Multivariate Discriminant Analysis Research Articles

Understanding factors associated with sarcopenic obesity in older African women from a low-income setting: a cross-sectional analysis

BackgroundHigh rates of food insecurity, obesity and obesity-related comorbidities in ageing South African (SA) women may amplify the risk of developing sarcopenic obesity. This study aimed to investigate the prevalence and correlates of sarcopenic obesity and its diagnostic components [grip strength, appendicular skeletal muscle mass (ASM) and body mass index (BMI)] in older SA women from a low-income setting.MethodsThis cross-sectional study recruited black SA women between the ages of 60–85 years (n = 122) from a low-income community. Testing included a fasting blood sample (markers of cardiometabolic risk, HIV), whole body and regional muscle and fat mass (dual-energy absorptiometry x-ray), anthropometry, blood pressure, functional movement tests, current medication use, demographic and health questionnaires, physical activity (PA; accelerometery), household food insecurity access scale, and a one-week quantified food frequency questionnaire. Foundation for the National Institutes of Health (FNIH) criteria (grip strength and ASM, adjusted for BMI) were used to classify sarcopenia. Participants with sarcopenia alongside a BMI of > 30.0 kg/m2 were classified as having sarcopenic obesity. Prevalence using other criteria (European Working Group on Sarcopenia in Older People, Asian Working Group for Sarcopenia and the International Working Group for Sarcopenia) were also explored.ResultsThe prevalence of sarcopenia was 27.9%, which comprised of sarcopenia without obesity (3.3%) and sarcopenic obesity (24.6%). Other classification criteria showed that sarcopenia ranged from 0.8–14.7%, including 0.8–9.8% without obesity and 0–4.9% with sarcopenic obesity. Using multivariate-discriminant analysis (OPLS-DA) those with sarcopenic obesity presented with a descriptive profile of higher C-reactive protein, waist circumference, food security and sedentary time than women without sarcopenic obesity (p = 0.046). A similar profile described women with low BMI-adjusted grip strength (p < 0.001).ConclusionsThe majority of women with sarcopenia were also obese (88%). We show a large discrepancy in the diagnostic criteria and the potential for significantly underestimating the prevalence of sarcopenia if BMI is not adjusted for. The main variables common to women with sarcopenic obesity were higher food security, lower PA and chronic inflammation. Our data highlights the importance of addressing obesity within these low-income communities to ensure the prevention of sarcopenic obesity and that quality of life is maintained with ageing.

Assessing the Validity of Mojave Desert Lake Mohave and Silver Lake Projectile-Point Types

ABSTRACT This study uses univariate and multivariate statistical analyses to assess whether Lake Mohave and Silver Lake projectile points from the Mojave Desert of western North America are statistically discrete, recognizable, and valid types. Univariate analyses run on 400 Lake Mohave and Silver Lake points reveal significant differences in six linear and three angle measures, though overlapping measurements pose difficulties for differentiating the types. To address the problem of overlapping measurements, multivariate principal components and discriminant function analyses were employed to statistically define groups of related attributes. Size- and shape-based attributes of the stem distinguish approximately 80% of the sample to type and reveal region-wide consistency among archaeologists who have classified these points to type. Though this study did not entirely overcome the challenge of using metrics to differentiate Lake Mohave from Silver Lake points, key discriminating variables are now better defined and the types deemed valid.

Differential DNA methylation and gene expression during development of reproductive and vegetative organs in Ilex species.

Differential epigenetic (DNA cytosine methylation) and gene expression patterns were investigated in reproductive and vegetative organs from Ilex paraguariensis and I. dumosa, at distinct developmental stages. We aimed at contributing towards elucidating major molecular changes underlying the sexual differentiation processes which, in these dioecious species, are completely unknown. Simultaneously, as a first step towards the development of an early sexing system, we searched for promising molecular markers. This was assessed through Methylation Sensitive Amplified Polymorphism (MSAP) and Amplified Fragment Length Polymorphism on cDNA (cDNA-AFLP) techniques, applying discriminant multivariate analyses, and bioinformatic characterization of differential fragments. A significant positive correlation was found between epigenetic and indirect 'genetic' information for both species, indicating influence of the genetic background on the epigenetic variation. Higher epigenetic than genetic diversities were estimated. Our outcomes showed up to 1.86 times more representation of mCG subepiloci than mCCG in all organs sampled. Along the maturing stages of floral buds, the frequency of mCG evidenced an incremental trend, whereas mCCG and unmethylated conditions showed opposite tendencies. Reproductive and vegetative samples tended to cluster apart based on epigenetic patterns; at gene expression level, organs exhibited clear-cut distinctive patterns, nonetheless profiles of young leaves and floral primordia resemble. Epigenetic and expression data allowed discrimination of I. dumosa´s samples according to the gender of the donor; more elusive patterns were observed for I. paraguariensis. In total, 102 differentially methylated and expressed fragments were characterized bioinformatically. Forty-three were annotated in various functional categories; four candidate markers were validated through qPCR, finding statistical differences among organs but not among sexes. The methylation condition of epilocus C13m33 appears as indicative of gender in both species. Thirty-three organ-specific and 34 gender-specific methylated markers were discriminated and deserve further research, particularly those expressed in leaves. Our study contributes concrete candidate markers with potential for practical application.

Sex estimation in a Turkish population using Purkait’s triangle: a virtual approach by 3-dimensional computed tomography (3D-CT)

Sex estimation is considered one of the first steps in the forensic identification process. Morphological and morphometrical differences between males and females have been used as means for morphoscopic and metric methods on both cranial and postcranial skeletal elements. When dry skeletal elements are not available, virtual data can be used as a substitute. The present research explores 3-dimensional (3D) scans from a Turkish population to test a sex estimation method developed by Purkait (2005). Overall, 296 individuals were used in this study (158 males and 138 females). Purkait’s triangle parameters were measured on computed tomography (CT) scans obtained from both right and left femora of each patient at the Bakirkoy Dr. Sadi Konuk Training Research Hospital (Istanbul, Turkey). Intra- and inter-observer errors were assessed for all variables through technical error of measurements analysis. Bilateral asymmetry and sex differences were evaluated using parametric and non-parametric statistical approaches. Univariate and multivariate discriminant function analyses were then conducted. Observer errors demonstrated an overall agreement within and between experts, as indicated by technical error of measurement (TEM) results. No bilateral asymmetries were reported, and all parameters demonstrated a statistically significant difference between males and females. Fourteen discriminant models were generated by applying single and combined parameters, producing a total correct sex classification ranging from 78.4% to 92.6%. In addition, over 67% of the total sample was accurately classified, with 95% or greater posterior probabilities. Our study demonstrates the feasibility of 3D sex estimation using Purkait’s triangle on a Turkish population, with accuracy rates comparable to those reported in other populations. This is the first attempt to apply this method on virtual data and although further validation and standardisation are recommended for its application on dry bone, this research constitutes a significant contribution to the development of population-specific standards when only virtual data are available. Key points CT analysis using Purkait’s triangle is a suitable tool for assessment of sex in unidentified individuals. The best overall estimation rate was achieved with the F11 model, with around 92% of accuracy. The results suggested 78.4% to 92.6% correct sex identification rates. More research is needed to expand the sample set and verify the results.

Comparative Evaluation of Some Quality Characteristics of Sunflower Oilseeds (Helianthus annuus L.) Through Machine Learning Classifiers

Sunflower seeds are rich in oil and oleic acid, thus having valuable nutritional properties. Sunflower is also resistant to dry conditions and can adapt easily to harsh environmental conditions. Physico-chemical properties play a great role in classification, grading, and quality assessment of sunflower seeds. In present study, six different machine learning algorithms (decision tree, DT; random forest, RF; support vector machine, SVM; multiple linear regression, MLR; Naive Bayes, NB; and multilayer perceptron, MLP) were used to evaluate the classification performance for six different sunflower oilseed varieties. Additionally, characteristic properties of the oilseeds were evaluated by multivariate tests (MANOVA) and discriminant analysis. The best accuracy values were recorded as 80.16, 79.68, and 78.89 for RF, SVM, and MLP, respectively, and the lowest MAE value (0.088) was observed in NB. The MANOVA, Wilks’ lambda, and Pillai Trace statistics revealed that differences in physical attributes of the sunflower varieties were significant (p<0.01). Colombi and Transol varieties with the lowest Mahalanobis distances had the similar attributes.

Machine learning approach to predict susceptible growth regions of Moringa peregrina (Forssk)

Moving towards sustainable products and services in regions with fragile ecosystems needs plant species such as Moringa peregrina (Forssk) that will contribute to the restoration of the land and the development of the societies. This tree species is known as a source of income for local people via preparing medicine, food, industrial oil, livestock feed, and an effective role in water and soil conservation. In recent years, the reduction of M. peregrina has damaged ecosystem services in south-eastern Iran. According, the main objective of this study is to use new Machine Learning (ML) models include: Support Vector Machine (SVM), Multivariate Discriminant Analysis (MDA), Random Forest (RF), and Classification and Regression Trees (CART) to predict the regions susceptible to M. peregrine recovery. South Baluchistan in Iran was selected as a study area due to its location in a represent amen region where sustainable environmental production is threatened by land degradation processes. The location of 83-plant mass of M. peregrina was recorded in field visits by a global positioning system (GPS) device to recognize the relationship between them and thirteen meteorological, morphometric, and geological indicators. Within the 83 selected sites, 70% of them were used for training and 30% used for ML models calibration to predict the susceptible growth regions of M. peregrina to determine the most important indicators affecting his presence and to determine the prediction accuracy for ML models, the Jackknife test method and the area under the receiver operating characteristics curve (AUC) were used, respectively. The results showed that rainfall was the key indicator that determines the success of the plant establishment. So that, it had the most value of the percentage of relative decrease (PRD) as the following was 20.68, 30, 24.52, and 14 for the SVM, MDA, RF, and CART models, respectively. Models validation showed that the RF model with an AUC value of 0.882, is an efficient and reliable model to predict the regions susceptible to growth M. peregrina. It followed by the CART (0.849), MDA (0.832), and SVM (0.827). The final map of the RF method demonstrated that the area with a higher probability for growing M. peregrina is the wettest one. The results of this investigation are the potential map of M. peregrina growth that will contribute to the restoration of the land and will increase primary production, water, and soil protection, increase local people's income and achieve the Sustainable Development Goals (SDGs).

Untargeted lipidomic approach in studying pinot noir wine lipids and predicting wine origin

An untargeted lipidomic profiling approach based on ultra - performance liquid chromatography – time-of-flight tandem mass spectrometry (UPLC-TOF-MS/MS) was successfully used to study the origin of commercial Pinot noir wines. The total wine lipids were extracted using a modified Bligh-Dyer method. In all wine samples, the total lipids were less than 0.1% (w/w) of wine. The wines analyzed consisted of 222 lipids from 11 different classes. 48 commercial Pinot noir wine samples were collected from producers in Burgundy, California, Oregon, and New Zealand. Lipidomic data was studied using advanced multivariate analysis methods, random forest, k-nearest neighbor (k-NN), and linear discriminant analysis. The overall classification accuracy was 97.5% for random forest and 90% for k-NN. Wine lipids showed a strong potential for classifying wines by origin, with the top 58 lipids contributing to the discrimination. This information could potentially be used for further study of the impacts of lipids on wine characteristics and authenticity.

Integrating remote and biogeochemical data: Analyzing the potential of gamma ray spectrometric data for mapping Cerrado vegetation types

This study integrates remote and chemical data to investigate the potential use of potassium (K), thorium (Th), and uranium (U) radioisotopes for mapping Cerrado physiognomies. Because soil and vegetation are interdependent, the vegetation over the substrate reflects this relationship. Moreover, the physiognomic extracts that accompany the distribution of elements associated with the movement of this substrate in soil can be identified. Gamma ray spectrometric data have been used primarily for mineral exploration; however, the present study addresses the potential of these data for identifying vegetation. Using a multivariate analysis, it is possible to compare radioisotope data and their relationship to vegetation. The current study area is located in the northwest of Goiás, an area of conserved phytophysiognomic diversity that enables studies of the Cerrado vegetation. An initial cluster analysis defined five vegetation cover types: cerradão, cerrado rupestre, cerrado sensu stricto and campo limpo. Dendrograms demonstrated a positive relationship in the radioisotopes absorbed by certain plants; furthermore, their availability in the soil confirmed that it is possible to identify vegetation groups using the same absorption behavior. This soil-plant relationship divides groups that have the capacity for the absorption of radioisotopes with remote gamma-spectrometry data. Even considering that each species might react differently because of absorption and the bioavailability of elements in the soil, a relationship between absorption and remote data was identified. Furthermore, this relationship is reflected in the physiognomy, as confirmed by a multivariate discriminant analysis. The result of the analysis showed the potential of Th and K radioisotopes with regard to phytophysiognomic mapping.

Tephrostratigraphy and Magma Evolution Based on Combined Zircon Trace Element and U-Pb Age Data: Fingerprinting Miocene Silicic Pyroclastic Rocks in the Pannonian Basin

We present a novel approach to use zircon as a correlation tool as well as a monitor for magma reservoir processes in silicic volcanic systems. Fingerprinting eruption products based on trace element content and U-Pb dates of zircon offers a promising, previously underestimated tephra correlation perspective, particularly in cases where the main minerals and glass are altered. Using LA-ICP-MS analyses, a rapid and cost-effective method, this study presents U-Pb dates and trace element concentration data of more than 950 zircon crystals from scattered occurrences of early to mid-Miocene silicic ignimbrites in the northern Pannonian Basin, eastern-central Europe. This magmatic phase produced &amp;gt;4000 km3of erupted material, which provide unique stratigraphic marker horizons in central and southern Europe. The newly determined zircon U-Pb eruption ages for the distal pyroclastic deposits are between 17.5 and 14.3 Ma, comparable with the previously published ages of the main eruptive events. Multivariate discriminant analysis of selected trace element concentrations in zircon proved to be useful to distinguish the main volcanic units and to correlate the previously ambiguously categorized pyroclastic deposits with them. Using the zircon trace element content together with published glass data from crystal-poor ignimbrites, we determined the zircon/melt partition coefficients. The obtained values of the distinct eruption units are very similar and comparable to published data for silicic volcanic systems. This suggests that zircon/melt partition coefficients in calc-alkaline dacitic to rhyolitic systems are not significantly influenced by the melt composition at &amp;gt;70 wt% SiO2at near solidus temperature. The partition coefficients and zircon trace element data were used to calculate the equilibrium melt composition, which characterizes the eruption products even where glass is thoroughly altered or missing. Hence, our results provide important proxies for tephrostratigraphy in addition to yielding insights into the complex processes of silicic magma reservoirs.

Multi-class financial distress prediction based on support vector machines integrated with the decomposition and fusion methods

Binary financial distress prediction (FDP), which categorizes corporate financial status into the two classes of distress and nondistress, cannot provide enough support for effective financial risk management. This paper focuses on research on multiclass FDP based on the support vector machine (SVM) integrated with the decomposition and fusion methods. Corporate financial status is subdivided into four states: financial soundness, financial pseudosoundness, moderate financial distress and serious financial distress. Three multiclass FDP models are built by integrating the SVM with three decomposition and fusion methods, i.e., one-versus-one (OVO), one-versus-rest (OVR), and error-correcting output coding (ECOC), and they are, respectively called OVO-SVM, OVR-SVM and ECOC-SVM. Empirical research based on data from Chinese listed companies shows that OVO-SVM overall outperforms OVR-SVM and ECOC-SVM and is preferred for multiclass FDP. In addition, all three models trained on the original highly class-imbalanced training dataset cannot obtain satisfying performance, and the data level preprocessing mechanisms that make class distributions balanced in the training dataset can greatly improve their multiclass FDP performance. Compared with multivariate discriminant analysis (MDA) and multinomial logit (MNLogit), OVO-SVM has significantly higher accuracy for financial pseudosoundness and moderate financial distress and lower accuracy for financial soundness and serious financial distress, resulting in no significant difference among their overall multiclass FDP performance. However, OVO-SVM is still more competitive than MDA and MNLogit in that financial pseudosoundness and moderate financial distress are much more difficult to predict by human expertise than the other two financial states.

ATR-FTIR spectroscopy based differentiation of typhoid and dengue fever in infected human sera

In this study, we have evaluated the potential of attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy to differentially diagnose bimolecular markers in Salmonella typhi and dengue infected freeze-dried sera samples along with healthy freeze-dried sera samples. Spectral signatures were recorded from 18 S. typhi infected, 23 dengue infected and 28 healthy freeze-dried sera samples. In order to achieve enhanced classification accuracy between the three sample classes, multivariate data classification algorithms principal component analysis (PCA) and linear discriminant analysis (LDA) were used. Outcomes of the PCA scatter plot showed 95% inter-class variation. A classification accuracy of 100% was achieved using LDA; therefore, we propose that ATR-FTIR coupled with chemo metric data classification algorithms holds substantial potential for bimolecular differentiation between S. typhi and dengue infected freeze-dried sera samples.

Discriminant analysis of mine water inrush sources with multi-aquifer based on multivariate statistical analysis

Accurate and effective identification of the source mine water inrush water is vital for warning system implementation and post-disaster rescue decision-making and is crucial for mine water disaster prevention plans. To fully excavate the hydrogeological information carried by the water samples of different water sources, and fully consider the influence of the correlation between the ions and the existence of multi-collinearity on the discrimination results, so as to improve the accuracy of the inrush water source discrimination, this study conducted multivariate statistical analysis and discriminant analysis on 37 water samples of three types of water sources in Xutuan coal mine, and established the Fisher discriminant model for mine water inrush sources based on fuzzy cluster analysis and factor analysis. The discriminant accuracy of the model was tested using re-substitution and cross-validation, and compared with the discriminant result of traditional Fisher discriminant model. The results showed that the discriminant accuracies of the re-substitution and cross-validation were 91.9% and 89.2%, respectively, while the discrimination accuracy of cross-validation of the traditional Fisher discrimination model was 86.5%. The discrimination accuracy of this model was higher than that of the traditional Fisher discrimination model. Therefore, the Fisher discriminant model for mine water inrush sources based on fuzzy cluster analysis and factor analysis established in this study can improve the accuracy of a water source discrimination model, and can provide a useful reference for mine water disaster prevention.

Binary classification on compositional data

Due to boundedness and sum constraint, compositional data are often transformed by logratio transformation and their transformed data are put into traditional binary classification or discriminant analysis. However, it may be problematic to directly apply traditional multivariate approaches to the transformed data because class distributions are not Gaussian and Bayes decision boundary are not polynomial on the transformed space. In this study, we propose to use flexible classification approaches to transformed data for compositional data classification. Empirical studies using synthetic and real examples demonstrate that flexible approaches outperform traditional multivariate classification or discriminant analysis.

Palaeoenvironmental reconstruction and oolitic ironstone mapping of the Agbaja Ironstone Formation in the Nupe Basin, North-central Nigeria: Insights from sedimentological and aeromagnetic analyses

This study focusses on the sedimentological and aeromagnetic characteristics within the Agbaja Ironstone Formation to establish the sedimentary depositional history and map oolitic ironstone zones in the Lokoja district of the Nupe Basin. Forty sandstone samples were collected for granulometric, sedimentary facies and petrographic analyses to reconstruct depositional processes of the Agbaja Ironstone Formation. Aeromagnetic data analysis was engaged to map the oolitic ironstone rich zones. The iron-rich sandstones in the Agbaja Ironstone Formation occur as oolitic ironstone, ironstone concretion and laterites. The bivariate grain size plots and multivariate discriminant analyses suggest that 92% of the sandstone in the formation were deposited in beach and coastal dunes under fluvial-river actions, while 8% are of the marine environment deposited under wave actions. The quartz-feldspar lithic (QFL) ternary diagram and palaeocurrent analyses of the samples revealed that the matured, sub-arkosic sandstones originated from the cratonic interior (Abakaliki uplifts). The bioturbation and reactivation by Ophiomorpha burrows and herringbone on the fine-medium grained sandstones in the formation contributed to the observed high magnetic intensity values. High magnetic signatures (−94.784 to 1.191 nT), analytic signal peaks and depth levels from the 2-D source parameter images are the basis for the produced oolitic ironstones prospectivity map in this study.

Financial Distress Prediction Models in Property Sector Companies Listed in Indonesia Stock Exchange

Along with the unstable national and global economic conditions, investors and consumers defend themselves to invest in the property sector. Companies go public in obtaining capital markets as a means to obtain sources of funds. Investors and creditors will see the financial condition required before the company will increase financial distress (financial distress) or not before investing their capital. Therefore, analysis and prediction of a company's financial problems is very important. This study uses the Financial Distress model by using discriminant analysis. The independent variables used are financial ratios which are divided into 4 categories (1) Liquidity Ratios, (2) Solvency Ratios, (3) Activity Ratios, (4) Profitability Ratios. This research uses quantitative with the Multivariate Discriminant Analysis (MDA) model. The sample data used in this study includes property, real estate, and construction sector companies listed on the Indonesia Stock Exchange in the 2014-2018 period. This study produces a financial distress model Z-score = -3,569 + 6,910DTA -1.107DTE + 7,515ROE + 3,573OPM with a cut-off value of -3,521. When the z-score of the company -3,521, the company is included in the non-financial pressure group.

Failure prediction models: development and comparison between the multivariate discriminant analysis and the support vector machine for Tunisian companies

In this study, we try to develop a model that would predict corporate default using a multivariate discriminant analysis (MDA) and a support vector machine (SVM). The two models are applied on the Tunisian context. Our sample consists of 212 companies operating in different industries, of which 106 are 'performing' companies and 106 are 'failing' companies, observed over the 2005-2010 period. The results of the use of a battery of 87 ratios showed that 16 ratios can build the model and that liquidity and solvency have more weight than profitability and management in predicting distress. Despite the slight superiority of the results provided by the SVM model, on the control sample, the results provided by the two models are good either in terms of correct classification percentage or in terms of the stability of discriminating power over time and space.

Failure prediction models: development and comparison between the multivariate discriminant analysis and the support vector machine for Tunisian companies

In this study, we try to develop a model that would predict corporate default using a multivariate discriminant analysis (MDA) and a support vector machine (SVM). The two models are applied on the Tunisian context. Our sample consists of 212 companies operating in different industries, of which 106 are 'performing' companies and 106 are 'failing' companies, observed over the 2005-2010 period. The results of the use of a battery of 87 ratios showed that 16 ratios can build the model and that liquidity and solvency have more weight than profitability and management in predicting distress. Despite the slight superiority of the results provided by the SVM model, on the control sample, the results provided by the two models are good either in terms of correct classification percentage or in terms of the stability of discriminating power over time and space.

Development of a predictive model for benthic macroinvertebrates by using environmental variables for the biological assessment of Korean streams

Predictive models for benthic macroinvertebrates based on changes in environmental variables can assess the biological integrity of streams by comparing observed biotic communities with those expected at reference sites. To develop a predictive model of the abiotic community, we used benthic macroinvertebrates and environmental variables collected from 2,700 sites from 2010 to 2019. First, we selected 357 reference sites by using the 5-day biochemical oxygen demand, ammonia nitrogen, total phosphorus, turbidity, and coarse particle percentage. Then, we used Two-Way Indicator Species Analysis to classify the reference sites into six groups based on benthic macroinvertebrates. Reference sites classified by biological characteristics were linked to environmental variables by multi-discriminant analysis. The relative influences environmental variables on the classified groups were in decreasing order of catchment area, latitude, velocity, water depth, altitude, and longitude. To develop the predictive model, we combined (1) identification level, (2) grouping method, and (3) probability of capture, and then used the normalized root mean square error (NRMSE) to check the fit of each model. The higher the probability of capture was at the family level compared to the species level, the lower was the NRMSE. The grouping method was not as consistent as the identification level and probability of capture because the NRMSE for the number of taxa was low when used as a weighted average. The NRMSE was also low for the Benthic Macroinvertebrates Index and the Benthic Macroinvertebrates Family-level Biotic Index (BMFI) when used for assignment to the group with the highest probability. We selected the predictive model which used family level, weighted average, and BMFI-proposed indicator taxa as the final assessment model due to its sensitivity and fit. This model was the most reasonable choice, but we had to reduce the error of the model and revise it elaborately by securing additional environmental variables.

Method to appraise financial and productivity indicators in small and medium enterprises in the tourist lodging sector of Cartagena-Colombia applying discriminant multivariate analysis

This research article presents the results of the appraising of the financial and productivity indicators of the small and medium enterprises of the tourist lodging sector in the City of Cartagena-Colombia. The multivariate discriminant data analysis (MDA) technique was used to determine the significance and classification of the groups of selected variables within the group of 75 SMEs that reported their financial statements at the Cartagena Chamber of Commerce for the years 2015 and 2018. The findings found contrast with the sustained good performance for the analysis period of the financial indicators, gross margin (IF1), operating margin (IF2) and net margin (IF3) and productivity, operating profit ratio and added value (IP2), added value ratio and working capital (IP4) and operating profit ratio and working capital (IP5). This is evidenced by the marking out and contribution of the tourist lodging sector in the business economic dynamics of the City of Cartagena.

A MATHEMATICAL MODEL FOR PREDICTING THE OUTCOME OF TREATMENT OF MULTIDRUD-RESISTANT TUBERCULOSIS

The aim: Predicting the effectiveness of treatment for MRI of the lungs by developing a mathematical model to predict treatment outcomes. Materials and methods: 84 patients with MRI of the lungs: group 1 (n = 56) – with signs of effective TB treatment at the end of the intensive phase; group 2 (n = 28) – patients with signs of ineffective treatment. We used the multivariate discriminant analysis method using the statistical environment STATISTICA 13. Results: During the discriminant analysis, the parameters of the clinical blood analysis (monocytes, stab leukocytes, erythrocytes) were selected, which were associated with high (r&gt; 0.5) statistically significant correlations with the levels of MMP-9, TIMP-1, oxyproline and its fractions and aldosterone in the formation of the prognosis. The mathematical model allows, in the form of comparing the results of solving two linear equations and comparing their results, to predict the outcome of treatment: “1” effective treatment, “2” – ineffective treatment. Early prediction of treatment effectiveness is promising, as it allows the use of the developed mathematical model as an additional criterion for the selection of patients for whom surgical treatment is recommended, in order to increase the effectiveness of treatment. Conclusions: An additional criterion for predicting ineffective MRI treatment, along with the criteria provided for by WHO recommendations, is a mathematical model that takes into account probably strong correlation (r = 0.5, p &lt;0.05) between the factors of connective tissue destruction, collagen destruction, aldosterone , and indicators of a clinical blood test (between levels of OBZ and monocytes (r = 0.82, p = 0.00001), OB and monocytes (r = 0.92, p = 0.000001) OB and stab leukocytes (r = – 0.87, p = 0.0003) OBZ and stab leukocytes (r = – 0.53, p = 0.017), aldosterone and ESR.