Predictive classification and regression models for bioimpedance vector analysis: Insights from a southern Cuban cohort

A descriptive, retrospective, randomized study was conducted on patients who visited the “Conrado Benítez” Teaching Oncology Hospital in Santiago de Cuba for suspected cancer during the periods of March–April and July–August 2002. The hospital was chosen for its suitable facilities and accommodations, despite participants hailing from various locations across eastern Cuba. The study comprised 367 subjects (235 females and 132 males) aged 18 to 86 years. Among them, 61 were diagnosed with different types of cancer pathologically, while 306 were healthy. Participants were recruited following strict ethical guidelines and medical practices as outlined by the Health General Law of the Ministry of Public Health of the Republic of Cuba (Number 41, July 13, 1983, updated in 2010).

Following the Helsinki Declaration, the research was approved by the ethics committees and scientific councils of the Oncological Hospital “Conrado Benítez.” Additionally, data on bioelectrical parameters of cancer patients and healthy individuals were retrieved from a database archived at the National Center for Applied Electromagnetism (CNEA); (ISBN: 978-959-207-679-2). The diagnosis of the patients was made through pathological anatomy. The samples were taken using the fine needle aspiration cytology technique. Anatomical pathology laboratory diagnoses revealed that female patients had various types of cancer with different stages, including breast and cervical cancer, whereas male patients were diagnosed with more aggressive cancers, such as skin melanoma, colon cancer, lung neoplasm. Further details can be found in Ref [11].

Informed consent has been obtained from all individuals included in this study.

The research related to human use has been complied with all relevant national regulations, institutional policies and in accordance with the tenets of the Helsinki Declaration, and has been approved by the authors' institutional review board or equivalent committee.

Achieving balanced data is essential for successful machine learning studies [32,33,34,35,36,37,38,39,40,41]. In our study, we ensured data balance by implementing random oversampling for the minority class (cancer) and random undersampling for the majority class (healthy). The final dataset included 621 individuals, aged between 18 and 86 years (382 females and 239 males), with 316 diagnosed with cancer and 306 healthy participants. To prevent overfitting, a cross-validation technique is used, in which 95% of the data is designated for training and the remaining 5% is reserved for validation. This approach ensures that the model generalizes well to unseen data rather than memorizing patterns specific to the training set [37,38,39,40,41].

For the machine learning study, the features include: health status (cancer, healthy), sex, high frequency resistance (R_inf), characteristic frequency (f_c), Cole parameter (α), corrected resistance (r_c), capacitive reactance Xc, height, weight, age, resistance (Rc), capacitive reactance (Xcc), impedance absolute value Zc=Rc2+Xcc2 {Z_c} = \sqrt {R{c^2} + Xc{c^2}} and phase angle (θ_c) at the characteristic frequency and location variables (BIVA status, quartile and centile). For the classification models, the response are the location features and the health status, while for the regression, the bioelectrical parameters at the characteristic frequency (Rc, Xcc, θ_c and Z_c). In this sense, one can explore the role of the anthropometric and bioelectric parameters for location assignments at the tolerance ellipses, usually made by bioimpedance vector analysis.

Several metrics can be used to assess the accuracy of machine learning models [39,40,41]. Metrics for classification models are derived from the confusion matrix [39,40,41]. For classification models, the accuracy is defined as: (1) Accuracy=TP+TNTP+TN+FP+FN Accuracy = {{TP + TN} \over {TP + TN + FP + FN}} where (TP ) is true positives, (TN) is true negatives, (FP) is false positives, and (FN) is false negatives.

The precision, which indicates the amount of the predicted positive instances that are actually positive is defined as follows [39,40]: (2) Precision=TPTP+FP Precision = {{TP} \over {TP + FP}}

The recall describes how well the model captures all the positive instances [39,40]: (3) Recall=TPTP+FN Recall = {{TP} \over {TP + FN}}

F1-Score is defined as [39,40]: (4) F1−Score=2×Precision×RecallPrecision+Recall F1 - Score = 2 \times {{Precision \times Recall} \over {Precision + Recall}} which estimate the balance between Precision and Recall.

In addition, for regression models the common metrics are: the coefficient of determination (R²), mean absolute error (MAE), root mean square error (MSE) and its root mean square error (RMSE) defined by equations (5) [39,40]: (5) R2=1−∑i=1n(yi−y^i)2∑i=1n(yi−y¯i)2MAE=1n∑i=1n|yi−y^i|MSE=1n∑i=1n(yi−y^i)2RMSE=MSE \matrix{{{R^2} = 1 - {{\sum\nolimits_{i = 1}^n {{{({y_i} - {{\widehat y}_i})}^2}}} \over {\sum\nolimits_{i = 1}^n {{{({y_i} - {{\overline y}_i})}^2}}}}} \hfill \cr {{\rm{MAE}} = {1 \over n}\sum\nolimits_{i = 1}^n {\left| {{y_i} - {{\widehat y}_i}} \right|}} \hfill \cr {{\rm{MSE}} = {1 \over n}\sum\limits_{i = 1}^n {{{({y_i} - {{\widehat y}_i})}^2}}} \hfill \cr {{\rm{RMSE}} = \sqrt {MSE}} \hfill \cr} where n represents the number of elements in the database, y_i the observed value of the dependent variable, ŷ_i the predicted value of the dependent variable, and ȳ_i the mean value of the observations. When R² ≅ 1 the model tends to be perfect, analogously for MAE, MSE and RMSE values [39,40].

Bioimpedance parameters were measured using a BioScan 98^® model bioimpedance analyzer (Biológica Tecnología Médica S.L., Barcelona, Spain) with a tetrapolar whole-body configuration. Participants, who fasted for at least 3 hours, emptied their bladders, and refrained from exercise and alcohol for 12 hours prior, were included in the study. MF-BIA measurements were taken at frequencies ranging from 10 to 250 kHz using Ag/AgCl electrodes model 3M Red Dot 2560 (3M, Ontario, Canada). The study was conducted in a room maintained at 23°C with 60–65% relative humidity. Volunteers lay on a non-conductive surface without clothing or pillows, with their arms positioned 30° away from the chest and legs spread 45° apart. The injector electrodes were placed (after cleaning the skin with 70% alcohol) on the inner side of the dorsal surfaces of the hands and feet, near the metatarsophalangeal and third metacarpal joints. The detector electrodes were positioned between the distal ends of the ulna and radius at the pisiform prominence and at the midpoint between both malleoli. A 5 cm gap was maintained between detector and injector electrodes during measurements.

With the balanced database, we perform classification models to predict the location features. Table 1 collects the best model and the metrics describing the model performance and generality of each location feature. The Fine Tree model is the most effective in describing health and BIVA statuses, with accuracies of 92.80% and 99.50%, respectively. Meanwhile, the Linear Support Vector Machine and Random under-sampling Boosted Tree approach (RUSBoosted Tree) are the top models for describing quartile and centile responses, achieving accuracies of 100% and 97%, respectively.

The confusion matrices presented in Figure 1 illustrate the model's performance across various classification tasks. For health status (Figure 1a), the matrix reveals a high true positive rate (TPR) for healthy individuals, with 96.9% correctly identified and only 3.1% misclassified. The model shows excellent accuracy in distinguishing between healthy individuals and those with health issues, demonstrated by the 100% correct classification of the cancer (C) class. For BIVA status (Figure 1b), which encompasses 44 classes, most achieved 100% classification accuracy. Minor misclassifications were observed between classes 33 and 34, with a small percentage (4.5%) incorrectly classified.

Fig. 1:

Confusion matrix of trained models: a) Health status, b) BIVA status, c) quartile and d) centile responses.

The overall TPR of 99.5% highlights the model's high precision in identifying BIVA statuses correctly. The Quadrant Responses matrix (Figure 1c) displays perfect classification, achieving 100% accuracy across all four classes, indicating an exceptional ability to differentiate quadrant responses without any errors. For Centile Responses (Figure 1d), the matrix shows slightly lower but still high performance, with true classes 50%, 75%, and 95% having some minor misclassifications. Notably, class 100% is perfectly classified. The overall TPR of 95.3% demonstrates robust model performance, though there is some room for improvement in distinguishing closely related centiles. Collectively, these matrices underscore the models' effectiveness in accurately classifying various health statuses, BIVA parameters, quadrant responses, and centile categories, with high true positive rates and minimal misclassifications.

Feature importance analysis using a Pareto chart is a powerful method for identifying and visualizing the most significant predictors in a classification model [37,38,39]. By ranking features according to their importance scores and displaying them in a Pareto chart, one can easily discern the few key features that contribute most to the model's predictive power [37,38,39]. Applied to feature importance, this means that a small number of features typically account for the majority of the model's performance. In the Pareto chart, features are ordered from highest to lowest importance, with a cumulative line illustrating their collective contribution. This visual representation aids in prioritizing features for model improvement, simplifying complex datasets, and focusing efforts on the most impactful predictors [37,38,39].

Figure 2 displays the feature importance of each response. For health status model (Figure 2a), it can be note that the most influencing feature is the age with a 95% of importance score, followed by α, fc, BIVA status (BIVA), R_inf, θ_c, Xc, weight and Rc, in descendent order. These findings align with the natural progression of life, influenced by biological changes, environmental factors, and lifestyle habits that accumulate over time. Cole parameter (α) and fc with a ~18% and ~8% of importance, respectively, also align with life evolution. Both parameters undergo logical variations in consequence of biological changes. In the case of BIVA status response (Figure 2b), there are two top ranking features: quartile (~97%) and centile (~31%). The quartile (Figure 2c) is highly influenced by the BIVA status (~96%) and centile response (Figure 2d) by the BIVA (~96%), Xcc (~5%) and R_inf (~2%) bioparameters. These finding align well with the BIA vector analysis location in the tolerance ellipse, where the quartile determine the body composition and hydration status and the centile offers insights into cell integrity, muscle mass and fluid balance [25,26,27,28,29,30,31].

Fig. 2:

Feature importance of trained models: a) Health status, b) BIVA Status, c) quartile and d) centile responses.

The phase angle is a well-established marker for assessing cell membrane health and integrity, bearing significant implications for cancer prognosis [41,42,43,44]. A comprehensive study with 2625 participants demonstrated a positive and substantial correlation between phase angle and cancer survival rates. Specifically, patients exhibiting low phase angle values were found to be 23% less likely to survive compared to those with higher values [41]. Additionally, phase angle at the time of diagnosis is recognized as a crucial prognostic factor for survival among patients with advanced head and neck cancer [42]. Previous research has indicated that phase angle shows a moderate to strong correlation with body composition and physical function, while its correlation with nutritional status, complications, survival, quality of life, and symptoms tends to be weaker. These findings underscore the utility of phase angle as a robust indicator in clinical assessments, particularly in the context of cancer prognosis [43,44].

In addition, phase angle, Xc and R determine the location in the tolerance elipses in BIVA studies [25,26,27]. By analysing the position of an individual's impedance vector within these ellipses, researchers can assess hydration status, cell membrane integrity, and overall cellular health.

Previous reports used single-frequency bioimpedance for BIVA studies. In our previous work, we demonstrated the use of impedance spectroscopy combined with BIVA for accessing the health status by constructing the tolerance elipses at the characteristic frequency instead of the common 50 kHz [31]. In the present study, we found that the bioparameters derived at the characteristic frequency play a crucial role determining the health status and the location parameters.

This section focuses on developing regression models to predict Zc, Rc, Xcc, and θ_c in order to assess their robustness in determining the location on the tolerance elipses. Table 2 collects the results of the model for each response and their respective accuracy values. The response vs. predicted plots in Figure 3 provides a visual assessment of the models' performance in predicting Zc, Rc, Xcc, and θ_c. For Zc, the top-left plot indicates that the model predictions are closely aligned with the actual values, as most data points fall near the line of perfect prediction. This high level of accuracy suggests that the model is highly reliable in predicting impedance values. The characteristic phase angle (θ_c), shows a similarly strong agreement between predicted and actual values. The close alignment of data points with the line of perfect prediction underscores the model's effectiveness in estimating phase angle, a critical indicator of cell membrane health and integrity [25,26,27,28,29,30]. In the bottom-left plot, which compares true and predicted values for reactance Xcc, the data points again closely follow the line of perfect prediction. This suggests that the model is adept at estimating reactance, an important measure for assessing cellular health and hydration status [25,26,27,28,29,30,31]. In the case of the characteristic resistance (Rc), shows that the model's predictions are also highly accurate. The data points close alignment with the perfect prediction line indicates that the model can reliably predict resistance values, essential for evaluating total body water and extracellular water content [25,26,27,28,29,30].

Fig. 3:

Response vs predicted plot of the selected responses.

The accuracy parameters listed in Table 2 further corroborate the visual findings from Figure 3. The Fine Tree model for health and BIVA statuses demonstrates an R² of 1.00 for characteristic impedance and resistance, indicating perfect prediction. The RMSE, MSE, and MAE values are very low for these models, further emphasizing their high accuracy. The phase angle has an R² = 0.98, with similarly low RMSE, MSE, and MAE values, highlighting its robust prediction accuracy.

For the characteristic reactance, the Linear SVM model shows an R² = 0.99, indicating slightly lower but still high accuracy. The RMSE, MSE, and MAE values reflect this slight decrease in precision but still demonstrate the strong performance.

Figure 4 displays the observable and predictions of Zc, θ_c, Xcc and Rc across various categories: Health Status (Cancer, Healthy), Sex, Quartile (1, 2, 3, 4), Centile (50, 75,95 and 100%), and BIVA status (11, 12, 13, 14, 21, 22, 23, 31, 32, 33, 41, 42, 43, 44).

Fig. 4:

observable and predictions of Zc, θ_c, Xcc and Rc across various categories: Health Status (Cancer, Healthy), Sex, Quartile (1, 2, 3, 4), Centile (50, 75,95 and 100%), and BIVA status (11, 12, 13, 14, 21, 22, 23, 31, 32, 33, 41, 42, 43, 44).

The box plots in Figure 4 illustrate the close alignment between the experimental and predicted values of Zc, θ_c, Xcc and Rc. The blue box plots represent experimental data, while the yellow box plots depict the predicted values. From Figure 4, a strong agreement is observed between the experimental and predicted values across all categories, suggesting that the model effectively captures the characteristic electrical parameters, with high accuracy. For instance, the median value of Zc of observable cancer patients is 585.9 Ω and 567.3 Ω for healthy individuals, and the predicted values are 585.8 Ω and 567.6 Ω for cancer and healthy subjects (Figure 4a). It can be attributed that cancer patients have more unbalanced body composition due to the proper evolution of the pathology [25,29,30]. By sex, female have higher median values of 610.5 Ω as compared with male individuals 497.2 Ω with similar predicted values. These findings can be attributed to the fact that woman accumulates more adipose tissues than man in general. Concerning the characteristic phase angle (Figure 4b), healthy subjects (11.94 degrees) has higher θ_c than cancer patients (9.96 degrees), in agreements with previous reports [25,29,30]. In terms of sex, the predicted θ_c values for both female and male participants are also highly consistent with the experimental data, indicating robust performance regardless of gender. Larger characteristic phase angle is observed in male subjects, in line with previous works [25,29,30,31]. The quartile categories show a similar level of accuracy. Lower θ_c values are found in subject located at quartile 3 and 4, where the majority of the cancer patients are located. For centile categories (50, 75, 95 and 100%), the effectiveness in predicting phase angles across different percentiles is demonstrated, subjects with lowest θ_c are located at 100% and the higher at 50% centiles. The BIVA status categories highlights the model's ability to predict θ_c across different BIVA statuses. In addition, from 31 to 44 BIVA statuses the characteristic phase angle decrease gradually, reaching its lower value at 44.

From Figure 4c, again, lower characteristic reactance is reasonably found for cancer patients, in accordance with cell membrane deterioration reported [25,26,27,28,29,30,31]. By sex, female subjects having higher Xcc indicates better cell membrane integrity and overall well-being [25,26,27,28,29,30]. Quartiles 3 and 4 have lower Xcc, where the majority of the cancer patients are located. Higher Xcc is encountered for subjects located at 50% centile, while 75% and 95% have similar values and at 100% centile has the lowest Xcc, at 50–100% centiles the cancer patients are located. Similar behaviour is found for the BIVA statuses. From Figure 4d, the characteristic resistance in cancer patients is slightly higher compared to that of the healthy individuals, which can be attributed to unbalanced body composition in cancer patients. Notably, lower Rc values are observed in male individuals, those in the third quartile, and within the 75–95% centile range. Additionally, Rc exhibits variations across different BIVA statuses.

In order to evaluate the model's performance, a schematic representation of BIVA is presented in Figure 5. The maximum and minimum values of Zc, θ_c, Xcc and Rc (relative to their respective medians) are located on the tolerance ellipses. As shown in the figure, the model identifies lean individuals with maximum Zc(Zcmax) {\rm{Zc}}\left({Z_c^{max}} \right) and Rc(Rcmax) {\rm{Rc}}\left({R_c^{max}} \right) at quartile 1, centile 100%, indicating less cellular mass and structure. Additionally, athletic individuals with maximum θc(θcmax) {\theta _c}\left({\theta _c^{max}} \right) and Xcc(Xccmax) {\rm{Xcc}}\left({X_{cc}^{max}} \right) are located at quartile 2, centile 50%, reflecting balanced hydration and cellular mass. The model predicts that obese subjects have minimum Zc(Zcmin) {\rm{Zc}}\left({Z_c^{min}} \right) , Rc(Rcmin) {\rm{Rc}}\left({R_c^{min}} \right) and Xcc(Xccmin) {\rm{Xcc}}\left({X_{cc}^{min}} \right) located at quartile 3 between the 75th and 95th percentiles. Meanwhile, cachectic subjects are located at quartile 4, centile 100%, with lower θc(θcmin) {\theta _c}\left({\theta _c^{min}} \right) and Xcc(Xccmin) {\rm{Xcc}}\left({X_{cc}^{min}} \right) .

Fig. 5:

Schematic representation of BIA vector analysis (BIVA), presenting the maximum and minimum values of Zc, θ_c, Xcc and Rc (relative to their respective medians).

Previous studies have reported that individuals with pathologies associated with hydration status are located in quartile 1, while athletes or people who exercise regularly are in quartile 2. The model can also assign the location of healthy individuals between quartiles 1 and 2, centile 50%. Additionally, obese subjects, hemodialysis patients, and individuals with chronic renal failure undergoing hemodialysis are found in quartile 3. Patients diagnosed with cancer, anorexia nervosa, human immunodeficiency virus (in various stages), COVID-19, etc., are located in quartile 4 [2,29]. Our predictive model aligns with these previous studies. Thus, the model developed in this work is significant for assigning locations without the need for BIVA methods, enhancing clinical assessments and health monitoring.