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STATISTICAL APPROACH TO SELECTING THE OPTIMAL PARAMETERS FOR DIAGNOSIS OF SOME CONNECTIVE TISSUE DISEASES
Mira J. Paskotaa, Sanvila S. Raskovicb
oc Aleksandra Z. PeriC-Popadicc, Vojislav D. Duricd,
^ Zikica M. Jovicice, Aleksandar M. Perovicf
3 a
O Universtiy of Belgrade, Faculty of Transport and Traffic Engineering,
° Belgrade, Republic of Serbia,
< e-mail: [email protected],
^ ORCID iD: http://orcid.org/0000-0002-7625-6155
^ b Universtiy of Belgrade, School of Medicine, Clinical Center of Serbia,
0 Clinic of Allergolorgy and Immunology, Belgrade, Republic of Serbia, e-mail: [email protected],
> ORCID iD: (3 http://orcid.org/0000-0002-4625-5485
< c Universtiy of Belgrade, School of Medicine, Clinical Center of Serbia, Clinic of Allergolorgy and Immunology, Belgrade, Republic of Serbia, e-mail: [email protected], ORCID iD: ©http://orcid.org/0000-0001-9718-2688
d Universtiy of Belgrade, School of Medicine, Clinical Center of Serbia, w Clinic of Allergolorgy and Immunology, Belgrade, Republic of Serbia,
e-mail: [email protected], ^ ORCID iD: (3 http://orcid.org/0000-0002-7544-8307
^ e Universtiy of Belgrade, School of Medicine, Clinical Center of Serbia,
Clinic of Allergolorgy and Immunology, Belgrade, Republic of Serbia,
1 e-mail: [email protected], '" ORCID iD: ©http://orcid.org/0000-0002-8805-8391
^ f Universtiy of Belgrade, Faculty of Transport and Traffic Engineering,
g Belgrade, Republic of Serbia,
> e-mail: [email protected], ORCID iD: http://orcid.org/0000-0002-8326-8007
DOI: 10.5937/vojtehg67-21023; https://doi.org/10.5937/vojtehg67-21023
FIELD: Mathematics
ARTICLE TYPE: Original scientific paper ARTICLE LANGUAGE: English
Abstract:
In order to choose the optimal parameters for easier diagnosis of systemic autoimmune diseases, the authors focused on data dimensionality reduction, using both feature selection and feature extraction.
ACKNOWLEDGMENT: This study is partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, through grants nos. III44006, III41013 and TR36001.
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The Multiple Correspondence Analysis was used as a feature extraction method, with the aim of exploring the underlying data structure and in detecting the crucial latent variables. The obtained latent variables were used as an input for the Discriminant Analysis which correctly classified 86.5% of all analyzed cases. The high rate of correctly classified objects indicates that it would be possible to automate diagnostic processes, which would lead towards the development of decision support systems in this area of medicine. In addition to their knowledge and experience, clinical experts would have further help in decision support systems. That can allow easier learning, faster checking of diagnostic steps, lower rates of misdiagnosed cases and easier communication with experts from other medical centers.
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Key words: multiple correspondence analysis, dimensionality reduction, discriminant analysis, connective tussue diseases,
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autoimmunity, diagnosis. °
Introduction
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Autoimmune systemic diseases like systemic lupus erythematosus, g progressive systemic sclerosis and Sjogren's syndrome can be very difficult to diagnose in practice. Doctors at the primary and secondary level of a typical health care system are usually not qualified enough to recognize connective tissue diseases. Even for specialists at clinics it can be a challenge. The additional problem lies in the fact that many & autoimmune diseases patients suffer from more than one condition at the same time. This is why a great number of different parameters are '-a. typically needed for the correct diagnosis of these diseases. o
In practice, various variables are used for the identification and ^ classification of patients with systemic connective tissue diseases n (Hoogen et al, 2013), (Shiboski et al, 2012). For the purpose of research, the American College of Rheumatology developed the Classification criteria for systemic lupus erythematosus in 1982. In 1997, these criteria were revised. The Systemic Lupus International Collaborating Clinics (SLICC) proposed new classification criteria in 2012 (Petri et al, 2012). % The SLICC variables were selected after the statistical analysis of patients' medical records by experts, using logistic regression analyses. These variables were then used for the recursive partitioning analysis. The final selection of the variables was performed by the committee of w" medical experts, but it was strongly influenced by the statistical analysis. Thus, both expert opinion and statistical methods were used in attempts
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to classify systemic connective tissues diseases (Nadashkevich et al, o
2004), (Vitali et al, 2002). |
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Even though we could not find any application of the Multiple Correspondence Analysis (MCA) in the research of the connective tissue or autoimmune diseases, the applications of the correspondence analysis in medicine are not new. Crichton and Hinde in (Crichton & Hinde, 1989) used a simple Correspondence Analysis (CA) to help diagnose patients with chest pain and acute abdominal pain. Greenacre in (Greenacre, 1992) gives several applications of the CA in different fields of medicine. The same author also gives an example of the application of the MCA in medicine. In (Almeida et al, 2009) the authors are using the MCA in building a logistic model for the predictor selection in living-donor kidney transplant data.
Concerning the other statistical methods applied in the study of autoimmune diseases, we refer the reader to (Armananzas et al, 2009), where a combination a multivariate correlation and certain machine learning techniques are used for the application of the microarray analysis in study of SLE and PAPS (primary antiphospholipid syndrome).
The rest of the paper is organized as follows: Section 2 gives a short description of the analyzed data set and the available variables. In Section 3, we describe the statistical methods used for the analysis of the data set. Section 4 presents and discusses the results, while the concluding remarks are given in Section 5.
The data set and variables description
The data set consists of 37 patients treated at the Clinic of Allergology and Immunology in Belgrade in the period 2012/2013. Among them, eleven were diagnosed as systemic lupus erythematosus (SLE), fourteen as Sjogren's syndrome (Sy Sjögren), nine as progressive systemic sclerosis (PSS) and three had both SLE and Sy Sjögren. The patients were diagnosed according to the ARA criteria (Hochberg, 1997).
The connective tissue diseases are relatively difficult to diagnose, requiring a broad picture of the patient's medical history, usually assessed through a large number of variables. All the subjects from our study were evaluated using 87 different variables belonging to three different groups, classified according to their 'availability' and 'cost'. The first group consists of 33 variables relatively easy to obtain, and consequentially considered to be 'cheap' (variables 1 to 33, Table 1). These were the variables obtained during the anamnesis and clinical examination of the patients. The second group of 37 variables (variables 34 to 70, Table 1) were the laboratory results of different blood tests, while the 17 variables from the third group (71 to 87, Table 1) are the
results of more invasive diagnostic procedures such as salivary gland histopathology or kidney histopathology, and therefore the most 'expensive' to obtain. It is important to note that the final diagnosis was « not included in the data set in any way.
The diagnostics process typically varies among individual patients depending on their condition, so not all of the mentioned diagnostics <8 procedures were needed for all patients and there are some missing cases in the data set.
Methods
A short description of the multivariate correspondence analysis and the discriminant analysis is given in order to familiarize the reader with them and make the text and the results easier to follow and understand.
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Multivariate Correspondence Analysis °
The MCA is an exploratory statistical technique suitable for analyzing nominal variables, usually applied with the aim of learning something previously unknown about the analyzed data. By the results researchers can get from it and the field of application, the MCA is considered to be the equivalent of the principal component analysis (PCA) for nominal variables. The main features of the MCA are the possibilities of underlying structure exploration/detection and dimension reduction, usually resulting in a set of latent variables. The MCA is a generalization of the Simple Correspondence Analysis (CA), a very popular method for the analysis of contingency tables (Benzecri, 1973), (Greenacre, 1984). While the CA is suitable for the analysis of only two ng nominal variables, the MCA can be used for the simultaneous analysis of n any number of nominal variables. Since the MCA is basically an optimal scaling method, it can also been used for the quantification of nominal variables. Good and detailed descriptions of the MCA, its characteristics and examples of application can be found in the literature, see for instance (Gifi, 1990), (Greenacre & Blasius, 2006), (Le Roux & Rouanet, & 2004).
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Discriminant analysis
The important results of the MCA are object scores, coefficients of « all objects regarding virtual dimensions of the solution. Since these coefficients are numerical, as opposed to original variables being
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quantification. However, it is important to mention that a one to one «
relationship between the original and quantified variables does not exist, because object scores are virtual variables, in many ways equivalent to principal components. Keeping that in mind, it is possible to apply any £ statistical method suitable for the analysis of numerical data on such ° virtual variables. In this study, the discriminant analysis was used to control the validity of classification.
As usually explained in the literature (Klecka, 1980), (McLachlan, oc 1992), the discriminant analysis in practice has two main purposes: to find a linear combination of the variables which separate the elements in the best possible way, and to allocate the sample elements into
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o previously defined groups using these linear combinations, usually called < discriminant functions. The first and necessary step, finding the ° discriminant functions, is also a form of data reduction. In some g applications, the functions are used as a linear classifier for the allocation m of the elements to the previously defined groups. In this research, the discriminant analysis was used with that purpose.
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Results and the discussion
The analysis of frequencies, as a necessary first step in every statistical analysis of nominal variables, showed that out of 87 total < variables, 29 had too many missing cases to be useful in the analysis. ^ The list of all variables showing if they are included in the analysis and о the reasons for the exclusion is given in Table 1. That left 58 variables in the initial set; all were included in the preliminary analysis.
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О Table 1 - List of all variables
Таблица 1 - Список всех переменных ^ Табела 1 - Листа свих промен^ивих
* LF (low frequency) ** HF (high frequency) *** LC (low contribution)
No Variable (number of categories) Step 1 Steps 2 & 3
Included Missing cases Included Reason for exclusion
1 Sex (2) Yes No LF* (3/37)
2 Age (4) Yes Yes
3 Malar rash (2) Yes Yes
4 Discoid rash (2) Yes No LF (3/37)
5 Photosensitivity (2) Yes Yes
6 Oral ulcers (2) Yes No LC***
No Variable (number of categories) Step 1 Steps 2 & 3
Included Missing cases Included Reason for exclusion
7 Dryness of the mouth (2) Yes Yes
8 Arthralgia (2) Yes No HF**(34/37)
9 Arthritis (3) Yes No LC
10 Dryness of eyes (2) Yes Yes
11 Proximal scleroderma (2) Yes Yes
12 Sclerodactyly (2) Yes Yes
13 Digital ulcers (2) Yes Yes
14 Raynaud phenomenon (2) Yes No LC
15 Livedo reticularis (2) Yes No LF (4/37)
16 Dysphagia (2) Yes Yes
17 Teleangiectasia (2) Yes No LC
18 Fever(2) Yes No LC
19 Weight loss (2) Yes No LC
20 Malaise (2) Yes No LC
21 Hair loss (2) Yes No LC
22 Lymphadenopathy (2) Yes No LF (4/37)
23 Epilepsy (2) Yes No LC
24 Psychiatric (2) Yes No LC
25 Psychologic (2) Yes No LC
26 Cerebrovascular disease (2) Yes No LF (2/37)
27 Miscarriage (2) Yes No LC
28 Thrombosis (2) Yes No LF (4/37)
29 Embolism (2) Yes No LF (1/37)
30 Pleural effusion (2) Yes Yes
31 Pulmonary fibrosis (2) Yes Yes
32 Calcinosis (2) Yes No LF (2/37)
33 Blood pressure (3) Yes No LC
34 Erythrocyte sedimentation rate (4) Yes No LC
35 Fibrinogen (3) Yes No LC
36 Anemia (3) Yes No LC
37 Leucopenia (3) Yes No LC
38 Lymphopenia (3) Yes Yes
39 Thrombocytopenia (3) Yes No LC
40 Iron (3) No 7
41 Erythrocyturia (3) Yes No LC
42 Cylindruria (2) Yes No LF (4/37)
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No Variable (number of categories) Step 1 Steps 2 & 3
Included Missing cases Included Reason for exclusion
43 Proteinuria (4) Yes Yes
44 Leukocyturia (2) Yes Yes
45 Coombs test (2) No 5
46 RF (2) No 8
47 CRP (3) No 5
48 ANA (3) Yes Yes
49 HEp-2 ANA (2) No 12
50 Anticentromere antibody (2) No 23
51 ANCA (2) No 15
52 MPO (2) No 32
53 PR3 (2) No 33
54 Anti Sm (2) No 30
55 RNP (2) No 19
56 Anti ds DNA (3) Yes Yes
57 SSA (3) No 14
58 SSB (2) No 24
59 SCl 70 (2) Yes Yes
60 AclA IgG (2) No 13
61 AclA IgM (2) No 13
62 B2GPI IgG (2) No 31
63 B2GPI IgM (2) No 31 No
64 LA (2) No 32
65 VDRL (2) No 25
66 KCT (2) No 18
67 Lowered complement (2) Yes No LC
68 Elevated IgG IgM (3) Yes Yes
69 Cryoglobulins (2) No 16
70 Paraprotein (2) Yes No LC
71 Keratoconjunctivitis sicca (2) Yes Yes
72 Funduscopic abnormalities (2) No 12
73 Other eye symptoms (2) No 9
74 Capillaroscopy (2) Yes Yes
75 Diffusing capacity (2) Yes Yes
76 Pericardial effusion (2) Yes Yes
77 Pulmonary hypertension (2) Yes Yes
78 Pulmonary scintigraphy (2) No 32
No Variable (number of categories) Step 1 Steps 2 & 3
Included Missing cases Included Reason for exclusion
79 Salivary scintigraphy (4) No 27
80 Endocranial NMR (3) No 22
81 Chest x ray (2) Yes Yes
82 Hand x ray (2) No 30
83 Esophageal dysfunction (2) Yes Yes
84 Lupus band test (2) No 33
85 Labial salivary gland histopathology (4) Yes Yes
86 Kidney histopathology (3) Yes Yes
87 Electroneuromyography (3) No 30
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Two-dimensional solution
Table 2 presents the results of the MCA in the two-dimensional space. Cronbach's alpha is very high for both dimensions, confirming their validity and importance for the interpretation. The first dimension explains 30.698% of the total variability, while the second one explains 25.603%. In the two-dimensional space, the total of 56.301% of the variance is explained. Even though more than 40% of the variability is not explained in this solution, reducing the dimensionality from 27 (number of variables entered in the final analysis) to only two is a very good result and worth further discussion and interpretation.
Table 2 - 2D results of the MCA Таблица 2 - Результаты 2Д анализа множественной корреспонденции Табела 2 - Резултати 2Д мултикореспонденционе анализе
Dimension Variance Accounted For
Cronbach's Alpha Inertia % of Variance Total
1 .913 8.289 .307 30.698
2 .888 6.913 .256 25.603
Total 15.201 .563 56.301
The object scores represent positioning of the patients in the two-dimensional space, the objects are labeled by the diagnosis. Figure 1 plots the objects (in our case, they are the patients with the connective tissue disease diagnosis), using their scores along the first two dimensions. At the first glance, it is obvious that the first dimension separates PSS on the right (higher values of the scores) from other
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patients, positioned at the left (lower score values). The separation is very clean along the line of x approximately equal to 0.5. The grouping along the second dimension is also very interesting, although the separation is not so clean. Positioned high are PSS, Sy Sjögren, the cases with both Sy Sjögren and SLE and several of the SLE cases. Most of the SLE cases are positioned lower. The second dimension shows both that the SLE cases are more heterogonous than the PSS or Sy Sjögren cases, and that the separation between SLE and Sy Sjögren is not clean.
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The clinical medical experience is in accordance with this result. The PSS patients are usually easy to distinguish by their characteristics from the SLE or Sy Sjögren patients, who are more similar regarding their clinical and biochemical characteristics.
In order to better understand the first two virtual dimensions, we are going to analyze the discrimination measures of all 27 variables (Table 3). The discrimination measures are the squared component loadings along the two virtual axes, and have the meaning of the variance of the quantified variables. As previously explained, in the last step of the variables selection, all variables with the mean discrimination measure in the 2D solution less than 0.1 were excluded from the final analysis.
Table 3 - Discrimination measures of the variables, 2D solution Таблица 3 - Дискриминативные значения переменных, 2Д решение Табела 3 - Дискриминационе мере промен^ивих, 2Д решете
Dimension Mean
1 2
Age .064 .466 .265
Malar rash .106 .137 .122
Photosensitivity .178 .122 .150
Dryness of the mouth .208 .506 .357
Dryness of the eyes .152 .616 .384
Proximal scleroderma .674 .002 .338
Sclerodactyly .840 .026 .433
Digital ulcers .468 .004 .236
Dysphagia .507 .052 .280
Pleural effusion .027 .408 .218
Pulmonary fibrosis .488 .011 .249
Lymphopenia .030 .434 .232
Proteinuria .034 .719 .376
Leukocyturia .572 .176 .374
ANA .097 .275 .186
Anti ds DNA .044 .746 .395
Scl-70 .512 .001 .256
Elevated IgG IgM .114 .338 .226
Keratoconjunctivitis sicca .131 .545 .338
Capillaroscopy .472 .052 .262
Diffusing capacity .601 .065 .333
Pericardial effusion .139 .205 .172
Pulmonary hypertension .507 .012 .260
Chest x ray .254 .117 .185
Esophageal dysfunction .673 .036 .354
Labial salivary gland histopathology .376 .316 .346
Kidney histopathology .018 .526 .272
Active Total 8.289 6.913 7.601
% of Variance 30.698 25.603 28.150
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The discrimination measure can take values between 0 and 1. The discrimination measure plot (Figure 2) is very helpful in the interpretation of the virtual space.
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Variables in 2D space
Labial salivary gland histopathology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Dimension 1 (30.7%)
Figure 2 - Discrimination measure plot, 2D solution Рис. 2 - Изображение 2Д решения, при применении дискриминативных значений Слика 2 - Приказ 2Д решена применом дискриминационе мере
There are a number of variables with a relatively high value of the discrimination measure along the first, but very low value along the second virtual dimension. In Figure 2, they are positioned very low, close to the x axis. The variables from this group are Diffusing capacity, Esophageal dysfunction, Proximal scleroderma, Sclerodactyly, Digital ulcers, Dysphagia, Pulmonary fibrosis, Scl-70, Capillaroscopy, and Pulmonary hypertension and they can be used to explain the role of the first virtual dimension in the solution. These variables are typical for the PSS patients; some of them like Proximal scleroderma and Esophageal dysfunction are used as the diagnostic criteria for PSS. Therefore, the first dimension was named 'Sclerosis'.
There are also several variables with relatively low values of the discrimination measure along the first, but quite high values along the second virtual dimension. In the discrimination measure plot (Figure 2), they are positioned very close to the y axis. Kidney histopathology, Proteinuria, Anti ds DNA, Pleural effusion and Lymphopenia are in this
group. These are the variables important for the diagnosis of SLE and lupus nephritis. The variables characteristic for Sy Sjögren (Dryness of eyes, Dryness of mouth, keratoconjunctivitis sicca) are also positioned relatively high and close to the y axis, but not as close as the SLE group of the variables. Some of the variables are characteristic for both SLE and Sy Sjögren (Elevated IgG i IgM, ANA). They are also leaning towards the y axis, but have lower discrimination measures. The second dimension was accordingly named 'SLE and/or Sy Sjögren'.
The rest of the variables have similar contributions towards both virtual dimensions. Most of the variables in the middle, especially the ones with relatively low discrimination measures, are typically seen in both SLE and Sy Sjögren. The variables like Malar rash, Photosensitivity and ANA are positioned closer to the coordinate center and not too close to any of the axes,since they can be observed in both SLE and Sy Sjögren, as is known from the clinical practice.
It is important to understand that the 2D solution explains only 56.301% of the total variability contained in the data, and that it is quite likely that some of these variables highly contribute towards the third (or a higher ranked) dimension, which would not be shown in the 2D representation. In order to better understand the role and importance of different variables for the connective tissue disease diagnosis, we are also going to look at the three-dimensional solution.
Three-dimensional solution
The three-dimensional solution keeps the first two dimensions described in Section 4.1 and adds one more dimension to the preexisting two-dimensional solution. The third dimension also has a relatively high value of Cronbach's Alpha (0.696) and adds 11.221% to the explained variability (Table 4). The first three dimensions together explain 67.522% of the total variance.
Table 4 - 3D results of the MCA Таблица 4 - 3Д результаты применения анализа множественной
корреспонденции Табела 4 - 3Д резултати примене мултикорепонденционе анализе
Dimension Variance Accounted For
Cronbach's Alpha Inertia % of Variance Total
1 .913 8.289 .307 30.698
2 .888 6.913 .256 25.603
3 .696 3.030 .112 11.221
Total 18.231 .675 67.522
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The positions of the objects in the 3D space (Figure 3) are revealing that the PSS patients are clearly separated from others, while the SLE and Sy Sjögren patients are not clearly separated from each other. However, the patients with both diagnoses (SLE and Sy Sjögren) are correctly positioned in the area where the two diagnoses are overlapping. It is also noticeable that the PSS and Sy Sjögren patients do not vary much along the third dimension. The SLE cases, however, are showing significant heterogeneity along the third dimension, as well as along the second dimension. As it was mentioned in the previous discussion, the SLE patients tend to be more different between them and more heterogonous, while the PSS and Sy Sjögren patients are more homogenous in their groups. The third dimension may give more insight in the causes of the SLE heterogeneity.
Figure 3 - 3D objects plot Рис. 3 - 3Д изображение объектов Слика 3 - 3Д приказ обjеката
The variables with very high values of the discrimination measure along the third dimension are Age, Kidney histopathology and
Leukocyturia, while the values of Proteinuria, Anti ds DNA are also relatively high. These variables are responsible for the variations among the SLE cases, and are indicating some level of the kidney dysfunction. « This is why the third dimension was named 'Renal Impairment'.
Lupus is a chronic inflammatory autoimmune disease which can affect any organ system, but mainly involves the skin, joints, kidneys and <8 the nervous system (Ching et al, 2012), (Edworthy, 2005), (Hahn et al, 2005), (Hahn et al, 2012), (Muscal & Brey, 2010). SLE has a multitude of presentations ranging from mild, localized disease to severe multi-organ involvement abruptly or sequentially over the course of months to even years. Some patients can have only 4 diagnostic criteria, but many of patients can have more, between 4 and all 11 criteria. This poses a challenge to practitioners as SLE can be a great mimicker of many diseases.
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One of the first steps in evaluating a patient with lupus is to ^ recognize that there are various subtypes of lupus (Arbuckle et al, 2009), (Melba & Ovalle, 2013). Autoantibodies alone would not be sufficient to diagnose SLE because these autoantibodies are also present in other rheumatologic diseases (Arbuckle et al, 2009), (Shiboski et al, 2012), (Heaton, 1959), (Tan et al, 2005), (Manoussakis et al, 2004). Sy Sjogren and SLE do have similarities. Their autoantibody profiles are similar. They effect women more than men and have similar HLA haplotypes and autoantibodies. Most likely this is not a coincidence, but it may not be clinically relevant (Manoussakis et al, 2004), (Scheinfeld, 2006).
Sjogren's syndrome may occur in patients with systemic lupus o erythematosus (SLE). The subset of patients with SLE and SY Sjögren has a distinct clinical and laboratory phenotype, with a higher frequency among older white women with photosensitivity, oral ulcers, Raynaud's phenomenon, anti-Ro antibodies, anti-La antibodies and a lower frequency of renal disease, anti-dsDNA antibodies and anti-RNP antibodies. cd
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Classification using the Discriminant Analysis ®
As it was already mentioned, the diagnosis of the patients was never used during the MCA analysis. Since the positions of the objects in the § virtual space (Figure 1) indicate that there is a natural grouping of the patients with the same diagnosis, it was necessary to check if that grouping is good enough to be used for the purpose of diagnosis, learning and automated separation of the objects. To accomplish that, w" the linear discriminant analysis was used.
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The object scores from the two-dimensional MCA were used as an input to the discriminant analysis. The grouping variable was the diagnosis, consisting of four different classes: SLE, PSS, Sy Sjögren and SLE + Sy Sjögren. The number of predictors (virtual numerical variables obtained as the result of the MCA analysis) was two, so the number of discriminant functions was also two - equal to the min(number of classes - 1, number of predictors).
Table 5 Таблица 5 Табела 5
Diagnosis Object scores, dimension 1 Object scores, dimension 2
Mean Std. Deviation Valid N Mean Std. Deviation Valid N
SLE -.372118 .3471989 11 1.188039 1.0299628 11
Sjögren -.635476 .1850666 14 .695795 .2670113 14
PSS 1.617873 .6588988 9 .260829 .5162426 9
SLE+Sjö -.523629 .3994424 3 .326613 .2201460 3
Total .000000 1.0137938 37 .000000 1.0137938 37
Table 5 presents the group means of both variables, while the results of the equality of means test are given in Table 6. The low values of Wilk's Lambda indicate that both variables are very important for the classification and are significantly contributing towards the objects separation (the significance asymptotically converging towards zero in both tests).
Table 6 Таблица 6 Табела 6
Wilks' Lambda F df1 df2 Sig.
Object scores dimension 1 .147 63.775 3 33 .000
Object scores dimension 2 .372 18.570 3 33 .000
The eigenvalues of both discriminant functions with their corresponding canonical correlations are given in Table 7; the first function explains 79.9%, and the second 20.1% of the total variability.
Table 7 Таблица 7 Табела 7
Canonical
Function Eigenvalue % of Variance Cumulative % Correlation
1 6.392(a) 79.9 79.9 .930
2 1.605(a) 20.1 100.0 .785
Based on the MCA virtual dimensions, the DA algorithm was very successful in predicting the group membership (Table 8). 86.5% of the cases were classified correctly. All of the PSS and SLE+Sy Sjögren patients were correctly classified. The only misclassifications were 3 of the SLE and 2 of the Sy Sjögren cases, all predicted as being SLE+Sy Sjögren patients.
Table 8 Таблица 8 Табела 8
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SLE 8 0 0 3 11
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PSS 0 0 9 0 9
SLE+Sjö 0 0 0 3 3
SLE 72.7 .0 .0 27.3 100.0
Sy Sjögren .0 85.7 .0 14.3 100.0
PSS .0 .0 100.0 .0 100.0
SLE+Sjö .0 .0 .0 100.0 100.0
The explanation could be that SLE and Sy Sjögren are frequently overlapping diseases; at the moment we see the patients for the first time it might not be obvious that they can have a mixed form of the disease, named the overlap syndrome. Also, patients with diagnoses of SLE can have some characteristics of Sy Sjögren, (such as dryness of mouth and eyes), but without enough criteria for both diagnoses. A number of patients who seem to have only Sy Sjögren can develop some
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manifestations of SLE (eg lymphopenia, ds DNA). The border between the diagnoses of SLE and Sy Sjögren is very subtle, and could be the explanation of the aforementioned misclassifications. Figures 4 and 5 show the corresponding discrimination measure plot for the 3D solution.
Variables in 3D space
Figure 4 Puc. 4 CnuKa 4
Figure 5 Puc. 5 CnuKa 5
Conclusion
This study has demonstrated that it is possible to significantly lower the number of parameters needed to diagnose the connective tissue diseases. Out of 87 available variables, 60 were discarded in the three-step eliminatory process. The remaining 27 variables were analyzed
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using the multiple correspondence analysis. The three-dimensional solution was enough to identify the most important parameters related to different diseases and clearly separate the cases. Even the two-dimensional solution was enough to give a significant insight into the relationships among the variables and spatial positioning of the patients. The close proximity of some of the variables in the three-dimensional solution might indicate that a further dimension reduction is possible, which can be the subject of a separate study.
The importance of the results is in a possible successful application of the methods of advanced statistics in the medical practice, especially in the process of learning. The discriminant analysis classification was based on the two-dimensional MCA solution. The high rate of correctly classified objects indicates that it would be possible to automate the diagnostic processes, which would lead towards development of decision support systems in this area of medicine. In addition to their knowledge and experience, clinical experts would have further help in decision support systems. Thist can allow easier learning, faster checking of the diagnostic steps, lower rates of misdiagnosed cases, and easier communication with experts from other medical centers.
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СТАТИСТИЧЕСКИЙ МЕТОД ВЫБОРА ОПТИМАЛЬНЫХ ПАРАМЕТРОВ ДЛЯ ДИАГНОСТИКИ НЕКОТОРЫХ ЗАБОЛЕВАНИЙ СОЕДИНИТЕЛЬНОЙ ТКАНИ
Мира Й. Паскотаа, Санвила С. Рашкович6, Александра Ж. Перич-Попадич6, Воислав Д. Джурич6, Жикица М. Йовичич6, Александар М. Перовича
а Белградский университет, Факультет транспорта и связи,
г. Белград, Республика Сербия 6 Белградский университет, Медицинский факультет, Клинический центр Республики Сер6ия, Клиника аллергологии и иммунологии, г. Белград, Респу6лика Сер6ия
РУБРИКА ГРНТИ: 27.00.00 МАТЕМАТИКА; 0
27.43.17 Математическая статистика
ВИД СТАТЬИ: оригинальная научная статья аЪ
ЯЗЫК СТАТЬИ: английский ю
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размерности данных, проведенная методом селекции и экстракции характерных атрибутов, с целью выбора оптимальных параметров для диагностики заболеваний иммунной системы. Анализ множественной корреспонденции проведен не только при экстракции, но и при исследовании самой структуры данных, а также при диагностике латентных переменных. Благодаря проведенному анализу множественной корреспонденции на материале экстрагированных латентных переменных с максимальной точностью было классифицировано 86,5% наблюдаемых случаев. Высокий уровень точно о классифицированных заболеваний свидетельствует о реальных возможностях автоматизации диагностических процессов, которая поможет в усовершенствовании системы поддержки диагностики системных заболеваний соединительной ткани. Данные системы отличаются надежностью и скоростью диагностики, они легко осваиваются и облегчают коммуникацию специалистов из различных медицинских учреждений. .
Ключевые слова: анализ множественной корреспонденции, редукция размерности, дискриминативный анализ, заболевания соединительной ткани, автоиммунные заболевания, диагностика.
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СТАТИСТИЧКИ ПРИСТУП ИЗБОРУ ОПТИМАЛНИХ ПАРАМЕТАРА У ДШАГНОСТИЦИ НЕКИХ БОЛЕСТИ ВЕЗИВНОГ ТКИВА
Мира ^ Паскотаа, Санвила С. Рашкови^6, §
Александра Ж. Пери^-Попади^6, Во]ислав Д. Ъури^6
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а Универзитет у Београду, Саобра^ни факултет,
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6 Универзитет у Београду, Медицински факултет, Клинички центар Й Ср6и]е, Клиника за алергологи]у и имунологи]у,
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о селекци}е и екстракци]е карактеристичних атрибута.
Вишеструка анализа кореспонденци]е коришЯена }е не само за екстракци/'у, веП и за испитиваъе саме структуре података, као и за детекци]у къучних латентних променъивих. На екстраховане ш латентне променъиве }е, применом дискриминантне анализе,
сЕ коректно класификовано 86,5% посматраних случа}ева. Висока
о успешност класификаци]е упуГ>у}е на реалне могуЬности
° аутоматизаци]е ди}агностичког процеса, што би резултирало
< разво}ем система за подршку у ди]агностици системских болести везивног ткива. Овакви системи омогуЯу]у лакше учеъе, бржу и поуздани}у диагностику и лакшу комуникаци]у са експертима из
ш других медицинских центара.
£ Къучне речи: вишеструка анализа кореспонденци}е, редукцц'а
< димензионалности, дискриминантна анализа, болести везивног ткива, аутоимуне болести, диагностика.
сл Paper received on / Дата получения работы / Датум приема чланка: 21.03.2019. fj Manuscript corrections submitted on / Дата получения исправленной версии работы / ^ Датум достав^а^а исправки рукописа: 01.06.2019.
Paper accepted for publishing on / Дата окончательного согласования работы / Датум коначног прихвата^а чланка за об]ав^ива^е: 03.06.2019. х
ш © 2019 The Authors. Published by Vojnotehnicki glasnik / Military Technical Courier q (www.vtg.mod.gov.rs, втг.мо.упр.срб). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license
О (http://creativecommons.org/licenses/by/3.0/rs/). >
© 2019 Авторы. Опубликовано в «Военно-техническии вестник / Vojnotehnicki glasnik / Military Technical Courier» (www.vtg.mod.gov.rs, втг.мо.упр.срб). Данная статья в открытом доступе и распространяется в соответствии с лицензией «Creative Commons» (http://creativecommons.org/licenses/by/3.0/rs/).
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