HGSOXGB: Hunger-Games-Search-Optimization-Based Framework to Predict the Need for ICU Admission for COVID-19 Patients Using eXtreme Gradient Boosting

Abstract

Millions of people died in the COVID-19 pandemic, which pressured hospitals and healthcare workers into keeping up with the speed and intensity of the outbreak, resulting in a scarcity of ICU beds for COVID-19 patients. Therefore, researchers have developed machine learning (ML) algorithms to assist in identifying patients at increased risk of requiring an ICU bed. However, many of these studies used state-of-the-art ML algorithms with arbitrary or default hyperparameters to control the learning process. Hyperparameter optimization is essential in enhancing the classification effectiveness and ensuring the optimal use of ML algorithms. Therefore, this study utilized an improved Hunger Games Search Optimization (HGSO) algorithm coupled with a robust extreme gradient boosting (XGB) classifier to predict a COVID-19 patient’s need for ICU transfer. To further mitigate the random initialization inherent in HGSO and facilitate an efficient convergence toward optimal solutions, the Metropolis–Hastings (MH) method is proposed for integration with HGSO. In addition, population diversity was reintroduced to effectively escape local optima. To evaluate the efficacy of the MH-based HGSO algorithm, the proposed method was compared with the original HGSO algorithm using the Congress on Evolutionary Computation benchmark function. The analysis revealed that the proposed algorithm converges better than the original method and exhibits statistical significance. Consequently, the proposed algorithm optimizes the XGB hyperparameters to further predict the need for ICU transfer for COVID-19 patients. Various evaluation metrics, including the receiver operating curve (ROC), precision–recall curve, bootstrap ROC, and recall vs. decision boundary, were used to estimate the effectiveness of the proposed HGSOXGB model. The model achieves the highest accuracy of 97.39% and an area under the ROC curve of 99.10% compared with other classifiers. Additionally, the important features that significantly affect the prediction of ICU transfer need using XGB were calculated.

1. Introduction

The recent coronavirus outbreak caused a global pandemic. SARS-CoV-2, a novel coronavirus, was first detected in Wuhan, China, in 2019. Recognizing its potential to trigger a worldwide public health crisis, the World Health Organization (WHO) declared this coronavirus disease (COVID-19) a global epidemic on 11 March 2020 [1]. The rise of COVID-19 led to a global health and financial catastrophe. As of 16 August 2023, the number of COVID-19 patients identified worldwide has crossed 760 million, with nearly seven million fatalities [2]; however, the real numbers are assumed to be considerably higher because of testing limitations. The first coronavirus case was detected in Bangladesh on 7 March 2020. According to the country’s Ministry of Health, the total number of COVID-19-infected patients in Bangladesh has increased by more than two million, with the total death toll surpassing twenty-nine thousand as of 16 August 2023 [3]. Although the COVID-19 pandemic has officially ended, novel variants of the virus still threaten public health.

The infection rates are rapidly increasing in Bangladesh and the world. Temperature and humidity have been identified as important factors in modeling COVID-19 mortality rates [4]. Common symptoms experienced by most COVID-19-infected patients include cold-like symptoms, continuous coughing, sore throats, a loss or alteration of taste and/or smell, fatigue, headaches, aches and pains, diarrhea, and sometimes other respiratory infections, as well as fever [5]. Note that the virus seems to be transmitted through droplets, direct contact, aerosols, blood, fecal–oral contact, from animals to humans, and even from mothers to children. Although COVID-19 has been recorded in patients of almost all ages, a higher death rate has been observed in older individuals who already suffer from cardiovascular disease, hypertension, chronic lung and kidney disease, diabetes, and other disorders. The initial step in effectively managing the allocation of critical care resources is identifying patients who are unlikely to require critical care and encouraging them to self-quarantine at home. Patients with severe conditions, such as respiratory failure and pneumonia, must be admitted to the ICU as soon as possible. However, 10–20% of total cases require ICU admission, whereas 3–10% require intubation and 2–5% die [6]. The remaining 80–90% of COVID-19 cases are mild or asymptomatic [7].

During a pandemic, the effective management of limited critical care resources and ICU beds is crucial [8]. Concerns have been raised worldwide regarding the scarcity of intensive care unit (ICU) beds for COVID-19 patients, particularly in developing countries. For instance, in Bangladesh, only 1200 ICU beds are available (including in public and private hospitals), indicating a significant shortage of critical healthcare resources. Nevertheless, prioritizing COVID-19 patients for specialized care with emergency medical support, particularly in an ICU, can significantly reduce fatality rates. Hence, frontline healthcare workers are forced to care for the “sickest of the sick” patients because of the immense pressure on the ICU admission queue. Owing to limited medical and human resources, healthcare professionals may rely on cutting-edge technologies and machine learning (ML) models to monitor and assess high-risk patients.

Several studies have addressed the issue of predicting patient outcomes in the context of COVID-19. For instance, Cheng et al. [9] employed a random forest (RF) model trained on time-series data, including major signs and patient laboratory reports as the input variables, and achieved an accuracy of 76.2% in predicting actual ICU admissions. Wollenstein-Betech et al. [10] took a comprehensive approach, employing four different classification methods, an RF, sparse support vector machine (SVM), logistic regression, and extreme gradient boosting (XGB) in each model to predict hospitalization, death, and the need for ICU care. Agieb [11] focused on predicting ICU necessity for COVID-19 patients using ML models—naive Bayes, K-nearest neighbor (K-NN), and SVM—trained on the features extracted from patients’ X-ray images. In a different vein, Weikert et al. [12] applied a deep-learning-based, fully automated extraction method for cardiothoracic CT metrics to predict the management of COVID-19 patients, including their ICU needs. Heo et al. [13] proposed an integer-based scoring method to identify COVID-19 patients requiring intensive care support. Age, dyspnea, sex, initial body temperature, history of kidney disease, hemoptysis, and the ADL scale were criteria for the scoring system. A study by Palomo et al. [14] adopted a slightly different approach and emphasized the bed demand for COVID-19 patients utilizing queuing models to show occupancy scenarios based on various patient arrival patterns.

The aforementioned studies demonstrated moderate accuracies in predicting ICU admission requirements using contemporary ML algorithms equipped with default hyperparameters. However, the classification and prediction performance can be significantly accelerated by optimizing the hyperparameters of ML algorithms using state-of-the-art optimization techniques [15,16,17,18]. Motivated by the need for hyperparameter optimization, this study adopts a novel HGSO algorithm [19], a recently introduced performance-based swarm optimization technique that demonstrates remarkable performance even when compared with an extensive collection of 23 reputable optimization functions and innovative algorithms, including the IEEE CEC 2014 benchmark test suite [20,21]. In addition, the Metropolis–Hastings (MH) algorithm was used instead of random initialization to adaptively initialize the hyperparameters [22,23]. Moreover, adaptive variational control (VC2) was required for robust optimization and to balance exploration and exploitation and thus converge to optimal solutions. Additionally, to escape the local optima effectively, the reintroduction of diversity is required to facilitate a broader explanation of the solution space. Considering these requirements, this study proposes an MH-based HGSO technique that introduces several novel contributions, which are summarized as follows.

• A novel HGSO algorithm, combined with a new fitness function, is adapted for the first time to predict the need for ICU transfer for COVID-19 patients using an XGB classifier (see Algorithm 1).
• Unlike the random initialization used in traditional HGSO, this study uses the MH algorithm to adaptively initialize the hyperparameter values (see Algorithm 2).
• This study employs an adaptive VC2 operator and reintroduces diversity to find the optimal solution and prevent premature convergence, respectively (see Section 2.4).
• This study identifies the most significant predictors for ICU transfer using XGB, providing valuable information for national policymakers (see Section 3.8).
• Comparing the proposed HGSOXGB model with cutting-edge classifiers reveals that the HGSOXGB obtains the highest accuracy (see Section 3.4 and Section 3.9).

Algorithm 1 XGB classifier implementation algorithm

Input: D-dimensional feature $X\in {\mathcal{R}}^{N\times d}$ and target $y\in {\mathcal{R}}^{N\times 1}$ with N samples Output: The probability of outcome $P\in [0,1]$ of unknown test dataset x, where ${\sum }_{i=1}^{cl}{P}_i=1$ for all $i\in cl=2$, $cl$ is the number of classes 1: Initialize model ${\displaystyle F_o\left(x\right)={argmin}_{\gamma }\sum _{i=1}^{N}L(y,\gamma )}$, where $L(y,F(x\left)\right)$ is the loss function 2: for $k=1\sim K$ do 3:    Compute the gradient of the loss function, $\hspace{1em}{r}_{ik}=-\alpha \left[\frac{\delta L(y,F\left(X_i\right))}{\delta F\left(X_i\right)}\right]$, where $i=1,2,...,N$ and $\alpha$ is the learning rate. 4:    Fit a base tree $h_k$ on the gradient at each step using training set $(X_i,r_{ik})$ 5:    Compute multiplicative factor ${\gamma }_k$ using  ${\displaystyle {\gamma }_k={argmin}_{\gamma }\sum _{i=1}^{N}L(y_i,F_{k-1}\left(X_i\right)+\gamma h_k\left(X_i\right))}$ 6:    Update the boosted model using $\hspace{1em}{F}_k\left(x\right)=F_{k-1}\left(x\right)+{\gamma }_k{h}_k\left(x\right)$ 7: end for 8: return$F_k\left(x\right)$ is the desired probability of outcome $P\in [0,1]$

Algorithm 2 Proposed population initialization algorithm using the MH method

Input: The number of XGB hyperparameter in the population (N), the number of XGB hyperparameter (H), and the lower ($lb$) and upper ($ub$) limits of each XGB hyperparameter. Output:  Initial population, $P_{init}$ 1: Initialize $P_{init}=zeros(N,H)$ to allocate memory 2: Initialize the first individual randomly as $population(1,:)=lb+(ub-lb)·rand(1,H)$ 3: for $i=2:N$ do 4:    Generate a candidate (C) individual as  $C=lb+(ub-lb)·rand(1,H)$, 5:    Calculate the acceptance probability ($\alpha$) as  $\alpha =min\left(1,\frac{J\left(C\right)}{J\left(population\left(i-1,:\right)\right)}\right)$, 6:    Accept or reject C with probability 7:    if ($rand\left(\right)\le \alpha$) then 8:      $population(i,:)=C;$ 9:    else 10:      $population(i,:)=population(i-1,:);$ 11:    end if 12: end for 13: $P_{init}=population;$ 14: return Initial population, $P_{init}$

2. Materials and Methods

Figure 1 shows the workflow of the proposed model. As illustrated, the columns containing 60% of missing values and unnecessary outliers were eliminated, and the remainder of the dataset underwent min–max normalization to convert all values to the same scale. Subsequently, the normalized dataset was divided into training and testing sets. To mitigate class imbalance, a large quantity of synthetic data was generated for the minority class inside the training set using the Synthetic Minority Oversampling Technique (SMOTE). Subsequently, the resulting balanced dataset was employed to train the ML models. The hyperparameters of the ML classifiers were finetuned using the HGSO algorithm. However, when comparing the performance of the original HGSO model with that of the CEC benchmark function (briefly discussed in Appendix A), we observed that the convergence of the HGSO algorithm requires further improvement. Another issue with the original HGSO is the random initialization of the hyperparameter values. Therefore, the MH algorithm was utilized to adaptively initialize the hyperparameter values, thereby accelerating the convergence speed of the HGSO algorithm. The model performance was evaluated using previously separated test data in the following steps. Various statistical analyses were performed in addition to feature importance calculations. Finally, the necessity of ICU care for COVID-19 patients was efficiently predicted and presented.

2.1. Data Source

A large COVID-19 dataset was collected from a publicly available repository of SARS-CoV-2 patient information in Mexico [24]. It contains 7233257 individual observations in 40 columns. The data contain demographic information, including age, nationality, location, origin, ethnicity, prior medical conditions, diabetes, asthma, hypertension, obesity, chronic obstructive pulmonary disease (COPD), chronic renal failure, immunosuppression, pregnancy, other prior diseases, and smoking information. In addition, they contained the dates of the first symptoms observed by the patient, the patient’s arrival in the ICU, and the patient’s death, and include columns that show whether the patient was hospitalized, had pneumonia, or required ICU care, as well as the results of the antigen test for SARS-CoV-2.

2.2. Data Preprocessing

Data preprocessing plays a pivotal role in machine learning classification. However, the raw dataset used in the proposed approach was impossible to work with because its column names were in Spanish and the data were considerably noisy, with nearly 60% missing values. Moreover, many columns in the dataset were irrelevant and did not influence the classification outcomes. In addition, the numerical values of the dataset were obtained at different scales. Given these challenges, achieving optimal results using raw datasets was impractical. Hence, data preprocessing was crucial for converting the data into a meaningful format and improving the ML performance. The steps taken to preprocess the dataset are outlined below.

1.

Column translation: initially, the Spanish names of each column were translated into English.

2.

Missing value removal: the columns containing almost 60% missing values were eliminated from the dataset because the interpretation and quality of the proposed approach can degrade if this large amount of missing values remains in the input dataset.

3.

Removal of unnecessary columns: because the proposed approach aims to anticipate ICU necessity for COVID-19 patients, the unnecessary columns—origin, sector, date of admission to the ICU, etc.—were removed from the dataset, as they are unrelated to ICU prediction. The columns (features) containing outliers were also eliminated from the dataset.

4.

Removing demographic variables: the columns of the demographic variables, such as ethnicity, region, nationality, location, and origin, were eliminated from the dataset such that the dataset can be utilized in all other countries.

Upon completing these steps, 18 fields were retained: intubated (identifying whether the patient required intubation), pneumonia, otras_com (identifying if the patient had other diseases), COPD, cardiovascular, inmusupr (indicating if the patient was immunosuppressed), another case (noting patient contact with other SARS CoV-2 cases), smoking, asthma, renal_cornica, age, pregnancy, obesity, diabetes, hypertension, sex, antigen_result (identifying the result of the antigen sample analysis), and ICU (determining if the patient required admission to an ICU). Following all previous steps, min–max normalization was performed to convert all data values to a scale ranging from 0 to 1, as the features may not be near the normal distribution. Furthermore, after successfully completing data preprocessing and before applying the ML algorithm, a sufficient amount of synthetic data was generated for the minority class of the training set (obtained through the train–test split) as part of data balancing.

2.3. Selection of Machine Learning Classifier

Owing to their remarkable success and effectiveness, ML and deep learning algorithms have gained substantial attention in various domains, including in the prediction of ICU needs for COVID-19 patients. Although deep learning has attained significant prominence in certain tasks, ML algorithms offer robust results owing to their superior generalization capabilities and the transparency of their outcomes. Researchers globally employ diverse ML algorithms to predict COVID-19 patients; however, XGB, a powerful, supervised ML algorithm, has exhibited robustness across a wide range of real-world applications [25]. For instance, Yan et al. [26] employed XGB to predict the mortality attributed to COVID-19. In addition, XGB was utilized in another study conducted by Awal et al. [27] to predict COVID-19 patients using inpatient facility data, leveraging its recursive tree-based decision system. Notably, XGB can assess the significance of each feature based on its cumulative usage in the decision-making process, thereby providing valuable insights into the feature importance. This information aids in identifying discriminative features, particularly those associated with clinically relevant parameters. Considering these factors, the proposed approach employed XGB, with its hyperparameters optimized using the HGSO technique. Equation (1) expresses the XGB objective function used to measure the model performance:

$$M\left(\theta \right)=L\left(\theta \right)+\Omega \left(\theta \right),$$

(1)

where $\theta$ denotes the parameters trained using the given data, $\Omega$ is the regularization term, and L is the training loss. The objective function defines the regularization term $\Omega \left(f_k\right)$ for a decision tree, as outlined in Equation (2):

$$\Omega \left(f_k\right)=\gamma T+\frac{1}{2}\lambda \sum _{j=1}^{T_L}{\omega }_j^2,$$

(2)

where $T_L$ denotes the number of leaves in a decision tree, $\gamma$ denotes the complexity of each leaf, $\lambda$ is a regularization parameter, and $\omega$ is the score of the leaves. Optimizing the objective function of XGB enables the change in model performance after a certain node split to be evaluated. If the performance of the decision tree in the XGB improves, the change is approved. Algorithm 1 shows the steps followed for XGB implementation.

To enhance the model performance, several hyperparameters must be optimized. The hyperparameters used in the proposed system are as follows:

• learning_rate: represents the shrinkage of each tree’s contribution.
• max_depth: specifies the maximum depth of the tree.
• Gamma: sets the minimum loss reduction required for further leaf node splitting.
• min_child_weight: defines the minimum instance load for a child node.
• colsample_by_tree: denotes the subsample of columns used to train each tree.
• subsample: determines the column ratio for tree building.
• alpha: represents the $L1$ regularization weight term.
• eval_metric: specifies the validation metric for validation data.

Tuning these hyperparameters in the COVID-19 dataset can enhance the performance of the ICU prediction models. In this study, various popular ML algorithms—Gaussian naïve Bayes (GNB), linear discriminant analysis (LDA), RF, KNN, light gradient boosting machine (LGBM), gradient boosting classifier (GBC), and linear regression (LR)—were utilized for comparison. Subsequently, their performances were evaluated and compared. Additional mathematical details about these classifiers can be found in standard textbooks and the literature [27,28].

2.4. Need for Hyperparameter Optimization and Proposed HGSO

The necessity for optimizing the specific hyperparameters used by the XGB classifier in this study arises from the fact that classification metrics, such as accuracy, sensitivity, and specificity, rely extensively on selecting appropriate hyperparameters. This requirement promotes the framing of this study as an optimization problem, as demonstrated in Equation (3):

$$\underset{h\in H}{min}J(XGB\left(h\right);H),$$

(3)

where $h=\{h_1,h_2,\cdots h_n\}\in H$ denotes the hyperparameters listed in

Table 1. The architecture of the HGSOXGB model with optimized hyperparameters.

Hyperparameters Symbol ($\mathit{h}\mathit{ϵ}\mathit{H}$)	Hyperparameters Name	Range	Optimal Value
$h_1$	learning_rate	[0.001, 1]	0.312896226
$h_2$	colsample_bytree	[0.5, 1]	0.5
$h_3$	gamma	[0, 1]	0.0622628129
$h_4$	max_depth	[1, 15]	14
$h_5$	subsample	[0.5, 1]	0.975913151
$h_6$	n_estimator	[1, 1000]	343
$h_7$	min_child_weight	[1, 30]	1
$h_8$	eval_metric		“logloss”

. The optimization problem is defined as follows: “select the optimal hyperparameters of XGB $\left(H\right)$ for which $J(·)$ is the minimum”. In this study, the kappa score loss obtained from a $k=5$-fold cross-validation of the training dataset was recommended as the fitness function $J(·)$, as expressed in Equation (4):

$$J=1-\frac{1}{5}\sum _{k=1}^5{\left. [\frac{2(TP\times TN-FP\times FN)}{(TP+FP)(FP+TN)+(TP+FN)(FN+TN)}\right]}_k$$

(4)

Hyperparameter optimization is required [29]. The HGSO technique, a metaheuristic algorithm, was employed to optimize the hyperparameters to precisely determine the necessity for ICU admission based on some preconditions of COVID-19 patients. This study adapted HGSO, a recent optimization technique that outperforms state-of-the-art optimization techniques; however, the original HGSO suffers from a random initialization issue, which often prolongs the convergence time and does not ensure that the highest global optimum is found. The existing problem with the traditional HGSO algorithm was addressed using the MH algorithm [23] to mitigate the population initialization problem of the traditional HGSO algorithm. The improved HGSO approach yields an enhanced convergence, requires fewer iterations, and achieves optimal values. Algorithm 2 illustrates the initialization process of the MH method. In this algorithm, the input parameters include the number of XGB hyperparameters in the population N, the number of XGB hyperparameters H, and the upper ($ub$) and lower ($lb$) bounds of each hyperparameter. The algorithm proceeded by allocating memory (line 1), initializing the first individuals randomly (line 2), generating an individual candidate, calculating the acceptance probability (lines 4 and 5), and accepting or rejecting the candidate based on a random number (lines 7–11). Finally, the MH-method-based initial parameters were adapted and returned (line 14).

The HGSO is an evolutionary and population-based competitive optimization algorithm that enhances exploratory and exploitative behaviors, and its tractability is challenging. Moreover, it addresses challenges posed by multimodal and local optima [19]. This draws inspiration from the cooperative behavior observed in animals; the search process is analogous to an animal’s response to hunger levels. In this context, evolutionary approaches are employed to modify and adapt processes to achieve high-quality outcomes and expedite convergence. The algorithm exhibits two characteristics during the search steps: exploration and exploitation. During the exploration stage, the randomness of the search space must be ensured to explore it comprehensively [19]. During the subsequent exploitation stage, the algorithm narrows its focus to a specific region in the feature space identified during the prior exploitation stage [19]. In the lives of animals, hunger is responsible for motivation and motivates behavior and decisions. Equation (5) expresses the proposed HGSO algorithm:

$$\overrightarrow{X(t+1)}=\left\{\begin{array}{cc}{G}_1:\overrightarrow{X\left(t\right)}·(1+randn\left(1\right)),\hfill & r_l<1\hfill \\ G_2:\overrightarrow{W_1}·\overrightarrow{X_b}+\overrightarrow{R}·\overrightarrow{W_2}·|\overrightarrow{X_b}-\overrightarrow{X_t}|,\hfill & r_l>l,r_2>E\hfill \\ G_3:\overrightarrow{W_1}·\overrightarrow{X_b}-\overrightarrow{R}·\overrightarrow{W_2}·|\overrightarrow{X_b}-\overrightarrow{X_t}|,\hfill & r_l>l,r_2>E\hfill \end{array}\right.,$$

(5)

where t represents the current iterations, $\overrightarrow{X_b}$ denotes the position of the XGB hyperparameter for the top individual in this iteration, $\overrightarrow{W_1}$ and $\overrightarrow{W_2}$ denote the weights associated with hunger, $\overrightarrow{X_t}$ indicates the position of the hyperparameter of each individual, and l describes the experimental parameter for algorithm development. $\overrightarrow{X_t}·(1+randn\left(t\right))$ indicates how an individual performs a random search for food around its current position. The quantity $|\overrightarrow{X_b}-\overrightarrow{X_t}|$ denotes the range of movement of the current individual hyperparameters during the current iteration. The parameter E controls the degree of variation across all hyperparameter positions, and $\overrightarrow{R}$ serves as a range control parameter. Algorithm 3 outlines the steps followed in the proposed HGSOXGB framework. The HGSOXGB algorithm uses random numbers $r_1,r_2,r_3,r_4,r_5,r_6$ which belong to $[0,1]$.

Algorithm 3 Proposed HGSOXGB algorithm

Input: The H-dimensional hyperparameters of XGB applied on training data, maximum iteration (T), number of search agents or individuals (N), upper ($ub$) and lower ($lb$) bounds of H, sum of hungry of all individuals ($SHungry$), l. Output: HGSOXGB model and best-fit value 1: Initialize the HGSO hyperparameters using Algorithm 2. 2: while (t ≤ T) do 3:    Calculate fitness function $J(·)$ using Equation (4) 4:    Update the Best Fit ($BF$), Worst Fit ($WF$), and H-dimensional hyperparameters positions of XGB 5:    Calculate the $hungry$ using $hungry\left(t\right)=\left\{\begin{array}{c}0,AllFitness\left(t\right)=BF\hfill \\ hungry\left(t\right)+newHungry\left(NH\right),\hfill \\ AllFitness\left(t\right)\ne BF\hfill \end{array}\right.$ 6:    Calculate the weight $\overrightarrow{W_1\left(t\right)}=\left\{\begin{array}{c}hungry\left(t\right)·\frac{N}{SHungry}\times r_4,r_3<l\hfill \\ 1,r_3>l\hfill \end{array}\right.$ 7:    Calculate the weight $\overrightarrow{W_2\left(t\right)}=\left(1-e^{-\left|hungry\right(t)-SHungry|}\right)\times r_5\times 2$, 8:    for $k=1\sim N$ do 9:      Calculate E, where $E=sech\left(\right|J\left(k\right)-BF\left)\right|)$ 10:      Update $\overrightarrow{R}$, where $\overrightarrow{R}=2(1-\frac{t}{T})(2\times r_6-1$) 11:      Update the H-dimensional XGB hyperparameter position using Equation (5) 12:    end for 13:    $t=t+1$ 14:    Reintroduce the diversity by reinitializing 20% of the population every $⌊\frac{T}{3}⌋$ iteration using Algorithm 2. 15:    Check for NaN values in the population space and if any, reinitialize using Algorithm 2 16: end while 17: return BF and H-dimensional HGSOXGB optimized hyperparameters.

Unlike the original HGSO algorithm, the current approach integrates the VC2 operator to achieve a balanced exploration of the entire solution space and exploitation to refine the optimal solutions. This algorithm can better switch between diverse and concentrated searching, thereby enhancing the probability of obtaining optimal solutions. Additionally, the optimization process may occasionally lead search agents to converge to local optima. To effectively counter this, diversity in the population space was reintroduced by reinitializing 20% of the population every $⌊\frac{T}{3}⌋$ iteration using the proposed MH-based population initialization method (Line 14). The diversity outlined here helps the algorithm escape the local optima and converge towards a global solution. Furthermore, in some situations, the agent positions can turn into non-number (NaN) values owing to numerical instability and extreme values, rendering them unproductive for the ongoing search process. To ensure the contribution of each agent to the optimization, agents with NaN values in their positions are identified and subsequently reinitialized using Algorithm 2 (Line 15). For the convenience of the research community, a Python implementation of the algorithm is available at https://github.com/awalece04ku/HGSO_ICU, accessed on 5 September 2023.

2.5. Model Performance Analysis

To evaluate the effectiveness of the proposed ML scheme, various performance evaluation metrics—the accuracy (ACC), F1-score, Matthew’s correlation coefficient (MCC), kappa score, sensitivity (recall), and area under the curve (AUC)—were determines, along with an assessment of the confusion matrix. In addition, novel statistical parameters—Cramer’s V, phi-squared, classification success index (CSI), Pearson’s C, and Scott’s Pi—obtained from Pycm, a Python library for multiclass confusion matrices [30], were used for evaluation. Equations (6) and (10) summarize these evaluation measures.

Cramer’s V: it expresses the relationship between two nominal variables and ranges from 0 to 1:

$$V=\frac{\varphi }{\sqrt{min(r-1,c-1)}},$$

(6)

where $\varphi$ is the phi coefficient and r and c are the numbers of rows and columns, respectively.

Phi-squared: it shows the relationship between two binary variables:

$${\varphi }^2=\frac{{\chi }^2}{n},$$

(7)

where ${\chi }^2$ is the chi-squared statistic and n is the total number of samples in the dataset.

CSI: it is an overall measure defined by averaging the individual classification success index (ICSI), ranging from −1 to 1, over all classes:

$$CSI=\frac{1}{\left|C\right|}\sum _{i=1}^{\left|C\right|}ICSI,$$

(8)

where ICSI is 1 minus the sum of the positive predictive value and true positive rate, and $\left|C\right|$ is the number of classes.

Pearson’s C: it is known as the Pearson coefficient, ranging from −1 to 1, and represents whether two variables are dependent on each other.

$$C=\sqrt{\frac{{\chi }^2}{{\chi }^2+n}}$$

(9)

Scott’s Pi: it explains how two nominal data points are internally reliable:

$$\pi =\frac{p_r\left(a\right)-p_r\left(e\right)}{1-p_r\left(e\right)},$$

(10)

where $p_r\left(a\right)$ is the observed agreement and $p_r\left(e\right)$ is the expected agreement.

Moreover, an ROC curve, a precision–recall curve, a bootstrap ROC curve, and the recall rate vs. decision boundary were created to assess the classifier’s performance.

2.6. Feature Importance Using XGB

An analysis of the feature set revealed that certain features were less important or even irrelevant in predicting the need for ICU admission. The dominant features were sorted using XGB, and a graph was generated to display the feature importance values in descending order. The graph lists the features on the Yaxis, and the corresponding importance values are shown on the Xaxis. The XGB algorithm utilizes the “gain” metric to assess the relative significance of each feature. Furthermore, “gain” plays a crucial role in determining the optimal node split during tree construction in the training phase. The average gain was subsequently used to derive the final importance score for each feature. Equation (11) gives the mathematical formulation for calculating the gain:

$$Gain=\frac{1}{2}\left. [\frac{G_L^2}{H_L+\lambda }+\frac{G_R^2}{H_R+\lambda }+\frac{{\left(G_L+G_R\right)}^2}{H_L+H_R+\lambda }\right]-\gamma ,$$

(11)

where $G_L$, $G_R$, $H_L$, $H_R$ are the first-, first-, second-, and second-order gradient of the left, right, left, and right nodes, respectively. $\lambda$ and $\gamma$ represent penalty and regularization parameters, respectively.

3. Results and Discussion

Having developed the proposed MH-based HGSO algorithm, a preliminary benchmark analysis was conducted to assess its performance before analyzing its viability for ICU prediction.

3.1. Initial Benchmark Analysis

The effectiveness of the proposed HGSO algorithm was tested on four benchmark functions: Sphere, Ackley, Levy, and Schaffer. Subsequently, it was compared with the original HGSO algorithm using the same number of generations and iterations, resulting in the proposed HGSO algorithm outperforming the original algorithm. Appendix B provides the complete analysis of the benchmark functions from the Congress on Evolutionary Computation (CEC) benchmark and their graphical illustrations.

3.2. ICU Prediction Results

The preceding section demonstrated the superior performance of the HGSO algorithm on the CEC benchmark dataset. Therefore, the optimal values of the XGB hyperparameter, which significantly influences ICU prediction, were determined using HGSO, as presented in Table 1. Note that the same training and testing datasets were employed across all classifiers to ensure the consistency of the analysis.

3.3. Confusion Matrix

The principal diagonal cells of each confusion matrix, visualized in Figure 2, represent the percentage of correct classifications achieved by the proposed approach compared with state-of-the-art classification algorithms, i.e., GNB, LDA, KNN, RF, LGBM, GBC, and LR. In particular, as depicted in Figure 2a, out of 6758 ICU-no instances, 6527 were accurately classified, with only 231 misclassifications; in contrast, among 6768 ICU-yes instances, 6646 were correctly classified, with 122 incorrect classifications, achieving an impressive accuracy of 97.39%. Figure 2b–h shows the accuracy scores of the other leading classification algorithms. For instance, LGBM secured the second position in correctly classifying the need for ICU beds for COVID-19 patients, and GNB exhibited the lowest accuracy among the algorithms. Consequently, the proposed HGSOXGB was concluded to outperform traditional classifiers.

3.4. Comparative Performance Analysis of Different Classifiers

This study rigorously evaluated the performance of the proposed model against a set of cutting-edge classifiers, including GNB, LDA, KNN, RF, LGBM, GBC, and LR. A comprehensive evaluation was conducted using multiple robust metrics (the ACC, F_score, kappa score, MCC score, sensitivity, and AUC) to evaluate the effectiveness of each classifier (as detailed in

Table 2. Performance comparison with different classifiers.

Classifiers	Accuracy	F1-Score	Kappa Score	MCC	Sensitivity	AUC
GNB	66.42%	70.75%	32.86%	34.42%	81.30%	78.30%
LDA	75.44%	71.99%	50.87%	52.47%	63.15%	82.80%
KNN	87.59%	87.21%	75.17%	75.30%	84.70%	94.10%
RF	92.90%	92.67%	85.80%	85.97%	89.78%	97.00%
LGBM	93.66%	93.63%	87.33%	87.33%	93.19%	98.10%
GBC	82.46%	81.03%	64.92%	65.66%	74.96%	89.80%
LR	75.59%	73.71%	51.17%	51.69%	68.48%	82.80%
HGSOXGB	97.39%	97.37%	94.78%	94.79%	96.58%	99.10%

). The tabulated data clearly show that the proposed HGSOXGB exhibits the best results in terms of all the classification metrics. For example, the accuracy score and AUC value of HGSOXGB were significantly higher than 97%, surpassing those of all other classifiers, whereas GNB remained at the bottom position with respect to the performance evaluation metrics.

Table 3. Performance comparison with other models.

Classifiers	Cramer’s V	Phi-Squared	CSI	Pearson’s C	Scott’s Pi
GNB	34.42%	11.85%	34.45%	32.54%	31.33%
LDA	52.47%	27.53%	52.50%	46.46%	50.12%
KNN	75.30%	56.70%	75.30%	60.15%	75.15%
RF	85.96%	73.89%	85.96%	65.18%	85.77%
LGBM	87.33%	76.27%	87.33%	65.78%	87.33%
GBC	65.66%	43.11%	65.67%	54.89%	64.73%
LR	51.69%	26.72%	51.69%	45.92%	50.92%
HGSOXGB	94.79%	89.86%	94.79%	68.80%	94.78%

compares the performance of HGSOXGB in terms of additional overall statistical parameters, illustrating that the proposed framework outperforms the original XGB algorithm.

3.5. ROC, Precision–Recall, and Bootstrap ROC Curves

The ROC curve illustrated in Figure 3 clearly shows the superiority of the proposed HGSOXGB model compared with the other classifiers. Figure 3b presents the precision–recall curve, summarizing the relationship between the true positive rate and positive predictive value along the y- and x-axes, respectively, to predict the need for ICU admission for patients with COVID-19 using the proposed HGSOXGB model at varying probability thresholds. The bootstrapped ROC curve displayed in Figure 3c shows whether the bias in the training dataset is prevalent during the training phase. Employing N_boot = 100 for the bootstrapping, the estimation of a mean AUC exceeding 99% provided insights into the model’s robustness against potential training dataset skewness. Furthermore, calculating a 90% confidence interval for the bootstrap ROC curve provides an additional layer of statistical validity.

3.6. Recall vs. Decision Boundary

The recall rate represents the number of ICU cases that must be predicted from a complete dataset. For this investigation, the classification task has been accomplished, given that “ICU-no” and “ICU-yes” were equally important with a decision boundary threshold of 0.5, as visualized in Figure 4a,b. The graphical illustration exhibits that the HGSOXGB approach had the highest recall rate, at approximately 96.58% (also displayed in Table 2), implying that over 96% of the time, the proposed approach can accurately classify the necessity for ICU admission for COVID-19 patients.

3.7. Ten-Fold Cross-Validation Performance of the Proposed Model

This study includes the violin plot presented in Figure 5, which illustrates the cross-validation accuracy of the various models. The plot clearly shows that the proposed HGSOXGB outperforms the other models in terms of cross-validation accuracy. The white dots represent the median value, the thick gray bars in the center denote the interquartile range, and the upper and lower thin gray lines indicate the values 1.5 times the interquartile range. A wider section of the violin plot indicates a higher likelihood, whereas narrower sections indicate a lower probability. Furthermore, the analysis of variance (ANOVA) test indicated that the HGSOXGB results are statistically significant ($p<0.05$).

3.8. Feature Importance Using XGB

The dominant features that significantly affect the necessity for ICU care for COVID-19 patients were categorized using XGB. The feature importance plot of this study in Figure 6 reveals that “intubated” is the most important feature in predicting ICU requirement, followed by “pneumonia”. Note that features such as “otras_com”, “smoking”, “COPD”, and “asthma” substantially influence the prediction for ICU requirement for COVID-19 patients [13,31].

In addition to influencing ICU prediction, the XGB-based feature importance technique can assist national policymakers. For instance, when individuals exhibit symptoms such as colds, continuous coughing, sore throats, the loss or alteration of one’s sense of taste or smell, fatigue, headaches, aches and pains, diarrhea, and other respiratory infections, including fever, a coronavirus infection is suspected. In such cases, policymakers should encourage workers to engage in remote work to mitigate the potential spread of the virus within their workplaces and broader communities. Notably, novel variants remain a threat, although the pandemic is officially over. Therefore, the feature importance technique may contribute to broader public health endeavors to mitigate the impact of the virus.

3.9. Performance Comparison with Other Studies

The effectiveness of the proposed HGSOXGB model was compared with that of other contemporary studies using various performance indices. Some methods utilized the same dataset as in this study, whereas others were employed using their original dataset, and we attempted to replicate their approach and compare the proposed model accordingly.

Table 4. Performance comparison with other studies.

Studies	Dataset	Classifier	Accuracy	Sensitivity	Specificity	AUC
Cheng et al. [9]	Mount Sinai Hospital Data	Random Forest	76.2%	72.8%	76.2%	79.9%
Zhao et al. [32]	New York Hospital Data	Logistic Regression	-	-	-	74%
Famiglini et al. [33]	San Raffaele Hospital (OSR), Milan (Italy) Data	Decision Tree	-	76%	73%	86%
		Logistic Regression	-	83%	70%	83%
		Ensemble	-	85%	74%	88%
Heo et al. [13]	South Korean Data	Logistic Regression	-	-	-	88%
Wollenstein-Betech et al. [10]	Mexican Data	XGB	89%	-	-	55%
Proposed Method	Mexican Data	HGSOXGB	97.39%	98.17%	98.20%	99.10%

presents the comparison results, which indicate that the proposed model outperforms existing methods.

3.10. Limitations and Future Works

The proposed framework was evaluated using a benchmark and one of the largest single-center datasets; thus, a multicenter dataset was required to achieve a broader generalization, although acquiring such a dataset is time-consuming. Another noteworthy aspect of using multicenter datasets is the opportunity to test across various datasets, facilitating valuable generalization. Additionally, although the proposed framework relies solely on clinical data, additional data sources such as genetic data or data containing social determinants of health (SDH)—non-medical factors that influence health outcomes—will be incorporated in the future to improve prediction accuracy. Another limitation of the proposed technique is its reliance on ML models. In the future, deep learning models will be implemented to evaluate the proposed technique and converge to the optimal solution for predicting ICU admissions. Note that the source code of the proposed framework has been released, and researchers are encouraged to contribute in this important area.

4. Conclusions

This study proposes an ML framework for predicting the need for ICU admission for COVID-19 patients based on clinical data using an XGB classifier with HGSO-optimized hyperparameters. Instead of randomly initializing the population, the MH method was adopted to enhance the performance of the proposed HGSO algorithm. The SMOTE algorithm was applied to the COVID-19 clinical data to balance the dataset. The proposed HGSOXGB achieved the highest accuracy and AUC values of 97.39% and 99.10%, respectively. Furthermore, XGB was used to identify pneumonia as the most crucial feature for predicting ICU requirements. Therefore, the dominant features categorized using the proposed XGB-based feature importance technique can significantly aid policymakers in imposing necessary rules during critical situations. This feature importance technique can then help safeguard communities from infections or pandemics caused by deadly viruses. Therefore, the findings of this study have the potential to predict individual ICU needs for COVID-19 patients and may be extended to other classification problems, such as asthma and diabetes.