on 9 or more visual field test results,
sensitivity was reduced to 0. With moderate- or large-sized progressive defects
(9 or 18 progressive locations) shown in Figure 3E through H, spatial filtering produced an improvement in
sensitivity for the greatest true rate of progression examined in this study
(-2.5 dB/y). For this rate of progression, the improvement in sensitivity
provided by spatial filtering was maximal when 6 years of follow-up were available
for analysis when unprocessed average sensitivity of around 40% was increased
to more than 80% by spatial processing. With the greater numbers of available
test results, the improvement in sensitivity afforded by spatial processing
was reduced. At -1 dB/y of progression, spatial processing did not produce
the same improvement in sensitivity. Modest improvement in sensitivity (10%
maximum increase) occurred when small numbers (7) of visual field test
results were available for analysis, but this improvement was lost when the
number of available fields increased to 8 or more.
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Figure 3. A through H, These show the sensitivity
of pointwise linear regression using (1) unprocessed (squares), (2) spatially
processed (circles), and (3) temporally filtered data (triangles). A and B,
Data are from 2 progressive test locations with progression rates of -1
dB/y and -2.5 dB/y. C and D, Data are from 3 progressive test locations
with progression rates of -1 dB/y and -2.5 dB/y. E and F, Data
are from 9 progressive test locations with progression rates of -1 dB/y
and -2.5 dB/y. G and H, Data are from 18 progressive test locations
with progression rates of -1 dB/y and -2.5 dB/y.
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Temporal processing (Figure 3,
triangles) produced an improvement in the ability of PLR over unprocessed
data to correctly identify truly progressive test locations for all sizes
of progressive defects and at all true rates of progression studied in this
investigation, as shown in Figure 3A
through H. The degree of benefit produced by temporal processing was found
to depend on the true rate of progression and number of visual field test
results available for use by regression analysis. Improvement in sensitivity
was unrelated to the number of test locations that were progressive. For a
true progression rate of -1 dB/y, an improvement in sensitivity of approximately
20% compared with unprocessed data was found (Figure 3A, C, E, and G). This improvement gradually decreased with
6 or more test results available for PLR and was reduced to between 5% and
10% after 10 "simulation years" of follow-up. At higher true progression rates,
such as -2.5 dB/y shown in Figure 3B, D, F, and H, temporal processing provided an improvement in sensitivity
of around 30% when 5 visual field test results were available, and it allowed
the sensitivity of PLR to exceed 70% with as few as 6 available test results.
At this rate of progression, temporal processing continued to provide benefit
to PLR for up to 10 available fields. In summary, when 10 or fewer test results
are available, the likely sensitivity gain provided by temporal processing
may permit PLR to detect progressive test locations up to 3 visual fields
earlier than when unprocessed data are used.
SPECIFICITY
Spatial processing produced a small improvement in the ability of PLR
to correctly identify nonprogressive test locations (up to 2%) compared with
analysis of raw data for all sizes of progressive defect at a true progression
rate of -1 dB/y (Figure 4A,
C, E, and G). It should be recognized that the criterion used in this study
for detection of progression (-1 dB/y [P<.05])
already yields high specificity levels ( 95%) prior to processing. For
the higher true progression rate of -2.5 dB/y, similar improvement occurred
for progressive defect sizes of 2, 3, and 9 test locations (Figure 4B, D, and F). However, as shown in Figure 4G and H, spatial processing caused a small reduction in
specificity when the size of progressive defect exceeded the spatial filter
size. This reduction was small (up to 3%) and seemed to be independent of
the number of visual field test results included in the regression analysis.
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Figure 4. A through H, These show the specificity
of pointwise linear regression using (1) unprocessed (squares), (2) spatially
processed (circles), and (3) temporally filtered data (triangles). A and B,
Data are from 2 progressive test locations with progression rates of -1
dB/y and -2.5 dB/y. C and D, Data are from 3 progressive test locations
with progression rates of -1 dB/y and -2.5 dB/y. E and F, Data
are from 9 progressive test locations with progression rates of -1 dB/y
and -2.5 dB/y. G and H, Data are from 18 progressive test locations
with progression rates of -1 dB/y and -2.5 dB/y.
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Figure 4 demonstrates that
temporal processing had a small negative effect on the specificity of PLR,
reducing specificity by up to 10% compared with unprocessed threshold data.
This detrimental effect decreased with more visual field test results available
for analysis. At no point was specificity below 89% by temporal processing.
COMMENT
Clinical management of glaucoma requires differentiation between cases
of stable and progressive disease to determine the efficacy of treatment regimens.
Currently, this determination is usually based on longitudinal series of visual
field test results. Visual field progression is also a primary outcome measure
for multicenter clinical trials in glaucoma. Unfortunately, the confounding
effect of variability present both within and between visual field tests complicates
identification of true progressive loss. This confound is such that unless
threshold sensitivity reduction due to active pathologic abnormality is sufficient
to exceed pathophysiologic variability, it is impossible to distinguish between
progressive visual field loss and variability. This means that small but clinically
important amounts of progressive loss are difficult to identify. One statistical
approach that has been applied to this problem is trend analysis, whereby
one or more visual field variables may be followed over time, permitting extraction
of progressive signal from variability noise. One type of this technique,
linear regression analysis, has been used on visual field summary (global)
indices, such as mean deviation and pattern standard deviation, glaucoma hemifield
test zones, and individual test locations (pointwise). For each of these,
several criteria exist that can be chosen to determine acceptable levels of
sensitivity and specificity. Generally, global indices have been shown to
be specific but relatively insensitive to detection of early, subtle changes
because small progressive regions are averaged out.22
Conversely, PLR may be highly sensitive to small progressive defects but may
lack specificity because of the high variability present at individual test
locations. The lack of an independent reference standard to quantify the success
of the methods used for the detection of progressive glaucomatous visual field
loss has produced considerable debate concerning which variable exhibits the
highest discriminatory power for detection of progressive loss when used with
linear regression and on criteria that should be applied to each. Each of
the current multicenter clinical trials in glaucoma uses different criteria
for defining progression of visual field loss.23-26
In this study we evaluated the use of 2 image processing techniques
that can be applied to threshold visual field data after collection and prior
to statistical analysis for change. The aim of such procedures is to help
increase the identification of progressing and stable visual fields using
available data. With the aid of computers, both techniques are relatively
quick and easy to apply to threshold data and are independent of thresholding
strategy or perimetric instrumentation, although consistency should be maintained
throughout the visual field series. Spatial processing was evaluated because
previous investigators have suggested its potential role in assisting detection
of progressive loss.16 Temporal processing
was evaluated because such a filtering technique represents a logical approach
to the temporal nature of threshold variability. Use of a validated simulation
model11 to generate longitudinal visual field
series with and without typical glaucomatous amounts of short- and long-term
fluctuations has enabled performance quantification for both processing techniques
with a variety of progressive defect sizes and true progression rates.
Previously investigators have shown that spatial processing improves
repeatability of full-threshold estimations.16
In this study it has been demonstrated that under most progression conditions,
spatial processing does modestly improve the ability of PLR to correctly identify
stable test locations. However, it was also observed that for small numbers
of clustered progressive test locations (less than or equal to spatial filter
size, 9 locations), or at a low true progression rate (-1 dB/y), spatial
processing reduced sensitivity to a level below that achieved by analysis
of raw data. It appears that although the particular Gaussian spatial processing
procedure used in this study reduced the threshold variability (noise) at
nonprogressive locations, thus improving specificity, it also reduced progressive
loss (signal) thereby resulting in decreased sensitivity. This finding was
expected given that use of spatial processing techniques in computer science
assumes that pixels (or in the case of visual fields, test locations) are
smaller than any of the important details,13
which is clearly not the case with the limited visual field matrix size. Furthermore,
the negative effect of spatial filtering was greatest under the conditions
at which it is most difficult to detect progression: small progressive defects
or low true progression rates. It was also observed that at the largest progressive
defect size (18 clustered locations) and highest true progression rate (-2.5
dB/y) combinations, spatial processing also produced a small but consistent
specificity reduction. This effect can be explained by artifactual increase
of thresholds of nonprogressive points directly adjacent to true progressive
locations by spatial processing. Although under our experimental conditions
the amount of specificity loss is negligible, it is possible that for scenarios
of noncontiguous and/or more rapid rates of true progression, the resultant
effect on specificity may become significant. A further interesting observation
is that progressive defects consisting of 9 or 18 test locations with -1
dB/y true rates of progressive loss initially receive a sensitivity gain from
spatial processing, which becomes a sensitivity reduction when 7 to 8 test
results are available. It is likely that this results from the gradual reduction
of the progression information signal by spatial processing as more information
becomes available to PLR.
The effect of temporal processing on longitudinal threshold data is
more predictable than spatial processing. We show that temporal processing
provides consistent sensitivity gain when fewer than 10 fields are analyzed
by PLR. Depending on the true rate of progression, temporal processing provides
a net saving of between 1 and 3 visual fields compared with unprocessed threshold
data when applied prior to PLR. As expected, the degree of benefit is reduced
with more available test results. However, temporal processing also had a
modest negative effect on specificity. Use of a rigorous progression criterion
(significant slope of -1 dB/y) that has been shown to demonstrate
high specificity ensured that specificity was not significantly compromised.
It can easily be seen from Figure 3
and Figure 4 that for fewer than
10 available visual field results, sensitivity gain always exceeds the specificity
loss providing a net discriminatory power gain.
CONCLUSIONS
These data show that image processing techniques can be applied to threshold
visual field data. Depending on the method of processing applied, either sensitivity
or specificity can be enhanced. When few test results are available for analysis,
it appears that temporal processing increases PLR sensitivity for detection
of progressive visual field loss, thereby reducing the number of test results
required to detect progression without significantly compromising specificity.
The use of spatial processing does not seem to offer a consistent benefit
over the analysis of raw data, and in some instances significantly inhibits
the ability to detect small, gradual progressive changes.
AUTHOR INFORMATION
Accepted for publication September 5, 2001.
This study was supported in part by grant EY-03424 from the National
Eye Institute, Bethesda, Md (Dr Johnson) and by the Glaucoma Research Foundation,
San Francisco, Calif (Drs Johnson and Chauhan).
This study was presented in part at the annual meeting of the Association
for Vision Research in Ophthalmology, Fort Lauderdale, Fla, May 2, 2000.
Corresponding author and reprints: Paul G. D. Spry, PhD, Bristol
Eye Hospital, Lower Maudlin Street, Bristol BS1 2LX, England (e-mail: paul.spry{at}ubht.swest.nhs.uk).
From Discoveries in Sight, Devers Eye Institute, Portland, Ore (Drs
Spry, Johnson, and Turpin and Mr Bates); the Bristol Eye Hospital, Bristol,
England (Dr Spry); and the Department of Ophthalmology, Dalhousie University,
Halifax, Nova Scotia (Dr Chauhan). The authors have no commercial, proprietary,
or financial interest in the products or companies described in this article.
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