Linear discriminant analysis and artificial neural network for glaucoma diagnosis using scanning laser polarimetry-variable cornea compensation measurements in Taiwan Chinese population.

GLAUCOMA

Linear discriminant analysis and artificial neural

network for glaucoma diagnosis using scanning laser

polarimetry

–variable cornea compensation measurements

in Taiwan Chinese population

Mei-Ling Huang&Hsin-Yi Chen&Wei-Cheng Huang&

Yi-Yu Tsai

Received: 22 June 2009 / Revised: 10 November 2009 / Accepted: 19 November 2009 / Published online: 15 December 2009

# Springer-Verlag 2009

Abstract

Background To determine whether linear discriminant analysis (LDA) and artificial neural network (ANN) can improve the differentiation between glaucomatous and normal eyes in a Taiwan Chinese population, based on the retinal nerve fiber layer thickness measurement data from scanning laser polarimetry–variable corneal compensation (GDx VCC).

Methods This study comprised 79 glaucoma (visual field defect, mean deviation: −5.60±4.23 dB) and 86 healthy subjects (visual field defect, mean deviation: −1.44±1.72 dB). Each patient received complete ophthalmological evaluation, standard automated perimetry (SAP), and GDx VCC exam. One eye per subject was considered for further analysis. The area under the receiver operating characteristics (AROC) curve, sensitivity, specificity and the best cut-off

value for each parameter were calculated. The diagnostic performance of artificial neural network (ANN) and linear discriminant analysis (LDA) for glaucoma detec-tion using GDx VCC measurements will be compared in this study.

Results The individual parameter with the best AROC curve for differentiating between normal and glaucomatous eye was nerve fiber indicator (NFI, 0.932). The highest AROCs for the LDA and ANN methods were 0.950 and 0.970 respectively.

Conclusion NFI, ANN and LDF method demonstrated equal diagnostic power in glaucoma detection in a Taiwan Chinese population.

Keywords Linear discriminant analysis . Artificial neural network . Scanning laser polarimetry–variable cornea compensation . Glaucoma diagnosis

Introduction

Some evidence shows that retinal nerve fiber layer (RNFL) analysis may improve the diagnosis of early glaucomatous damage [21, 24]. Scanning laser polarimetry (SLP) is an imaging modality available for assessing RNFL thickness. The accuracy of SLP in diagnosing glaucoma was limited, because the measurements obtained could be affected by the factor of corneal polarization; therefore, a new model of SLP employs a variable corneal polarization (GDx VCC; Carl Zeiss Meditec, Inc.) compensator that allows for eye-specific compensation [8,9,27]. Some studies have shown that GDx VCC demonstrates moderate to good discrimi-nating power for glaucoma detection [2,3,6,18–20, 23]. GDx VCC includes a summary parameter called the nerve Presented in part at: Asia ARVO, March 2007, Singapore and ARVO,

May 2007, Fort Lauderdale, Florida, America.

The authors have full control of all primary data, and we agree to allow Graefe's Archive for Clinical and Experimental Ophthalmology to review our data.

Commercial relationships policy: N M.-L. Huang

Department of Industrial Engineering & Management, National Chin-Yi University of Technology,

35, Lane 215, Section 1, Chung-Shan Road, Taiping City, Taichung County 411, Taiwan H.-Y. Chen (*)

:

:

China Medical University Hospital, No. 2, Yuh-Der Road,

Taichung City 404, Taiwan e-mail: [email protected] DOI 10.1007/s00417-009-1259-3

fiber indicator (NFI), which was developed from a machine-learning classifier known as the support vector machine (SVM) [26]. Some studies have reported that NFI has superior diagnostic performance compared with indi-vidual parameters [3,19,23,27]. To increase the diagnostic accuracy for glaucoma detection, some analytic tools that use different SLP measurements as input parameters were developed, by using statistical methods such as linear discriminant analysis (LDA) [3, 18]. The LDA method assumes that data representing different groups are linearly separable. If this assumption is not well-met, the classifier’s performance is degraded. Furthermore, several machine-learning methods have been proposed to increase the accuracy of diagnosing glaucoma disease [2, 6, 20]. However, different study designs and different ethnic groups have led to conflicting outcomes. Therefore, the aim of this study was to evaluate the accuracy of GDx VCC in glaucoma detection in a Taiwan Chinese population. We apply the parameter selection technique to retrieve GDx-VCC variables for the LDA and ANN analyses. The performance of the LDA and ANN methods for evaluating GDx VCC parameters will be compared based on the AROC curve in the current study.

Subjects and methods

This observational cross-sectional study included one randomly selected eye from each of 165 study participants (79 patients with glaucoma and 86 healthy controls) who had sought treatment at the Department of Ophthalmology, China Medical University Hospital (CMUH). This research follows the tenets of the Declaration of Helsinki. Informed consent was obtained from all participants, and the study was approved by the Institutional Review Board of the CMUH.

Each subject underwent a complete ophthalmic examina-tion, including slit-lamp biomicroscopy, gonioscopy, pachy-metry, Goldmann applanation tonopachy-metry, stereoscopic examination of the optic disc and fundus, and standard automated perimetry (SAP, 30-2 mode, Humphrey Field Analyzer, model 750, HFA; Carl Zeiss Meditec, Inc.). All subjects underwent GDx VCC imaging within 3 months of the clinical examination and visual field testing. Subjects with a best-corrected visual acuity of less than 20/40, a spherical equivalent outside ±5.0 diopters, and a cylinder correction >3.0 diopters were excluded. Patients with eyes with coexisting retinal disease, uveitis, or nonglaucomatous optic neuropathy were also excluded from this study.

Normal control eyes had normal findings in clinical examination, intraocular pressures (IOP) of 21 mm Hg or less with no history of increased IOP, normal-looking

optic nerve [14] (intact rim, no evidence of hemorrhage, focal rim thinning , notching, glaucomatous excavation or RNFL defects ) and a normal visual field result. A normal visual field was defined as a mean deviation (MD) and pattern SD (PSD) within 95% confidence limits, and a Glaucoma Hemifield Test (GHT) result within normal limits.

Eyes were classified as glaucomatous if they had repeatable (two consecutive) abnormal visual field test results, defined as a PSD outside the 95% normal confidence limits, or a GHT result outside 99% normal confidence limits, regardless of the appearance of the optic disc. To avoid bias in the evaluation of the optic disc, the definition of glaucoma was based on the visual field result, which is not dependent on RNFL or optic disc morphology [7].

SLP measurements

SLP measurements were obtained by the same trained and experienced technician. The images were analyzed with software version 5.5.0. The software also provided an image quality check score (1–10) to ensure accurate corneal measurement. In our study, the images had to be of high quality, i.e., a well focused, even, centered optic disc without any motion artifact. In addition, a score of 7 was the minimum standard for imaging quality. The 15 GDx VCC-measured RNFL thickness parameters comprised TSNIT average (total average RNFL thickness), superior average, inferior average, the TSNIT standard deviation, nerve fiber indicator (NFI), symmetry, superior ratio, inferior ratio, superior/nasal, maximum modulation, su-perior maximum, inferior maximum, ellipse modulation, normalized superior area, and normalized inferior area. All parameters, except for NFI, were used in the LDA and ANN.

Entropy-based feature selection

The traditional definition of entropy refers to changes in the status quo of the system, a measure of “molecular disorder”, and the amount of energy wasted in a dynamical energy transformation from one state or form to another [10]. Entropy change has often been defined as a change to a more disordered state at a molecular level [16]. In this study, we removed the irrelevant GDx parameter by calculating the value of entropy. The procedure starts from the complete data set including fourteen GDx-VCC parameters, and the parameter of which the removal most retains the distinctness among the clusters should be removed first. The similarity measure (S) was used to assume a very small value (close to 0.0) for very close pairs of instances, and a very large value (close to 1.0) for very

distant pairs [4]. For a dataset of N instances, the entropy measure is given as:

E¼
X N i¼1 XN j¼1 Sij log Sijþ 1
Sij
  log 1
Sij

 ð1Þ where Sij is the similarity value, normalized to [0,l],

between the instances xiand xj.

Sij¼ e
aDij ð2Þ

where Dij is the distance between the instances xi and xj,

andα is a parameter.

A sequential backward selection algorithm for unsuper-vised data (SUD) was used to determine the relative importance of features [4]. We used Matlab software version 6.5 to run the SUD to determine the importance of 14 GDx VCC parameters.

Linear discriminant analysis (LDA)

Linear discriminant analysis (LDA) is a statistic method which can classify objects into two mutually exclusive groups based on the dataset in which researchers are interested. LDA combines input parameters into a discrimi-nant function to classify cases in different groups. The idea underlying this classification method is to develop a linear discriminant function, F, of n variables as F¼ b₁x1þ

b2x2þ . . . þ bnxn with values for β1, β2, ..., βn chosen so

as to maximize the between-group to within-group sum of squares ratio, where the independent variables (x) are the features that can describe the objects; the result represents the best discrimination between the two groups. In this study, we analyzed 14 parameters, obtained from GDx VCC, by LDA, for their ability to differentiate between glaucomatous and healthy eyes. Detailed descriptions of the statistical proce-dures involved in the assessment and use of LDA models

can be found in the literature [15]. SAS software version 10.0 was used for LDA.

Artificial neural network (ANN)

An ANN can be structured to perform classification [22], An ANN consists of one input layer, one output layer, and one or more hidden layers that extract essential information during learning. ANNs can mimic the behavior of biological neural nets, and have successfully solved problems through generalization of a limited quantity of training data, overall trends in functional relationships. A well-trained ANN can be used to simulate and predict the output response for various control factor-level settings. In this study, for different inputs of parameter combina-tions generated from entropy, two to fourteen neurons in

0 3 6 9 12 15 18 -20 -15 -10 -5 0 5 MD PSD

Fig. 1 The scatter plot of MD vs PSD in whole eyes

Table 2 GDX- VCC measured RNFL thickness in both groups Normal Glaucoma P-value TSNIT average(μm) 59.77±5.33 50.56±8.67 <0.001 Superior average(μm) 72.76±6.39 58.80±10.04 <0.001 Inferior average(μm) 70.81±9.50 56.47±12.09 <0.001 TSNIT SD (μm) 24.33±4.42 19.86±5.98 <0.001 Nerve fiber indicator (NFI) 14.94±6.52 40.91±19.53 <0.001 Symmetry 1.01±0.15 0.99±0.20 0.542 Superior ratio 3.05±1.09 2.28±1.03 <0.001 Inferior ratio 3.06±1.19 2.34±1.01 <0.001 Superior/nasal 3.23±0.80 2.74±0.85 <0.001 Max modulation 2.81±0.98 2.25±1.05 <0.001 Superior maximum(μm) 86.34±10.63 71.76±14.82 <0.001 Inferior maximum(μm) 86.36±11.45 74.35±18.81 <0.001 Ellipse modulation 4.04±1.49 3.71±1.69 0.190 NSA* 0.152±0.0209 0.116±0.0327 <0.001 NIA* 0.154±0.0272 0.117±0.0399 <0.001 NSA: normalized superior area; NIA: normalized inferior area; SD: standard deviation.

*Compared by Student's t-test Table 1 Demographics of the normal and glaucoma groups

Normal (n=86) Glaucoma (n=79) P-value Gender Male, n (%) 40 (47%) 42 (53%) 0.393 Female, n (%) 46 (53%) 37 (47%) Age (years) 40.20±15.54 44.30±14.72 0.083 Pattern standard deviation (dB) 1.95±1.17 5.86±4.89 0.000 Refraction -2.02±2.23 -2.38±3.15 0.407 Mean deviation (dB) -1.44±1.72 -5.60±4.23 0.000 * compared by t-test method

the ANN hidden layer were executed. The neural network classifier is trained to detect a relationship between input (GDx VCC parameters) and a predefined gold-standard diagnosis by comparing its prediction with the labeled diagnosis, and by learning from its mistakes [25]. Ten-fold cross-validation was applied. The whole dataset was divided into ten sets. Each set contained one tenth of the normal people and one tenth of the glaucoma patients in the original dataset. The first set was treated as a test set; the second set was treated as a validation set, and the remaining eight sets were used as training sets. Each set was iterated as a test set, and the whole procedure was run ten times. Finally, the test results from all eyes were then used to plot the ROC curve. Matlab software version 6.5 was used for ANN application.

Statistical analyses

Statistical analyses were performed on a personal computer using SPSS (Ver.12.0; SPSS, Chicago, IL, USA). Differ-ences in age, visual field mean deviation (MD), and average RNFL thickness measured with GDx VCC between groups

were evaluated by the t-test. The AROC curve was used to assess the ability of each testing parameter to differentiate between normal and glaucomatous eyes (MedCalc soft-ware, version 9.0). In all statistical analyses, we set significance at 0.05/N, where N is the number of tests used (Bonferonni correction). The standard methods of compar-ing the areas under receiver operatcompar-ing characteristic curves were described by Delong DM et al. [5] and Hanley & McNeil [11]. In this work, pair-wise comparisons of AROC between LDA and ANN, between LDA and NFI, and between ANN and NFI were made by MedCalc software version 9.0 according to the method proposed by Hanley and McNeil [11].

Results

Table1shows the demographics of each group. The mean age was 40.20±15.54 years in the control group and 44.30± 14.72 years in the glaucoma group. There was no significant difference in age between the groups (p=0.083). The average MD of visual field was−1.44±1.72 dB in the control group Table 4 Entropy values by removing one parameter from the entire data set

Order 1 2 3 4 5 6 7

Attribute Superior maximum Inferior maximum Inferior average Superior average TSNIT SD TSNIT average Ellipse modulation Entropy 98.01 97.6 77.09 72.56 58.83 55.94 47.44

Order 8 9 10 11 12 13 14

Attribute inferior ratio superior ratio max modulation superior/nasal symmetry normalized inf. area normalized sup. area Entropy 46.66 46.62 46.24 46.05 45.25 45.24 45.24

Parameter Normal vs glaucoma

AROC Sensitivity Specificity Best cut-off value TSNIT average 0.815 62.03 98.84 <51.24 Superior average 0.879 72.15 97.67 <62.99 Inferior average 0.835 67.09 87.21 <62.22 TSNIT SD 0.748 70.89 68.60 <22.3 NFI 0.932 83.54 93.02 >23 Symmetry 0.537 31.65 86.05 <0.88 Superior Ratio 0.734 58.23 84.88 <2.1 Inferior Ratio 0.698 63.29 68.60 <2.39 Superior/Nasal 0.675 63.29 63.95 <2.85 Max Modulation 0.669 43.04 87.21 <1.73 Superior Maximum 0.809 68.35 87.21 <75.01 Inferior Maximum 0.723 59.49 86.05 <75.50 Ellipse Modulation 0.573 29.11 90.70 <2.31 Normalized Sup. Area 0.835 69.62 91.86 <0.1225 Normalized Inf. Area 0.792 55.70 94.19 <0.1224 Table 3 The AROC, sensitivity

& specificity and best cut-off value of each parameter for differentiating normal from glaucomatous eyes

and −5.60±4.23 dB in the glaucoma group. The average PSD of visual field was 1.95±1.17 dB in the control group and 5.86±4.89 dB in the glaucoma group. There were significant differences in MD and PSD values between the control and glaucoma groups (p<0.05). To test the feasibility of our study sample, we evaluated the correlation between MD and PSD in each eye as shown in Fig.1, and the result showed that they were highly correlated. Table 2 lists the GDx VCC data from both groups. There were significant differences in all parameters between control and glaucoma groups, except for the two parameters symmetry and ellipse modulation).

Table3 lists the AROC for differentiating normal from glaucomatous eyes for each parameter. The parameter with the best AROC curve was NFI (0.932, C.I. 0.882–0.965).

Table 4 shows the entropy values with respect to the situation when one specific parameter was removed from the whole data set. We obtained the order list of variables based on the result of SUD, and the GDx VCC variables were ranked as inputs both for LDA and ANN in the following sequence: inferior maximum, superior maximum, inferior average, superior average, TSNIT SD, TSNIT average, ellipse modulation, inferior ratio, superior ratio, max modulation, superior/nasal, symmetry, normalized inferior area, and normalized superior area.

Table 5 and Fig. 2 show the AROCs for LDA when different numbers of variables were used. The highest AROC (0.950) was achieved when 14 variables were fed as the input dataset for LDA. Figure3 shows the AROCs for ANN when different numbers of neurons were used. The performance of parameter selection using SUD was very successful; the highest AROC achieved was 0.970 when 11 variables were used as the input dataset.

Figure 4 shows the AROCs curves using the LDA method, ANN method and NFI parameter. The highest AROC with the LDA method is 0.950 (C.I. 0.905 to 0.978); and the highest AROC with the ANN method is 0.970 (C.I. 0.932 to 0.990). The difference between the best ANN and best LDA AROCs was not statistically significant (p=0.357); the difference between the best ANN and NFI AROCs was not statistically significant (p=0.117); the difference between NFI and the best LDA AROCs was not statistically significant (p=0.310).

Discussion

Our study confirms the previous work in which GDx VCC demonstrated a good discriminating power in glaucoma detection [2,3,6,18–20,23], and we also agree with the concept that NFI is the most important parameter in glaucoma detection. Interestingly, we found that both ANN and LDF methods cannot improve upon standard software-provided GDx VCC measurement, NFI, in glau-coma detection. The value of NFI was generated from an advanced form of neural network analysis. It was trained on a large sample of representative healthy and glaucomatous eyes, and utilized information from the entire RNFL thickness map to optimize the discrimination between the two. In our preliminary report, we found that the LDA method slightly improved the diagnostic capability of glaucoma based on the GDx VCC measured parameters (2007, Huang WC & Chen HY, et al. Asia ARVO E-Abstract

AROC 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0 2 4 6 8 10 12 14 16 Number of Variable

Fig. 2 The AROCs for LDA when different numbers of variables were used

Table 5 The AROCs of LDA with different number of parameters as LDA input

Number of variables AROC Number of variables AROC

1 0.809 8 0.948 2 0.809 9 0.949 3 0.895 10 0.948 4 0.922 11 0.948 5 0.922 12 0.947 6 0.928 13 0.949 7 0.930 14 0.950

307). The parameter with the best AROC curve (glaucoma visual field, average MD,−3.32±2.20 dB) was NFI (0.795). For LDA with stepwise method, the AROC for glaucoma detection was 0.845 with four input parameters (TSNIT average, superior, inferior, and Inferior maximum). In addition, we also reported that the ANN method could improve the diagnostic capability of glaucoma (average MD, −6.83±7.21 dB) based on the GDx VCC-measured parameters (AROC from ANN, 0.984; NFI, 0.82) (2007, Chen HY et al., ARVO E-Abstract 500). Here in the current study, we directly compare the two classification methods in the same study population (glaucoma, visual field severity, MD, −5.60±4.23 dB). The current result suggests that LDA and ANN trained on SLP RNFL thickness measurements are similar, and provide accurate classification of glaucomatous and healthy eyes.

Glaucoma diagnosis based on medical image data is common in medical decision-making. For group classifica-tion, LDA is a well-established method for classifying patients into different groups, and is commonly used in glaucoma [1,12,13,28]. The LDA method has also been applied to the Heidelberg Retina Tomograph (HRT) parameters [1] and the Stratus OCT parameters in glaucoma diagnosis [12]. Previously, Weinreb et al. [28] also developed a structural LDA based on SLP readings which could increase the diagnostic ability in glaucoma detection. In this study, we first applied the LDA method to evaluate the GDx VCC database in a pure Chinese population. However, the result shows that the diagnostic performance of the LDA method is no better than the NFI parameter. NFI is developed using a machine-learning classifier, the support vector machine (SVM). SVM is a popular machine classification method that directly minimizes the classifica-tion error without requiring a statistical data model. Because of its simple implementation and consistently high classification accuracy, many real-world classification situa-tions have been applied. Bowd C et al. [1] reported that HRT-based neural network techniques performed as well as or better than HRT-based LDFs. We believe that our current

study is the first one to directly compare the LDF method with the ANN method in the same population using GDx VCC parameters. And the result also confirms the pervious work of Bowd C et al., although different optical imaging machines were used and a different population was chosen. Machine-earning methods have recently been applied in the issue of glaucoma diagnosis. Bowd C et al. [2] reported that AROC curves for optimized RVM (0.93) and SVM (0.91) were significantly larger than those for NFI (AROC, 0.87). In our study, the ANN method shows excellent performance in glaucoma detection (AROC, 0.970) in a Taiwan Chinese population. Although the result is promising, it is inadequate for directly comparing the ANN result with that of the NFI, because of the differences in selection criteria for study inclusion.

There are some limitations of our study, although the results are interesting. The primary limitation is that, although the present sample size was adequate, a larger sample size is needed to obtain a standardized classification function. Second, the substrate for studies is usually a

0 20 40 60 80 100 100 80 60 40 20 0 100-Specificity Sensitivity ANN LDF NFI

Fig. 4 The AROC curves using the LDA method, ANN method and NFI parameter AROC 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0 2 4 6 8 10 12 14 16 Number of Variable

Fig. 3 The AROCs for ANN when different number of neurons were used

clinic-based population of patients with glaucoma. These patients are identified on the basis of particular patterns of structural and functional abnormality which meet precon-ceived notions that bias the outcome of the comparisons [17]. Moreover, the selection of a high-quality image process might produce some bias. Therefore, there is still some room for improving glaucoma detection using different methods.

Although the results from LDA and ANN trained on GDX VCC measurements are similar, and provide adequate classification between glaucomatous and healthy eyes in Taiwan Chinese population, the machine-learning classifier shows good potential in glaucoma diagnosis.

Acknowledgments The authors would like to thank for the National Science Council of the Republic of China for financially supporting this research under Contract No. 97-2628-E-167-001-MY3& DMR-93-046, DMR-94-043.

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