Transcript ARVO - Brunel University

Program # 2131
Bayesian networks to classify visual field data
A
1
Tucker,
1Dept
V
1
Vinciotti,
• The purpose of this study is to use statistical and classification models
to classify, detect and understand progression in visual fields (VFs)
• We intend to make use of the vast amount of data available to build
models which avoid inherent problems of ‘black box’ paradigms
• Integration of different types of clinical data for the diagnosis and
detection of glaucoma progression would be helpful to clinicians
• Bayesian network models are ideal for classifying VF data whilst
facilitating the understanding of VF progression:
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They are learnable from data
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They model knowledge explicitly (graphical structure and probabilities)
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They can incorporate different types of data (e.g. clinical and VF)
• A comprehensive comparison of machine-learning classifier systems
was carried out for glaucoma (Goldbaum et al, 2002). Many of these
classifiers are ‘black box’ in nature.
DF
2
Garway-Heath
Info Systems and Computing, Brunel University, UK;
2Moorfields
PURPOSE
XH
1
Liu,
Eye Hospital, London, UK
2. A Time Series of VF tests from 24 subjects converting from
ocular hypertension to glaucoma:
• VFs of 255 subjects attending the Ocular Hypertension Clinic at Moorfields
Eye Hospital were examined at 4-monthly intervals (Kamal 2003)
• A subset of 24 patients were taken who had converted to glaucoma in their
right eye (mean age = 63.0; SD = 12.4)
• All subjects initially had normal VFs and developed reproducible
glaucomatous VF damage in a reliable VF during the course of follow-up
(‘conversion’)
• Conversion was defined as the development of an AGIS score 1 from initial
score of 0, on three consecutive reproducible and reliable Humphrey 24-2 full
threshold strategy VFs, with at least one location consistently below the
threshold for normality
• The average number of fields in each patient's series was 24, the SD was 8,
the maximum was 45, and the minimum was 1
• The distribution of point-by-point light sensitivity has been explored in
normal (Hejl, 1987) and glaucomatous populations (Weber, 1992).
Much remains unknown about the behaviour of the VF test.
Table 1. A Breakdown of the datasets
Dataset
1 (Single field)
2 (Time series)
54
54
age, gender
age, gender
# VF test points
• We know of little research using Bayesian networks to understand
and classify VF data (Tucker, 2003)
Clinical variables
Glaucoma Visual Field Classification
# VF tests
180
588
# Patients
180
24
43:57
39:61
Glaucomatous:non-glaucomatous
Glaucomatous field loss
(1)
Bayesian classifiers:
1. Naïve Bayes classifier (NBC)
Assumes feature independence
2. Tree-augmented Bayes classifier (TAN)
(2)
Relaxes independence assumption
(3)
Tree Structure Learnt Between Features
3. Bayesian network classifier (BNC)
Bayesian network including class node
Figure 1. Two Sample Visual Fields from a Healthy Eye (left) and a Glaucoma Sufferer (right)
Figure 2. The Architectures of the different Bayesian classifiers
[(1) naïve Bayes; (2) tree-augmented network; (3) Bayesian network]
Statistical classifiers:
METHODS
Datasets:
1. Single VF tests from 180 subjects
•Subjects included 78 with established early glaucomatous VF loss
(mean age = 57.5 years; SD = 12.4) and 102 normal volunteers known
not to be sufferers (mean age = 65.1 years; SD = 10.1)
•One VF per subject was used for analysis
•Early glaucomatous VF loss was defined as an AGIS (Advanced
Glaucoma Intervention Study 1994) score between 1 and 5, on three
consecutive reproducible and reliable Humphrey 24-2 full threshold
strategy VFs, with at least one location consistently below the threshold
for normality in subjects with pre-treatment IOPs > 21mmHg
•Normal subjects had VF tests scoring 0 in the AGIS classification , IOP
< 21mmHg and no family history of glaucoma
RESULTS
ROC curve analysis
• ROC in Figure 3 (left)
reveals BNC performs
best out of the
Bayesian methods
• Figure 3 (right)
shows that BNC
comparable to both LR
and KNN
Figure 3. The ROC curves generated for the different classifiers learnt from single VF data
Network Analysis
• Various relationships
found that relate to
known anatomical
information:
- Nasal step and arcuate
paracentral defects
are influential in
classification (Figure 4)
- Mean optic nerve
head angular distance Figure 4. The direct descendants of the
glaucoma class node
(Garway-Heath, 2001) of
parent and child of a link
was 15.3 degrees (Figure 5)
• Temporal VF found to be useful for
classification although conventionally not
thought important (Figure 4)
Testing on time-series data
• Classification accuracy was only 66%
• However, there are several reasons for
such a low score. Four characteristics
appeared (Figure 6):
a) Slow build up in probability of
glaucoma prior to clinician’s decision
b) Fluctuations prior to clinician’s
decision
c) Classified as glaucomatous
throughout
d) Fluctuations throughout
Figure 5. The resultant network structure
learnt from single VF data
Figure 6. Four sample results of testing the Bayesian
network models on the time series dataset comparing to
clinician’s conversion decisions (denoted by a dotted line)
4. Linear regression (LR)
Attempts to classify using straight line fit to data
5. K nearest neighbour (KNN)
Classifies based upon majority of k nearest neighbours (calculated using distance metric)
References
Goldbaum MH, Sample PA, Chan K et al.Comparing machine learning classifiers for diagnosing glaucoma from standard
automated perimetry. Invest Ophthalmol Vis Sci. 2002; 43; 1: 162 – 169.
Heijl A, Lindgren G, Olsson J. Normal variability of static perimetric threshold values across the central visual field. Arch
Ophthalmol 1987; 105: 1544 – 1549.
Weber J, Rau S. The properties of perimetric thresholds in normal and glaucomatous eyes. Ger J Ophthalmology 1992; 1: 79
– 85.
Tucker A, Garway-Heath DF, Liu X. Spatial operators for evolving dynamic probabilistic networks from spatio-temporal data.
Proceedings of the Genetic and Evolutionary Computation Conference. Chicago: Springer-Verlag, 2003; pp. 12–17.
Advanced Glaucoma Intervention Study. 2. Visual field test scoring and reliability.Ophthalmology 1994; 101: 1445 – 1455.
Kamal D, Garway-Heath DF, RubenS et al. Results of the betaxolol versus placebo treatment trial in ocular hypertension.
Graefes Arch Clin Exp Ophthalmol 2003; 241:196–203.
Garway-Heath DF, Fitzke F, Hitchings RA. Mapping the visual field to the optic disc. Ophthalmology 2000; 107: 1809–1815.
DISCUSSION
• A number of Bayesian classifiers have been investigated for identifying VF deterioration
associated with glaucoma, while relationships between variables have been explicitly
modelled
• The resulting classifiers can be used to help understand VF deterioration through
network structure analysis and comparison with clinician’s decisions
• Various characteristics typical of early VF damage, such as the ‘nasal step’, are
identified within the Bayesian network structures, although the finding should be
interpreted with some caution because the models used in this study may be learning
clinical classification processes (in this case, AGIS)
• The relationship between clinician’s decisions and the model’s decisions has shown the
potential to understand how clinicians come to their decisions and possibly use the
information to improve upon the current VF classification methods