Abstract
Objectives
Falls are a major patient safety concern in inpatient care. This study aimed to develop machine learning models using multidimensional clinical factors to improve early identification of high-risk patients.
Methods
A retrospective dataset of 483,174 adult inpatients was analyzed. Logistic Regression, Support Vector Machine, Random Forest, Extreme Gradient Boosting, and Multi-Layer Perceptron were applied. Models were trained with and without SMOTENC and evaluated using five-fold cross-validation, with emphasis on AUC-ROC, recall, and F1-score.
Results
Key predictors included fall history, medication use, dizziness, sensory impairment, and reduced functional status. Without SMOTENC, models achieved moderate AUC-ROC values ranging from 0.62 to 0.72, but exhibited extremely low recall and F1-scores for fall events. After applying SMOTENC, AUC-ROC remained stable in the range of 0.67 to 0.70, while recall improved substantially to approximately 50 to 60 percent. Random Forest and XGBoost demonstrated relatively stable AUC-ROC performance, whereas MLP showed limited generalization ability.
Conclusions
Machine learning models can capture clinically relevant fall risk factors, with AUC-ROC indicating moderate discrimination. Severe class imbalance substantially limits minority event detection. Although SMOTENC improves recall, it introduces a precision–recall trade-off, underscoring the need to interpret AUC-ROC alongside class-specific metrics in imbalanced clinical datasets.
Keywords
Introduction
Falls represent a potential risk for all hospitalized patients, regardless of age, sex, or diagnosis. They not only lead to physical injuries and mobility restrictions but may also trigger psychological consequences such as fear and loss of confidence, thereby negatively affecting overall care and recovery. The occurrence of falls is often sudden and unpredictable, and even younger or middle-aged patients may be affected. These findings highlight that falls are not confined to specific patient groups but are broadly present across the continuum of hospital care. Current research suggests that multifactorial interventions may effectively reduce fall incidence, 1 though such measures may restrict patient mobility. Thus, identifying optimal assessment tools or intervention strategies requires interdisciplinary collaboration. 2 Some studies have reported that surgical wards have the lowest fall incidence, 3 which warrants further investigation. Moreover, fall events substantially increase healthcare costs compared to patients without falls. 4 In clinical practice, nurses are primarily responsible for fall risk identification and prevention. Previous studies have shown that the accuracy and consistency of nursing assessments may be influenced by factors such as staffing patterns, patient load, years of experience, and workplace support. 5 If assessment outcomes are not promptly translated into effective care actions, opportunities for fall prevention may be missed. Beyond the limitations of human judgment, fall occurrence is also closely associated with specific risk factors, including the use of central nervous system medications, sedatives, and hypnotics. 6
In recent years, numerous studies have focused on developing predictive models for fall prevention. Some scholars have collected data specifically from medical inpatients and demonstrated that incorporating fall-prevention variables into the models significantly improved predictive accuracy. 7 Others analyzed data from 15 hospital wards and evaluated variables at four distinct time points during hospitalization, finding that multi-temporal assessments enhanced predictive performance. 8 Another study trained a model using 46 features and reported an accuracy as high as 95.11%. 9 Research on patients undergoing spinal and lower extremity surgery further revealed that with each additional year of age, the risk of falls increased, underscoring age as a critical risk factor. 10 In addition, face-to-face interviews combined with anthropometric and functional assessments were used to predict falls within a 6-month follow-up period. 11 Other investigators have utilized inpatient fall records with feature selection techniques to identify optimal subsets of predictors and subsequently developed three displacement-based models, demonstrating that machine learning approaches achieved favorable performance when applied to the Fall Risk Assessment Tool (FRAT). 12 More recently, the use of real-time location systems to capture patients’ dynamic movement patterns has been proposed to enhance predictive accuracy, with findings indicating that higher fall probability was significantly associated with sedative use and increased red blood cell distribution width. 13
Despite these advancements, several important gaps remain. Many existing studies emphasize overall accuracy or AUC without adequately reporting class-specific performance, such as recall or F1-score for fall events, which are critical in highly imbalanced clinical datasets. The issue of class imbalance is often insufficiently addressed or not explicitly discussed, potentially leading to overestimation of model performance and limited real-world applicability. Few studies systematically evaluate the impact of different imbalance handling strategies, particularly in large-scale inpatient datasets with mixed-type clinical variables. To address these limitations, the present study develops and evaluates multiple machine learning models using a large-scale inpatient dataset and explicitly investigates the effect of class imbalance on model performance. Unlike prior work, this study not only compares models using both discrimination metrics and class-specific measures, but also examines the effectiveness of resampling techniques, including SMOTE and SMOTENC, with particular attention to the latter’s ability to handle mixed categorical and numerical features. By doing so, this study aims to provide a more realistic and clinically meaningful evaluation of fall prediction models and to clarify the methodological challenges associated with imbalanced clinical data. This study aims to develop and systematically evaluate machine learning models for predicting fall risk among hospitalized patients by integrating multidimensional clinical factors, including demographic characteristics, functional status, medication use, sensory function, and activities of daily living (ADL). Given the highly imbalanced nature of fall-related data and the complexity of clinical tabular features, appropriate data preprocessing strategies are incorporated to enhance model learning and improve the detection of rare fall events. Multiple machine learning algorithms with distinct modeling mechanisms are compared to assess their predictive performance, generalization ability, and clinical applicability. Falls represent clinically significant adverse events and key indicators of patient safety in inpatient care, often leading to physical injury, functional decline, psychological distress, and increased healthcare utilization. Therefore, this study seeks to establish a robust and quantifiable prediction framework to support early risk stratification and facilitate targeted fall prevention strategies, ultimately contributing to improved patient safety and healthcare quality.
Materials and methods
Ethical approval
The study was approved by the Institutional Review Board of Changhua Christian Hospital (approval no.: 241105). The Institutional Review Board waived the need for informed consent considering the retrospective nature of data collected. All methods were performed in accordance with the relevant guidelines and regulations or declaration of Helsinki.
Study setting, design, and ethical considerations
This study was a retrospective analysis conducted at Changhua Christian Hospital in central Taiwan. The study population consisted of adult inpatients aged 18 to 111 years. Nursing and clinical information documented at the time of admission were collected and analyzed. To address the substantial imbalance between fall and non-fall cases, fall-related data were collected over a 10-year period from 2014 to 2024. A total of 483,174 records were included in the analysis, comprising 2,557 fall cases and 480,617 non-fall cases. The dataset was randomly divided into a training dataset (N = 386,539; falls = 2,046; non-falls = 384,493) and an independent testing dataset (N = 96,635; falls = 511; non-falls = 96,124). To ensure robust model development and evaluation, five-fold cross-validation was applied within the training dataset. In each fold, approximately 80% of the data were used for model training (N ≈ 309,231–309,232), and the remaining 20% were used for validation (N ≈ 77,307–77,308), while maintaining class distribution consistency across folds, as shown in Figure 1. The study protocol was reviewed and approved by the Institutional Review Board of Changhua Christian Hospital. All data were de-identified prior to analysis to ensure patient confidentiality. Due to the retrospective design and the use of secondary data, the requirement for informed consent was waived. Dataset distribution and five-fold cross-validation scheme for fall prediction modeling.
Model training
Based on effect size measures derived from univariate analysis (Cramer’s V and Cohen’s d) and clinical relevance, a set of variables was selected as input features. Based on effect size analysis and clinical relevance, a set of key variables was selected as input features for model development. These included age, Barthel Index total score, unstable gait, need for walking aids, history of falls within one year, dizziness or vertigo, abnormal foot sensation, use of fall-risk medications, number of medications, activity level, mobility, stair climbing, walking on level ground, transfer ability, and toileting.
This study compared multiple machine learning models, including Logistic Regression, Random Forest, Extreme Gradient Boosting (XGBoost), Support Vector Machine (SVM), and Multi-Layer Perceptron (MLP). These models were selected due to their distinct learning mechanisms and representativeness across different categories of machine learning approaches. Logistic Regression is a linear model that provides high interpretability and serves as a baseline for comparison. 14 Random Forest is an ensemble learning method based on bagging, which improves robustness and reduces variance through multiple decision trees. 15 XGBoost is a gradient boosting framework, focuses on sequential learning and error correction, often achieving superior performance in structured data tasks. 16 SVM is a margin-based classifier that is effective in high-dimensional spaces and can model non-linear relationships through kernel functions. 17 MLP is a neural network-based model capable of capturing complex non-linear patterns through multiple hidden layers. 18
The Synthetic Minority Over-sampling Technique for Nominal and Continuous features (SMOTENC) was applied prior to model training to address class imbalance. Unlike standard SMOTE, SMOTENC is specifically designed for datasets containing both numerical and categorical variables, allowing synthetic samples to be generated while preserving the integrity of categorical feature distributions. SMOTENC generates synthetic minority class samples within the feature space to reduce bias caused by imbalanced class distributions, while minimizing distortion of categorical attributes. This approach improves the model’s ability to learn decision boundaries for minority classes without introducing unrealistic data patterns. In addition, it enhances model robustness, reduces overfitting to majority class patterns, and improves sensitivity in detecting rare events such as falls. To systematically evaluate the impact of SMOTENC, two sets of models were constructed: one without SMOTENC and one with SMOTENC, and their performances were compared. All models were trained and validated using 5-fold cross-validation to ensure consistency in class distribution across folds. This design enabled a comprehensive assessment of performance differences under different sampling strategies and evaluated whether SMOTENC improved the models’ ability to identify minority fall cases.
Experimental environment
The experiments in this study were conducted on a workstation equipped with the Windows 10 64-bit operating system, an Intel Core i9 processor, 128 GB of RAM, and an NVIDIA RTX 4090 GPU. All software implementations were developed in Python 3.10. Machine learning models were implemented using the scikit-learn library version 1.6.0 and the XGBoost package version 2.0.3. Data processing and analysis were performed using NumPy version 1.26.0 and pandas version 2.3.3.
Detailed hyperparameter settings for all machine learning models.
Model evolution
Confusion matrix
The performance of the models was evaluated using multiple classification metrics. Accuracy was employed to measure the overall proportion of correct predictions, as shown in Eqs. (1). Recall reflects the model’s ability to correctly identify positive cases among all actual positive samples, as presented in Eqs. (2). Precision emphasizes the proportion of true positives among all samples predicted as positive, as illustrated in Eqs. (3). The F1-score, defined as the harmonic mean of Precision and Recall, provides a balanced measure that accounts for both completeness and correctness of positive predictions, making it particularly suitable for imbalanced datasets, as shown in Eqs. (4).
Statistical analysis
This study first performed descriptive statistical analyses to examine the distributional characteristics of each variable and to explore their potential associations with fall events, serving as the basis for subsequent variable selection. Categorical variables were presented as frequencies and percentages. The Chi-square test of independence was applied to assess whether the distributional differences between the fall and non-fall groups were statistically significant. In addition to p-values, effect sizes were quantified using Cramér’s V to evaluate the strength of associations. For continuous variables, given the potential deviation from normality, the data were summarized using the median, first quartile (Q1), and third quartile (Q3). The Mann–Whitney U test, a nonparametric method, was then employed to compare differences between the two groups. Effect sizes for continuous variables were further assessed using Cohen’s d to quantify the magnitude of differences between groups. To quantify the direction and strength of associations between predictors and fall events, odds ratios (ORs) with 95% confidence intervals were estimated, providing an interpretable measure of risk for both categorical and continuous variables.
Results
Baseline characteristics associated with fall risk.
Comparison of continuous variables between fall and non-fall groups.
Mean ± standard deviation of overall model performance metrics without SMOTENC across five-fold cross-validation for training, validation, and test sets.
Mean ± standard deviation of class-specific performance metrics without SMOTENC for fall and non-fall predictions across five-fold cross-validation.
Mean ± standard deviation of confusion matrix components without SMOTENC across five-fold cross-validation for training, validation, and test sets.
Mean ± standard deviation of overall model performance metrics with SMOTENC across five-fold cross-validation for training, validation, and test sets.
Mean ± standard deviation of class-specific performance metrics with SMOTENC for fall and non-fall predictions across five-fold cross-validation.
Mean ± standard deviation of confusion matrix components with SMOTENC across five-fold cross-validation for training, validation, and test sets.
The SHAP summary plot ranks features according to their overall contribution to the model and illustrates the direction of their effects as shown in Figure 2. The Barthel Index total score was identified as the most important predictor. Lower functional scores were associated with positive SHAP values, indicating an increased risk of falls, whereas higher functional independence contributed to reduced risk. Age was the second most influential factor, demonstrating a clear positive relationship with fall risk, as higher age values were associated with increased SHAP values. Among functional variables, transfer ability, mobility, and activity level showed substantial contributions. Impairment in these functions was associated with higher SHAP values, indicating elevated fall risk. In addition, history of falls within one year exhibited a strong positive effect, with higher values contributing to increased risk. Other clinically relevant factors, including dizziness or vertigo, sensory perception, medication use, and caregiver status, also contributed to the model, although their overall impact was smaller compared to functional and mobility-related variables. SHAP summary plot illustrating feature importance and directional effects of predictors in the Random Forest model for inpatient fall risk prediction.
The SHAP summary plot illustrates both the relative importance of each predictor and the direction of its effect on inpatient fall risk as shown in Figure 3. The Barthel Index total score is identified as the most influential predictor. Lower values, indicating reduced functional independence, are associated with higher SHAP values and thus a higher predicted fall risk. This finding emphasizes that functional dependency is the dominant driver of inpatient falls. Age is the second most important feature and shows a clear monotonic pattern, where increasing age corresponds to progressively higher SHAP values. This indicates that older patients have a substantially increased risk of falls, consistent with clinical evidence. Among functional variables, transfer ability, mobility, and activity level demonstrate strong contributions. Lower functional performance in these domains is associated with positive SHAP values, indicating increased fall risk. Similarly, sensory perception shows a meaningful effect, suggesting that impaired perception contributes to instability and fall occurrence. SHAP summary plot illustrating feature importance and direction of impact on inpatient fall risk prediction using the XGBoost model.
Discussion
This study compared the performance of multiple machine learning methods for predicting fall risk among hospitalized patients and further examined the impact of SMOTENC on addressing class imbalance. The results indicate that model performance varied substantially depending on the evaluation metric used. In the absence of SMOTENC, Random Forest and XGBoost demonstrated relatively stable discrimination performance, with AUC-ROC values of approximately 0.62–0.72. However, despite moderate discrimination, most models exhibited extremely limited ability to identify fall events, as reflected by near-zero recall and F1-scores. This suggests that high overall accuracy in imbalanced datasets may be misleading and does not necessarily reflect clinically meaningful predictive performance. Similar findings have been reported in previous machine learning–based fall prediction studies, where severe class imbalance frequently resulted in high overall accuracy but poor minority-class detection performance. In clinical fall prediction, optimizing sensitivity for rare fall events often leads to a substantial increase in false-positive predictions, reflecting the inherent recall–precision trade-off commonly observed in imbalanced healthcare datasets. Therefore, evaluation of fall prediction models should not rely solely on overall accuracy or AUC-ROC, but also incorporate clinically relevant metrics such as recall, precision, F1-score, and precision–recall curves to better assess minority-event prediction performance. After applying SMOTENC, model behavior changed notably. Recall for fall events increased substantially across Logistic Regression, Random Forest, XGBoost, and SVM, reaching approximately 50–60%, indicating improved sensitivity to minority cases. This improvement was accompanied by a pronounced reduction in precision, which remained below 1% in the test and validation sets. Consequently, F1-scores for fall prediction remained low, reflecting the trade-off between detecting minority events and increased false positive predictions. These findings suggest that while SMOTENC effectively mitigates prediction collapse, it does not fully resolve the challenges associated with imbalanced clinical data. This observation suggests that algorithmic resampling alone may be insufficient for achieving clinically deployable fall prediction performance in extremely imbalanced inpatient datasets, highlighting the need for multimodal feature integration and more clinically informative representations of patient mobility and functional decline. Random Forest and XGBoost demonstrated relatively consistent performance across training, validation, and test sets, indicating better robustness compared with other approaches. In contrast, MLP exhibited strong performance in the training set but showed reduced AUC-ROC and recall in the test and validation sets, suggesting limited generalization under resampled conditions. Logistic Regression and SVM showed improved recall after SMOTENC but remained constrained by low precision, limiting their practical applicability.
To further enhance model interpretability, SHAP analysis was conducted for tree-based models. The results consistently demonstrated that functional status, particularly the Barthel Index, was the most influential predictor, followed by age and mobility-related variables such as transfer ability, activity level, and mobility. Lower functional independence and impaired mobility were strongly associated with increased fall risk, highlighting that functional decline is the primary driver of inpatient falls. In addition, the Random Forest model emphasized the importance of prior fall history, suggesting that historical events contribute additional predictive value. In contrast, variables such as medication use, dizziness, and caregiver status showed comparatively smaller contributions in the SHAP analysis. These findings indicate that, although such clinical factors are relevant, their predictive impact is secondary to functional and mobility-related impairments in this dataset. The SHAP results provide clinically interpretable evidence that fall risk is predominantly driven by functional dependency and mobility limitations rather than isolated clinical conditions. This aligns with the model performance findings and reinforces the importance of incorporating functional assessments into fall risk prediction frameworks. These findings are consistent with recent studies demonstrating that multidimensional functional assessments, including functional balance tests and computerized dynamic posturography, can substantially improve both predictive performance and clinical interpretability in fall risk prediction models. Previous machine learning studies have shown that combining physical characteristics, co-morbidities, and objective balance measurements enables more comprehensive characterization of mobility impairment and balance dysfunction. Importantly, although advanced balance systems may enhance predictive accuracy, prior studies have also suggested that simpler functional assessments combined with routinely available clinical variables may still achieve strong predictive capability without requiring specialized equipment or additional bedside procedures. 19 In this context, the present study further supports the clinical value of functional and mobility-related variables derived from routine inpatient assessment workflows.
This study compared the characteristics of patients with and without falls, demonstrating that multiple demographic, clinical, and functional factors were significantly associated with fall events. Among demographic variables, the proportion of males was significantly higher in the fall group, consistent with prior studies suggesting that male inpatients may be at increased fall risk in certain populations due to physical or functional conditions. 20 The higher prevalence of smoking among fall patients also aligns with evidence linking smoking to an increased likelihood of falls. 21 Clinically, a history of falls within the past year emerged as a strong predictor, in agreement with previous findings. 22 The use of sedatives, psychiatric medications, antidiabetic drugs, antiepileptics, and hypnotics was significantly more frequent in the fall group, supporting established evidence that these medications elevate fall risk.23,24 Furthermore, the higher prevalence of polypharmacy highlights medication burden as another potential risk factor. In terms of functional and sensory status, dizziness, abnormal foot sensation, and impairments in vision and hearing were all more common in the fall group, underscoring the role of sensory deficits as important fall risk factors. 25 Significant differences were also observed in activities of daily living (ADL), including personal hygiene, bathing, feeding, toileting, and dressing, with fall patients demonstrating greater dependency. This finding is consistent with prior studies showing that ADL assessments are valuable tools for identifying high-risk inpatients. 26 Mobility-related factors, such as unstable gait, the need for walking aids, and greater difficulty with stair climbing and level walking, were also markedly higher in the fall group, further confirming the strong link between reduced mobility and fall risk. Additionally, patients in the fall group were significantly older, reaffirming advanced age as a critical determinant of fall risk. Age-related declines in muscle strength, balance, and the presence of multiple comorbidities are likely contributors to this association. 27 Lower body weight and BMI in the fall group further suggest that malnutrition and reduced muscle mass may play a role in increasing fall susceptibility. Low BMI and weight loss have been closely associated with sarcopenia, impaired balance, and elevated fall risk. 28 Finally, the fall group had significantly lower Barthel Index scores compared with the non-fall group, indicating greater dependence in daily activities. As a widely used clinical measure, the Barthel Index effectively reflects patient self-care ability and further emphasizes the connection between functional limitations and fall events. The findings suggest that routinely collected functional assessments, particularly measures related to mobility and activities of daily living, may provide substantial value for early inpatient fall risk stratification. Because these variables are already embedded within standard nursing assessment workflows, they may facilitate scalable implementation of automated fall risk screening systems without imposing additional burden on healthcare providers. Compared with studies incorporating specialized balance assessment systems or sensor-based monitoring technologies, the present study focused on routinely collected electronic medical record variables obtained during standard inpatient care. Although this approach may provide lower predictive precision than highly instrumented assessment frameworks, it offers important advantages in scalability, automation, and feasibility for large-scale hospital deployment. These findings suggest that clinically accessible functional and mobility assessments remain highly valuable for practical inpatient fall risk prediction in real-world healthcare settings.
Comparison of recent machine learning studies and the present study for inpatient fall risk prediction.
Despite the promising results, several limitations merit consideration. The use of retrospective clinical data introduces a potential risk of data leakage, including both temporal and target leakage, as certain variables may implicitly encode information related to the outcome, thereby leading to overestimated model performance. Although efforts were made to appropriately structure the dataset, the possibility of unintended information leakage cannot be entirely excluded. The application of the SMOTENC algorithm may also introduce bias if not rigorously controlled, as synthetically generated samples may not fully capture the underlying clinical heterogeneity, and inappropriate implementation before dataset partitioning may further exacerbate information leakage between training and validation sets. Although accuracy and AUC-ROC remain widely used metrics in machine learning studies, these measures may inadequately reflect minority-event prediction performance in highly imbalanced clinical datasets because they are strongly influenced by majority-class dominance.
Future investigations should incorporate more discriminative evaluation metrics, including precision–recall curves, F1-score, and class-specific recall, to more accurately reflect minority class performance in highly imbalanced fall prediction datasets. In addition, the limited interpretability of the developed models may constrain their clinical applicability because the underlying decision-making processes remain insufficiently transparent; therefore, the integration of explainable artificial intelligence techniques is warranted to improve model transparency, enhance clinician trust, and support real-world deployment. Future studies may also further improve predictive performance by integrating wearable sensor data, computerized dynamic posturography, or longitudinal mobility monitoring, as suggested in previous fall prediction research. 19 Combining routinely collected electronic medical record data with objective balance assessments and real-time movement analysis may enable more comprehensive characterization of patient mobility, balance dysfunction, and functional decline, thereby enhancing both predictive performance and clinical interpretability. Furthermore, the incorporation of continuous monitoring technologies and explainable artificial intelligence frameworks may facilitate earlier intervention, individualized risk stratification, and more effective clinical decision-making in hospital settings. Future multicenter prospective studies with external validation are warranted to further evaluate the generalizability, robustness, and clinical applicability of machine learning–based fall prediction systems across diverse patient populations and healthcare environments.
Conclusions
This study integrated multidimensional clinical characteristics with multiple machine learning models to develop a predictive framework for inpatient fall risk. The findings confirmed that prior fall history, medication use, reduced functional independence, impaired mobility, and sensory deficits are key determinants of fall events. Model comparisons showed that Random Forest and XGBoost achieved relatively stable performance, with moderate AUC-ROC values of approximately 0.62–0.72, indicating acceptable but limited discrimination ability. Under severe class imbalance, most models demonstrated limited capability in identifying fall events, as reflected by extremely low recall and F1-scores despite moderate AUC-ROC performance. After applying SMOTENC, recall for fall events improved substantially to approximately 50–60% across several models; however, precision remained below 1%, resulting in persistently low F1-scores. In addition, certain models, such as MLP, exhibited unstable generalization performance, with reduced AUC-ROC on the test and validation sets. These findings indicate that, although machine learning models can capture clinically relevant risk factors, their effectiveness in detecting rare events is strongly constrained by class imbalance. While SMOTENC alleviates prediction collapse and improves sensitivity, it introduces a notable trade-off with precision. Therefore, model performance in imbalanced clinical datasets should be evaluated using both discrimination metrics, such as AUC-ROC, and class-specific measures, with appropriate imbalance handling strategies considered essential for improving clinical applicability.
Supplemental material
Supplemental material - Admission clinical and functional assessments for predicting inpatient fall risk using machine learning models
Supplemental material for Admission clinical and functional assessments for predicting inpatient fall risk using machine learning models by Ya-Wen Lee, Ying-Lin Hsu, Shu-Mei Lai, Chih-Hao Lin, Chih-Ming Lin, Jia-Lang Xu in DIGITAL HEALTH
Footnotes
Acknowledgments
This study acknowledge the use of ChatGPT for language editing support during manuscript preparation. The authors retained full responsibility for the content and accuracy of the manuscript. The authors would like to thank the referees and the editors for their comments and valuable suggestions.
Author Contributions
Conceptualization, Y.-W.L. and J.-L.X.; methodology, Y.-L.H.; validation, C.-M.L. and S.-M.L.; formal analysis, Y.-L.H.; investigation, S.-M.L.; data curation, J.-L.X. and C.-H.L.; writing—original draft preparation, Y.-L.S. and J.-L.X.; writing—review and editing, Y.-W.L., C.-M.L., Y.-L.S. and J.-L.X.; supervision, C.-M.L. All authors have read and agreed to the published version of the manuscript.
Funding
The authors wish to thank the National Science and Technology Council (NSTC) of the Republic of China for financially supporting this research under Contract Grants (No. NSTC-115-2222-E-025-001).
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
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References
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