Different Routes or Methods of Application for Dimensionality Reduction in Multicenter Studies Databases

  Citation: Boukichou-Abdelkader, N.; Montero-Alonso, M.Á.; Muñoz-García, A. Different Routes or Methods of Application for Dimensionality Reduction in Multicenter Studies Databases. Mathematics 2022,10, 696. https://doi.org/10.3390/ math10050696 Academic Editor: Basil Papadopoulos Received: 11 January 2022 Accepted: 21 February 2022 Published: 23 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). mathematics Article Different Routes or Methods of Application for Dimensionality Reduction in Multicenter Studies Databases Nisa Boukichou-Abdelkader 1,2 , Miguel Ángel Montero-Alonso 3,* and Alberto Muñoz-García4 1 School of Doctorate in Sciences, Technologies and Engineering, University of Granada, 18012 Granada, Spain; [email protected].es 2Data Science Unit, Health Innovation of La Rioja, Rioja Health Foundation, CIBIR, 26006 Logroño, Spain 3Department of Statistic and Operational Research, University of Granada, 18016 Granada, Spain 4Department of Statistic, University Carlos III of Madrid, 28903 Madrid, Spain; [email protected] *Correspondence: [email protected]; Tel.: +34-958-24-87-11 Abstract: Technological progress and digital transformation, which began with Big Data and Artificial Intelligence (AI), are currently transforming ways of working in all fields, to support decision-making, particularly in multicenter research. This study analyzed a sample of 5178 hospital patients, suffering from exacerbation of chronic obstructive pulmonary disease (eCOPD). Because of differences in disease stages and progression, the clinical pathologies and characteristics of the patients were extremely diverse. Our objective was thus to reduce dimensionality by projecting the data onto a lower dimensional subspace. The results obtained show that principal component analysis (PCA) is the most effective linear technique for dimensionality reduction. Four patient profile groups are generated with similar affinity and characteristics. In conclusion, dimensionality reduction is found to be an effective technique that permits the visualization of early indications of clinical patterns with similar characteristics. This is valuable since the development of other pathologies (chronic diseases) over any given time period influences clinical parameters. If healthcare professionals can have access to such information beforehand, this can significantly improve the quality of patient care, since this type of study is based on a multitude of data-variables that can be used to evaluate and monitor the clinical status of the patient. Keywords: PCA; MICE; RF&IV; simulation; eCOPD MSC: 65C20; 65C60; 68W40 1. Introduction In recent years, technological progress and digital transformation, which began with Big Data and Artificial Intelligence (AI), have transformed society. In a parallel way, the current COVID-19 pandemic has had a devastating effect on the world population at all socioeconomic levels and has significantly impacted healthcare and biomedical research. This has led institutions to explore possible synergies between the fields of computational statistics and healthcare with a view to analyze the large quantity of data in medical records. The information in these databases could be effectively used to support decision-making and thus improve the quality of patient care [1]. In this sense, computational statistics, a field currently in exponential growth, has developed new statistical analysis tools and algorithms in an effort to deal with new needs in all knowledge areas, but particularly in biomedicine [ 2 ]. However, innovative technological methods that work with large data repositories have created new problems, such as those related to dimensionality and missing data [ 3 , 4 ]. More specifically, this study highlights the need to explore more effective ways of improving data searches in clinical profiles. Mathematics 2022,10, 696. https://doi.org/10.3390/math10050696 https://www.mdpi.com/journal/mathematics Mathematics 2022,10, 696 2 of 14 Missing data are a common problem in most research fields since they introduce an element of ambiguity in data analyses. This ambiguity may occur for different reasons such as sample mishandling, measurement errors, dropped outliers, or simply a lack of analysis. It is well known that in healthcare, missing data [ 5 ] can significantly reduce the size of the sample if the analysis only considers complete cases. When missing data are ignored, this can result in biased parameter estimations. For this reason, multiple imputation by chained equations (MICE) has emerged as the leading strategy to replace missing epidemiological data because of its simplicity and capacity to maintain unbiased effect estimates and valid inferences. According to the literature on the topic, non-parametric tree-based imputation methods outperform parametric methods in terms of bias and coverage when there are interactions or other nonlinear effects between variables. However, these studies do not provide a fair comparison, since they do not follow the generally accepted recommendation that any effect on the final analysis model (including interactions) should be included in the parametric imputation model. In fact, simulation has been used to show that the incorporation of interactions in the parametric imputation model leads to a much better performance. This analysis used two different MICE techniques. The first technique was the sample method that performs a simple random sample, based on the observed values, and returns them as imputations under the assumption that the data are missing at random (MAR). The second technique is predictive mean matching (PMM), which reduces the bias in a dataset by drawing real values sampled from the data and building a small subset of observations where the outcome variable matches the outcome of the observations with missing values. In this sense, data applications in the context of functional data analysis (FDA) are of particular importance since they provide a new access route for similar situations in multicenter studies [6,7]. This study addresses the problem of dimensionality by contrasting results obtained with different dimensionality reduction techniques. These include the principal components analysis (PCA) [ 8 ] and the random forest (RF) [ 9 ] by the Gini index and information value by weight of evidence (WOE) (RF&IV), [ 10 , 11 ]. It also used parallel analysis with simulated data and data resampling (PA-RES) for optimal factor-variable selection and the reduction of the analysis space in order to generate new profile groups with similar characteristics [ 12 ]. 2. Materials and Methods In order to deal with dimensionality and missing data and thus obtain optimal patient profile grouping, clinical practice guidelines currently place great emphasis on improving existing healthcare models. The objective is to coherently classify patients, based on an accurate diagnosis and effective clinical and healthcare management. Evidently, the evolution of comorbidities in these patients is an important healthcare challenge that depends on a wide range of factors, such as strict adherence to prescribed treatments, healthy lifestyle habits, and the ability to recognize the signs and symptoms of COPD exacerbation with a view their prevention and/or treatment by means of a self-management plan. In this context, we selected 32 epidemiological, clinical, and outcome variables to optimize dimensional reduction and obtain a coherent classification of patients. At the same time, our study also focused on the search for clinical profiles with a set of characteristics linked to the development of a chronic disease. This points the way to a new access route for dealing with similar situations in multicenter studies. To best achieve our objectives, multivariate imputation was used to solve the problem of missing data. The MICE method [ 13 ] was thus implemented along with other techniques, such as the sample method and predictive mean matching [ 14 ], which perform well with the clinical data and reduce the bias in the feature selection process. In this sense, missing values are the first obstacle to modeling when there is 5–20% or more data loss. This problem can be solved with the use of imputation techniques. In fact, the choice of technique greatly influences the predictive capacity of the model. In most statistical analysis methods, listwise deletion is the default method used to impute missing Mathematics 2022,10, 696 3 of 14 data. Nevertheless, it does not always perform well since it tends to lead to information loss, and sometimes these data are necessary since they make other less relevant factor variables meaningful for the analysis. Some software packages work better with continuous variables and others with categorical ones. It is thus a question of selecting the method best suited to the research data and objectives. In this case, the package chosen was Multiple Imputation by Chained Equations (MICE) because it is one of the most widely used in R and also because it creates multiple imputations. The use of multiple imputations helps to reduce bias and has the advantage of increasing efficiency in comparison to a single imputation (e.g., the mean) that deals with uncertainty in missing data. In addition, one of the most important characteristics of MICE is that it assumes that missing data are missing at random (MAR). This means that the probability of a missing value only depends on observed values and can be predicted by using them. For these particular data, we assume that the missing data are missing at random (MAR) because the missing value is related to some of the observed data of these measured variables, which was not completed due to lack of clinical follow-up. In addition, the observed and missing data are visualized to see if they present any type of specific behavior. The missing value shows a general pattern with scattered missing data randomly throughout the data matrix, and that may be conditioned by the observations of other variables of the data set different from the main one, so they can be estimated from these observations. Therefore, we assume that the missing data are MAR. Furthermore, one of the advantages of MICE is that it imputes data on a variable-byvariable basis by specifying one imputation model per variable. It is also able to handle different types of variables and can manage the imputation of variables defined on a subset of the data. However, depending on the type of variable, there are also other methods that can be used for the imputation of missing data [ 15 ]. These include Amelia [ 16 ], missForest [ 17 , 18 ], Hmisc [ 19 ], and mi [ 20 ]. Despite the advantages of the previously described methods, MICE was still regarded as the best choice for our study because it is a very versatile and adaptable technique for all types of clinical variables. It imputes data on a variable-by-variable basis and then combines the results to reduce the uncertainty in the missing values. It goes without saying that handling missing values is a crucial step in data preprocessing with machine learning. It is a fact that most of the algorithms used for data in the feature selection process and the classification or estimation process only analyze complete datasets. For this reason, in many cases, the strategy used for missing values [ 21 ] only consists of analyzing instances with complete data or of replacing missing values with a mean, mode, median, or a constant value. Generally speaking, discarding missing samples or replacing missing values often causes biases in subsequent analyses of the data sets. For this reason, the decision was taken to apply multivariate imputation using MICE. Similarly, different multivariate techniques were applied by means of principal components analysis (PCA) to reduce dimensionality. RF&IV defined the selection of variable importance with random forest methods [ 22 , 23 ] by the Gini index and information value by weight of evidence (WOE). The objective was to contrast and, when possible, further reduce the dimensional space of the data-variables. Also applied was parallel analysis with simulated data and data resampling (PA-RES) based on the random correlation matrix. These techniques help to reduce the selection of variable importance by simplifying the analysis space and only saving and considering relevant and accurate information. Our aim was to thus provide a better clinical solution that is a true reflection of the actual population, and at the same time, generate patient profile groups with identical affinities. Our study shows that this method was able to effectively deal with the reduction of dimensional space. After these analytical phases, the objective was to improve the performance capacity of the high dimensional clinical database by optimally extracting the results and specifically focusing on the problem of dimensionality reduction. It was also a question of Mathematics 2022,10, 696 4 of 14 dealing with the problem of missing values in order to properly classify patients based on shared characteristics. In this sense, the calculations were performed with the statistical software R [ 24 ]. All hypothesis contrasts had a p-value of 0.05. The procedure was carried out in various steps. Firstly, MICE was used to impute the missing values. Secondly, different techniques were applied to reduce the dimensional space of the set of data-variables. Of the different methods tested (i.e., PCA, RF&IV, and PA-RES), PCA was found to yield the best results. The final step was the description of the preliminary classification of the profile groups. Their shared characteristics highlight the clinical results obtained by means of optimal dimensional reduction. The source of information for this study was the original database of the AUDIPOC Study [ 25 ]. The descriptive–exploratory analysis (Table 1) of the 5178 patients admitted for exacerbation of chronic obstructive pulmonary disease (eCOPD) showed that (i) 87% were men and 13% women (with a mean age 73 years); (ii) 83% were smokers; and (iii) only 68% had spirometry performed on admission or discharge. All of the patients presented diverse characteristics and clinical pathologies, depending on the severity and progression of the primary disease. More specifically, 35% of the patients had an average hospital stay of 10 days; 11% required ventilation support; and 28% were readmitted for exacerbation of COPD. Of these patients, almost all of them (27%) were readmitted after 90 days with a 5% rate of positive exitus. Table 1. DESCRIPTIVE. Summary of epidemiological–clinical results. Variables Mean SD Variables n(%) (No/Yes) AGE 73.39 10.08 SEX (Male/Female) 4526 (87.4) 652 (12.6) DUR_ADM 9.96 7.82 SMOKING_HABIT 906 (17.5) 4272 (82.5) HEIGHT 1.64 0.08 SPIROMETRY_PA 1644 (31.8) 3534 (68.2) WKG 74.85 15.55 ADM 3343 (64.6) 1835 (35.4) BMI 27.88 6.03 VS 4596 (88.8) 582 (11.2) SBP 136.4 23.85 EXACER_90DAYS 3793 (73.2) 1385 (26.8) DBP 75.04 13.84 ReADM_EXACER 3751 (72.4) 1427 (27.6) TEMP 36.78 0.82 DEATH_90DAYS 4873 (94.1) 305 (5.90) RR 24.26 6.62 EXITUS 4919 (95.0) 259 (5.00) HR 94.44 18.50 CHF 4058 (78.4) 1120 (21.6) FEV1P 45.02 16.82 CCVSDM 2961 (57.2) 2217 (42.8) FVCP 64.88 19.21 DM 3844 (74.2) 1334 (25.8) FEVFVC 72.67 28.48 VD 3588 (69.3) 1590 (30.7) CVD 4620 (89.2) 558 (10.8) PVD 4422 (85.4) 756 (14.6) MI 4505 (87.0) 673 (13.0) NEPH 4691 (90.6) 487 (9.40) ST 4506 (87.0) 672 (13.0) ME 3828 (73.9) 1350 (26.1) 3. Results The statistical software R [ 24 ] (version 4.1.0) is used to perform the analysis because it is able to compensate aspects of the imputation of missing values [ 26 ] in certain variables of the dataset. This is achieved with various methods in the MICE package [ 27 ] (sample and predictive mean matching), with a view to completing and improving the final results. Similarly, R provides the platform for the application of the different multivariate analysis techniques using PCA, RF&IV, and PA-RES in order to reduce and optimize the dimensional space of the dataset. Figure 1shows the status of the missing values in the database after an imputation process is performed on certain variables of this dataset, using the MICE package [ 28 ] to complete the information and optimize the final results. Mathematics 2022,10, 696 5 of 14 Figure 1. MICE. Dataset situation with > 5–20% of missing data before imputation. Original Dataset. Variables sorted by number of missings: Variable Count HEIGHT 0.6237930 WKG 0.6210892 RR 0.5264581 FVCP 0.4103901 FEV1P 0.3810351 HR 0.1568173 TEMP 0.1465817 SBP 0.1145230 DBP 0.1145230 The outputs confirm that the same original results are obtained with both procedures and that existing information is not affected. The satisfactory solution of the problem is followed by new exploratory analyses. The imputation ultimately obtained a more complete, accurate and real dataset for the application of multivariate techniques. Proof of this is the graphical display in Figure 2, where, in each variable, the percentage is zero in the pattern of missing data. This is reflected in the coincidence in the scatterplot, where information is free of missing values and identical to the original. This signifies that it is possible to extrapolate these results to the general population. Based on the results of the imputation procedures (Figure 1), the success of the pre-post application results is assured with 100% of the completed data (Figure 2) related to the epidemiological–clinical variables (Table 1). Slightly altered average results pertain to height, 1.64 m; weight in kilograms (WKG), 74.85 kg; and body mass index (BMI), 27.88 kg/m2. Systolic blood pressure (SBP), 136.4 mmHg, is above the normal range of 90–120 mmHg , which indicated a possible risk of CVD. However, diastolic blood pressure (DBP), 75.04 mmHg , is within the normal range (60–80 mmHg), as is temperature (TEMP), 36.78 ◦ C. Respiratory rate (RR), 24.26 resp./min, is outside the normal range with 12–18 breaths per minute, though heart rate (HR), 94.44 beats/min, is within the normal range (60–100 beats per minute). In regard to spirometry, FEV1 spirometry in % of theoretical (FEV1P), 45.02%, showed severe alteration since the forced expiratory volume in the first second in normal conditions is around 80%; FVC spirometry in % of theoretical (FVCP), 64.88%, reflected severe symp- Mathematics 2022,10, 696 6 of 14 toms since the forced vital capacity % is considered normal when it is greater than 70% though the percentage varies with age. The previous FEV1/FVC ratio or high spirometry (FEVFVC), 72.67%, indicates the presence of an undefined alteration in terms of obstruction when the reference range is between 70–85%. Figure 2. MICE. Dataset situation with > 5–20% of missing data after imputation. Modified dataset. Similarly, the percentage detected in each of the pathologies associated with the development of the main disease are the following: congestive heart failure (CHF), 22%; cardiovascular comorbidity (CCVSDM), 43%; diabetes mellitus (DM), 26%; vascular disease (VD), 31%; cerebrovascular disease (CVD), 11%; peripheral vascular disease (PVD), 15%; myocardial infarction (MI), 13%; nephropathy (NEPH), 9%; solid tumor (ST), 13%; and malleolar edema (ME), 26%. In addition, the single presence of COPD is 32%, since the vast majority of patients (68%) are also suffering from other pathologies, which, depending on the progression and severity of the main disease, often coexisted with COPD. The following sections describe the three procedures applied as well as the results obtained with each. This evaluation highlighted which is the best technique and its advantages for this type of analysis [29]. 3.1. Principal Components Analysis The choice of the principal components analysis (PCA) [ 30 ] is motivated by the fact that the inertia of the first dimensions is an indicator of the possible existence of strong relationships between variables, as well as of the number of dimensions to be studied. In addition, the PCA method is designed to work with numerical variables, so we convert the binary or dichotomous categorical variables to numeric. There is the analogous procedure for categorical variables, which is multiple correspondence analysis (MCA), which we will use in the extension of these analyzes to obtain better results. Moreover, the first two dimensions express 19.24% (Table 2) of the total inertia of the dataset. This means that the cloud total variability of the individuals (or variables) is explained by the 1:2 plane. Obviously, this is a very low percentage, and the first plane represents only a small portion of the data variability. Nevertheless, this value is larger than the reference value (7.19%), which is equivalent to the 0.95 quartile of the distribution of inertia percentages obtained by simulating 501 data tables of equivalent size, based on a normal distribution. For this reason, the variability explained by this plane is significant. For even better results, dimensions greater than or equal to the third can also be interpreted for the sake of completeness. Mathematics 2022,10, 696 7 of 14 Table 2. Dimensional reduction with PCA—Eigenvalues. Eigenvalues Dim.1 . . . . . . . . . . . . . . . . . . . . . Dim.32 Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7 Dim.8 Dim.9 Variance 3.246 2.911 1.981 1.744 1.601 1.472 1.387 1.281 1.235 % of var. 10.143 9.098 6.191 5.451 5.004 4.600 4.336 4.002 3.860 Cumulative% of var. 10.413 19.241 25.432 30.883 35.887 40.487 44.823 48.825 52.685 Dim.10 Dim.11 Dim.12 Dim.13 Dim.14 Dim.15 Dim.16 Dim.17 Dim.18 Variance 1.144 1.097 1.041 0.982 0.964 0.950 0.920 0.910 0.874 % of var. 3.574 3.427 3.254 3.069 3.012 2.970 2.867 2.843 2.731 Cumulative% of var. 56.259 59.687 62.941 66.010 69.022 71.992 74.868 77.711 80.442 Dim.19 Dim.20 Dim.21 Dim.22 Dim.23 Dim.24 Dim.25 Dim.26 Dim.27 Variance 0.846 0.830 0.806 0.793 0.734 0.720 0.597 0.407 0.218 % of var. 2.465 2.593 2.519 2.478 2.294 2.250 1.684 1.272 0.682 Cumulative% of var. 83.087 85.680 88.199 90.677 92.971 95.221 97.085 98.357 99.039 Dim.28 Dim.29 Dim.30 Dim.31 Dim.32 Variance 0.183 0.058 0.043 0.020 0.004 % of var. 0.571 0.183 0.133 0.061 0.013 Cumulative% of var. 99.610 99.792 99.925 99.987 100.000 Consequently, the results of the analysis show that the estimation of the number of axes worth interpreting meant restricting the description to the first 12, which are the most informative. In fact, they present an amount of inertia (62.94%) that is greater than those obtained by the 0.95 quartile of random distributions (40.78%). Since these axes are the only ones carrying real information, the relevant description is thus located in them, primarily in the first two, which are the ones that most contributed to the total inertia (Figure 3). Figure 3. Decomposition of the total inertia in percentage of the explained variance. 3.2. Parallel Analysis Similarly, a second verification of existing data is performed by applying parallel analysis (Figure 4) with simulated and resampled data [ 31 ] (PA-RES). The function (fa.parallel) is used to optimally confirm the number of final components. This analysis is an alternative technique that compares the data display with that of a random data matrix (or random correlation matrix) that is of the same size as the original. The function plots the eigenvalues for a principal component and factor solution and does the same for random matrices of the same size as the original data matrix. Furthermore, for raw data, the random matrices have two functionalities: (i) a matrix of univariate normal data and (ii) random samples (randomized across rows) of the original data [32]. In short, in view of the results obtained, this analysis also suggests that 12 components should be studied, which confirms the same number of components as the PCA analysis. Mathematics 2022,10, 696 8 of 14 Figure 4. Parallel analysis with simulated and resampled data. 3.3. Analysis with Random Forest and Information Value To further optimize the number of components, a third verification (Table 3) is performed with random forest, [ 33 ] by Gini index and information value by weight of evidence (WOE) [ 34 , 35 ] to ascertain whether it is possible to effectively reduce dimensional space by calculating the importance of variables, based on the data-variables explored. Table 3. Application of the RF&IV method (Gini index and WOE). VARIABLE IMP_RF IMP_IV RANKING_RF RANKING_IV RANKING_TOT 1 WKG 224.86344 0.0244 3 5 8 2 FEV1P 206.09781 0.0487 6 3 9 3 AGE 171.82978 0.2186 10 2 12 4 ReADM_EXACER 242.19560 0.0000 1 12 13 5 FVCP 192.07075 0.0310 9 4 13 6 HEIGHT 158.79108 0.2265 13 1 14 7 ADM 196.81619 0.0000 7 9 16 8 CCVSDM 209.72344 0.0000 5 16 21 9 EXACER_90DAYS 164.83231 0.0000 12 11 23 10 DUR_ADM 140.31719 0.0000 16 7 23 11 VD 194.26879 0.0000 8 18 26 12 SMOKING_HABIT 36.84869 0.0000 25 6 31 13 SPIROMETRY_PA 39.30613 0.0000 24 8 32 14 FEVFVC 233.34052 0.0000 2 31 33 15 BMI 212.88434 0.0000 4 30 34 16 CHF 87.92548 0.0000 20 15 35 17 SBP 166.60532 0.0000 11 25 36 18 PVD 90.87474 0.0000 19 20 39 19 VS 23.62432 0.0000 30 10 40 20 DBP 157.85915 0.0000 15 26 41 21 CVD 78.67005 0.0000 22 19 41 22 MI 85.35488 0.0000 21 21 42 23 HR 158.19131 0.0000 14 29 43 24 DM 36.56857 0.0000 26 17 43 25 TEMP 129.89077 0.0000 17 27 44 26 DEATH_90DAYS 22.99425 0.0000 31 13 44 27 RR 128.07834 0.0000 18 28 46 28 EXITUS 22.95276 0.0000 32 14 46 29 ME 39.31523 0.0000 23 24 47 30 NEPH 25.97349 0.0000 28 22 50 31 ST 23.82815 0.0000 29 23 52 Mathematics 2022,10, 696 9 of 14 Based on the outputs, the conclusion coincided with that of the PCA analysis. Variables could be reduced to 11 or 12, as reflected in RF (Gini Index). This method for the selection of the importance of final variables is the most widely used and least restrictive because it is a random process. Each time it is executed, it can show different output variables. In contrast, another more demanding reduction (only five variables) is that carried out with IV (WOE). This method significantly restricts final selection because it involves a measure that determines the predictive power of a certain characteristic. Nevertheless, it should not be applied in cases such as ours, in which the results would suffer from the loss of relevant information contained in the main variables of the dataset and where there is prior knowledge that these data are vital to clinical patient profiles. In this sense, the best solution is provided by the PCA analysis with 12 principal components. Figure 5shows a detailed visualization of the results described by the 1:2 plane on the two most relevant axes. As previously mentioned, these are the axes that can provide the most significant data in the specification of patient profile groups and which can be extended to other more specific classification methods for pattern grouping. Figure 5. Description of the 1:2 plane (variables vs. patients). Given these results, Dimension 1 shows individuals characterized by a strongly positive coordinate on the axis (to the right of the graph) versus a negative one (to the left of the graph): • Group 1 shows high values for the following variables ordered from strongest to weakest: CCVSDM, EXACER_90DAYS, ReADM_EXACER, ADM, VD, CHF, PVD, MI, DEATH_90DAYS, and CVD; and low values for these other variables: SEX, FVCP, DBP, TEMP, HR, and SMOKING_HABIT. • Group 2 has high values for the following variables: VD, CCVSDM, PVD, MI, CHF, CVD, AGE,DM, NEPH andFEVFVC;incontrast, low valuesfortheseothers: EXACER_90DAYS, ReADM_EXACER, ADM, SPIROMETRY_PA, EXITUS, SMOKING_HABIT, HR, DBP, DEATH_90DAYS, and SBP. • Group 3 shows high values for the following variables listed by strength: DBP, SMOKING_HABIT, FVCP, SEX, SPIROMETRY_PA, HR, EXITUS, SBP, and TEMP. It shows low values for these others listed by weakness: EXACER_90DAYS, ReADM_EXACER, ADM, CCVSDM, VD, CHF, PVD, AGE, ME, and DM. •Group 4 shows high values for the following variables: EXACER_90DAYS, ReADM_EXACER , ADM, HR, VS, SPIROMETRY_PA, DEATH_90DAYS, EXITUS, ST, and DUR_ADM; and low values in these others: CCVSDM, VD, CHF, PVD, MI, CVD, FEV1P, NEPH, FEVFVC, and DM.