Machine Learning for Assessing Vital Signs in Humans in Smart Cities Based on a Multi-Agent System

Abstract

Healthcare professionals face numerous challenges when analyzing data and providing treatment, including determining which parameters to measure, the frequency of measurement, i.e., how frequently to measure them, and the responsibility for monitoring patient health with new medical devices. Machine learning (ML) techniques are efficient predictive models used to improve early prediction of patient care and reduce the cost of implementing healthcare systems. This study proposes a new model (data prediction and labeling using a negative feature based on a multi-agent system (PLPF-MAS)) that provides a smart city-based healthcare system for the continuous monitoring of patients’ vital signs, such as heart rate, blood pressure, respiratory rate, and blood oxygen saturation. It also predicts future states and provides suitable recommendations based on clinical events. The MIMIC-II database of the MIT physio bank archive is used, which contains 1023 patient records. Additionally, the EHR dataset is used, which contains 10,000 patient records. The models were trained and evaluated for six bio-signals. The PLPF-MAS model is distinguished from traditional methods in its advanced system, which combines the activities of several agents and the intelligent distribution of responsibilities among them. The LR agent measures the model’s reliability in parallel with the AE-HMM agent to predict the Prisk; it then sends the data to a coordinator and a supervisory agent to monitor and manage the model. Our model is characterized by strong flexibility and reliability, the ability to deal with large datasets, and a short response time. It provides recommendations and warnings about risks, and it can predict clinical states with high accuracy. The new model achieved an accuracy of 98.4%, a precision of 95.3%, a sensitivity of 99.2%, a specificity of 99.1%, an F1-Score of 97.1%, and an $R^2$ of 98%, when the MIMIC-II dataset was used. Conversely, it achieved an accuracy of 93%, a precision of 92%, a recall of 94%, an F1-Score of 93%, an AUC-ROC of 94%, and an AUC-PR of 89% when the EHR dataset was used.

1. Introduction

Urban infrastructure improvements, commercial development, and data center installation have been investigated in the literature [1]. Furthermore, smart tourism, smart driving, and digitalization have aided the growth of the digital industrial economy [2]. The IoT contributes to the development of smart cities by collecting data from different areas that contribute to improving people’s lives [3,4,5,6]. In the IoT, Wireless Sensor Network (WSN) nodes serve as the underlying technical backbone [7].

IoT devices and sensors collect various data from different events and conditions, including temporal and geographical data. These tools are becoming smarter and are quickly able to communicate and perform complex tasks [8]. The IoT continuously collects data through diffuse devices worldwide [9] and contributes to different fields, such as healthcare, disaster management, and learning [10]. The use of artificial intelligence (AI) to improve healthcare is a major challenge due to advances and new research in medicine [11]. Consequently, the software and infrastructure of healthcare that are supported by IoT must be developable to accommodate the latest updates in the field [12]. Data analysis and decision-making based on IoT are important issues in the healthcare system, in addition to monitoring vital signs to predict the patient’s future state [13]. Indeed, patient lives could be at risk, especially people who live alone, so monitoring data and vital signs is very important [14,15,16]. However, the development of healthcare applications and software is a major challenge for developers due to the important, sensitive, and varied information related to patients, diseases, and treatment. However, medical applications and software based on IoT must be extremely accurate to analyze data and provide treatment, with legal approval from medical expert committees [17,18].

Professional, relevant information helps in monitoring serious cases and long-lasting diseases. Still, analyzing this information produces open questions like the parameters to be measured, the frequency of measuring, and the responsibility of new medical devices to monitor a patient’s health [19]. Machine learning (ML) approaches are considered more efficient predictive models that use signs or other relevant patient data [20]. Early detection is essential to preventing declines in health; furthermore, early prediction optimizes patient healthcare and reduces the cost of implementing related systems [21].

The contributions of this study are as follows:

• To create a new model called PLPF-MAS. This model consists of a multi-agent system that distributes tasks to independent agents (LR, AE, HMM, a coordinator, and a supervisor), making the model robust and expandable.
• To improve the reliability of the model using two criteria (Prisk, $R^2$) to make decisions, provide warnings, and make recommendations.
• To reduce data noise using an AE agent that compresses data by extracting important features to ensure the best training for the HMM agent.
• To monitor and manage the model using a supervisory agent to retrain it depending on the risk state.

2. Related Work

An ML approach with a Kalman filter was employed to recognize movements related to various signals. This work demonstrated the efficiency of ML techniques, which are far better than the classical signal processing methods used in smart application analysis [22]. Heart rate, blood pressure, and respiration were analyzed using a switching linear dynamic model whose function is identical to the Gaussian Learning Model (GLM). This model produced an accuracy of 74%, whereas the accuracy of GLM was 35.3% [23]. Several investigations have been conducted to determine applications for ML techniques, showing that when mobile health data are used in smart applications, health conditions improve [24].

One study investigated a plausible analytical transformation related to digital health data. The objective was to use digital health data drawn from wearable sensor-based smartphone devices [25]. Structured and unstructured health information was analyzed using machine learning, artificial intelligence, and natural language processing methods to detect the level of risk among patients [26]. In another study, the authors developed a cognitive dynamic system for a smart e-health system to automatically screen defective or abnormal datasets [27]. A defective dataset may have poor labeling and/or insufficient training patterns. To mitigate the adverse effect of such a defective dataset, a decision-making system inspired by human decision-making processes used in cases of conflicts-of-opinion (CoOs) was developed [28].

Our hybrid system uses ML social Internet of Things (SIoT) to address the problem of distributing medical services efficiently and overcoming the challenges of traditional models. It does so by favoring the social relationships between the objectives so that patients can access services quickly [29]. The Internet of Medical Things (IoMT) plays a role in the development of the healthcare system in smart cities. Its main function is to provide continuous monitoring and check the patient’s health state, which improves the quality of the healthcare system [30]. We present a proof-of-concept implementation of this framework to automatically identify people experiencing arrhythmia using single-lead electrocardiogram (ECG) traces. The proposed CDS algorithm performs well with diagnosis errors and can be incorporated into the autonomic computing layer of smart-e-health–home platforms to achieve a pre-defined degree of screening accuracy in the presence of defective datasets [31]. An IoT-based non-invasive automated patient discomfort-monitoring detection system is presented and implemented, using a deep learning-based algorithm. The system is based on an IP camera; the patient’s body movement and posture are detected without wearable devices. The Mask-RCNN method extracts different key points from the patient’s body. These key points are then associated with six major body organs using data mining association rules [32].

This study was conducted using ECG and sleep audio signals. The ECG data included RMSSD, SDNN, and pNN50, and audio analysis produced parameters such as spectral moments, components, and MFCCs. Then, these parameters were used as inputs in a radio-frequency classifier, which was previously trained to recognize different types of breathing events (normal, snoring, gasping, and wheezing) [33]. An autoencoder model (AE) reduces the dimensions of the healthcare dataset and then reconstructs this compressed data. This improves the classification of a Multilayer Neural Network [34]. LSTM improves the accuracy of risk assessment for patient health states by analyzing the EHR dataset to determine the risk state in order to monitor the critical condition. The LSTM model results are superior to traditional models in risk assessment, leading to enhanced decision-making in healthcare [35].

A hidden Markov model is used to predict the onset and progression of (SARS-CoV-2) infection using heart rate variability (HRV) data from smart wearable devices. The HMM is trained on a dataset prepared by the Welltory Lab, which includes participants’ self-reported (SARS-CoV-2) symptoms and HRV measurements. The data used depends on the hidden and observed states [36].

The HMM model is a probabilistic model based on highly correlated HR data used to predict BP. Consequently, these vital signs do not require continuous measurement to be monitored, saving time and energy. The dynamic thresholds used in this system are calculated using the 3-sigma method, depending on interruptions in the previous data, to determine if vital signs are normal or within risk ranges. The HMM model is trained using data from patients with elevated heart rates and blood pressure, classifying sequences into “critical” (tachycardia and hypertension) and “normal” states based on the probability of the observed sequence in each model. Only critical data is stored during interruptions, reducing memory usage and transmission needs upon reconnection. The Viterbi algorithm estimates the most probable hidden states (blood pressure) from the observed heart rate data to develop a reliable and energy-efficient method of continuously monitoring vital signs in elderly patients using an HMM. This addresses the challenges of data loss and high energy consumption [37]. The importance of monitoring the clinical state of people at home improves models used to predict future vital signs and clinical events [38].

In a model based on MAS for managing and evaluating the interaction between devices, a dynamic trust source is created using assessments, which helps to eliminate invalid agents and devices [39]. A multi-agent system can enhance accuracy and improve results for patients, simplifying operations and clinical decisions [40]. A multi-agent system is used to make the devices connect and cooperate in order to make decisions flexibly and independently, using learning models to meet patient needs [41]. A multi-agent system can deal with a linguistic model for prior authorization in healthcare, where a special agent checks a patient’s clinical records and compares them with clinical instructions to provide justifications and interpretations based on decisions [42] (Table 1).

Table 1. Summary of previous works.

Ref.	Method	Aim	Merits	Demerits
[30]	IoMT	Provides continuous monitoring and checks the patient’s health state in smart cities	Continuous monitoring and improved care efficiency	Data privacy, infrastructure costs, and complexity
[31]	CDS	Automatically checks human health conditions (healthy and unhealthy)	Simple and fast	Low accuracy
[32]	Mask-RCNN	Classification of movements associated with normal or abnormal conditions of patients	Speedy responses, privacy, low costs, and flexibility	Needs powerful computing, is complex, and has difficulty dealing with noise
[33]	SRBDs	Develop, evaluate, and diagnose the system	Strong classification, accuracy, low costs, and low hassle	Conducted a preliminary study of clinical data, but only a small sample was used
[34]	AE	Enhances the accuracy of medical classification	High classification accuracy	Limited data; lacks applicability
[35]	LSTM	Improves the accuracy of risk assessment	High accuracy; supports clinical decision-making	High costs and difficulty with interpretation
[36]	HMM	Predicts the onset and worsening of SARS-CoV-2 infection	Early detection and non-surgical intervention	Limited data and scope
[37]	HMM	Monitoring of vital signs in elderly patients	Accuracy, adaptability, reliability, and energy conservation	Limitations, complexity, and reliance solely on the accuracy of the data used
[38]	HMM, PCA	Predict abnormal clinical events	High accuracy; analysis of hidden correlations	Restricted evaluation; need more cloud resources
[39]	Agent-Based Trust	Enhances the security of smart cities	Manages agent trust; reliable interactions	Complexity, slow evaluation, and consumption of resources
[40]	MAS	Improves and simplifies the healthcare system and supports clinical decisions	High accuracy; more efficient	Low data accuracy; high costs
[41]	MAS	Prevents IoT medical data duplication and reduces costs	High flexibility and scalability	Overhead communication; complexity
[42]	MAS	Uses different large language models to calculate the accuracy of performance	High efficiency and transparency	Complex; agents must be tuned

Previous studies have relied on multiple methods to classify and analyze data and have faced multiple challenges in converting this data into real-time and reliable decisions for clinical cases due to a lack of data quality verification. There have also not been many investigations into response times, which are important in healthcare. Consequently, this study provides a new model, PLPF-MAS, for analyzing and classifying data, real-time decision-making, providing recommendations, and reducing response times. This model is classified using observed and passive features based on a multi-agent system, and the results are compared with studies by [35,38].

2.1. The Taxonomy of the Methods

Healthcare methods for monitoring and diagnosis.

2.1.1. Signal-Based Analysis

• Electrocardiogram (ECG) Analysis
  • Cognitive Dynamic System (CDS) [31]: This method automatically screens for arrhythmias from single-lead ECG traces, even with defective datasets, and can develop a decision-making system inspired by human conflict-of-opinion (CoO) processes.
  • Sleep-Related Breathing Disorder (SRBD) Analysis [33]: This method develops, evaluates, and diagnoses SRBDs. This technique uses ECG data (SDNN, RMSSD, and pNN50) and sleep audio signal parameters (spectral moments; MFCCs) as inputs for a radio-frequency classifier.
• Vital Parameter Monitoring [43]: This method monitors health in real time through vital parameters. It employs a Random Forest algorithm to accurately classify health-related data.
• Biomarker Pattern Identification [44]: This method predicts in-hospital cardiac arrest (IHCA). It uses robust statistical methods to identify unique biomarker patterns (e.g., low systolic blood pressure and fluctuating heart rates).
• +Heart Rate Variability (HRV) Analysis:
  • SARS-CoV-2 Prediction [36]: This predicts the onset and progression of SARS-CoV-2 infection. It employs a hidden Markov Model (HMM) trained on HRV data from smart wearable devices.
  • Blood Pressure Prediction [37]: This method predicts blood pressure based on heart rate data. It employs a Probabilistic HMM model with dynamic thresholds.
• EEG Signal Analysis [45]: This method predicts student attentiveness during online learning. It uses machine learning (Logistic Regression, SVM, and Ridge Regression) to classify EEG data. Feature importance analysis (CART, Random Forest, and XGBoost) and clustering algorithms (K-means; hierarchical clustering) are also used.

2.1.2. Image/Video-Based Analysis

• Patient Movement and Posture Detection [32]: This method performs non-invasive automated patient discomfort monitoring. It employs the Mask-RCNN method, which extracts key points from the patient’s body using an IP camera.
• Human Activity Recognition (HAR) [46]: This achieves real-time HAR using data from a smartwatch. It uses a pre-trained ResNet50 deep neural network to classify images based on histograms generated from the raw accelerometer and gyroscope data.

2.1.3. Combined Data Analysis

Hypertensive Disorders in Pregnancy Detection [47]: This method aims to detect hypertensive disorders during pregnancy early. It employs an electronic prototype that acquires blood pulse and weight data transmitted via Bluetooth and processes it using Random Forest.

This taxonomy categorizes the methods based on the type of data they analyze and further breaks down the specific techniques and aims within each category, as shown in Figure 1.

Figure 1. Taxonomy of methods.

2.2. Initial Analysis

Vital signs are interrelated and provide important information that we can utilize to predict future clinical states [32]. For example, when the heart rate is abnormal, it indicates a problem in the heart, possibly because of low blood pressure; shock; congestive heart failure; or a benign cause, such as exercise. It is difficult to determine the reason without checking all vital signs. Consequently, it is important for specialists to continue monitoring vital signs.

In this study, two datasets were used for a reliable comparison with previous studies [35,38]. The first dataset used in [38] is the MIMIC-II database of the MIT physio bank archive [48], which contains 1023 patient records. This number represents the total number of patient records, which also contain vital sign records. Because these vital signs are presented in a continuous time series (extending over hours and days at unequal intervals), we separated each patient record using a segmentation method. These cases were solved by dividing them into fixed-length segments and recording clinical events every 30 min [38], as shown in Table 2. We used the vital sign values in Table 3 and classified them independently either as normal or abnormal cases, depending on the clinical event. Thus, from all patients, we created a new matrix, L, containing X rows and Y columns, where X is the number of samples after recording vital signs every 30 min for all patients. Consequently, new samples were created (2420 rather than 1023) to train the proposed model more efficiently, where multiple samples are taken from each patient’s records. In Figure 2a, each square represents a correlation coefficient between two corresponding variables on the horizontal and vertical axes of the MIMIC-II dataset, and the numbers within are the actual correlation coefficient values. This makes the relationship between HR, RR, ABP, and SpO2 easy to discern. The second dataset is the EHR dataset [49], used in [35], which contains 10,000 patient records. This dataset is also a continuous time series of vital signs (HR, RR, SpO2, and BP); thus, we separated each patient’s records according to the segmentation method. In Figure 2b, each square represents the correlation coefficient between its two corresponding variables on the horizontal and vertical axes of the EHR dataset, and the numbers within are the actual correlation coefficient values. This makes the relationship between HR, RR, SpO2, SBP, and DBP easy to discern.

Table 2. Clinical events and their codes.

Clinical Event	Clinical Code
Simultaneous Tachycardia, Hypotension, Tachypnea, and Hypoxia for More than 30 min	THTH
Simultaneous Bradycardia, Hypotension, Tachypnea, and Hypoxia for More than 30 min	BHTH
Simultaneous Tachycardia, Hypertension, Tachypnea, and Hypoxia for More than 30 min	TTTH
Simultaneous Tachycardia, Hypotension, Bradypnea, and Hypoxia for More than 30 min	THBH
All Six Bio-Signals Are in the Normal Range	NNNN

Table 3. Vital signs and normal values.

Bio-Signal	Normal Range	Vital Sign
Heart rate	60–100 beats per min	HR
Systolic blood pressure	90–120 mmHg	SBP
Diastolic blood pressure	60–90 mmHg	DBP
Arterial blood pressure	60–110 mmHg	ABP
Respiratory rate	12–18 breaths per min	RR
Blood oxygen saturation	95–100%	SpO2

Figure 2. (a) Correlation matrix for HR, RR, ABP, and SpO2. (b) Correlation matrix for HR, RR, SpO2, SBP, and DBP.

Figure 3a,b present the distributions of each type and how these distributions overlap or diverge across different heart rates, showing complex relationships and types that may not be determined through numerical correlations, especially with influential differences, such as HR of the MIMIC-II dataset and the EHR dataset.

Figure 3. (a) Pair plots for HR, RR, ABP, and SpO2 by HR category. (b) Pair plots for heart rates, respiratory rates, systolic BP, diastolic BP, and oxygen saturation by HR category.

Clinical States and Vital Signs

To detect early clinical signs, we considered four vital signs (HR, RR, BP, and SpO2) dependent on six bio-signals, drawn from the MIMIC-II and EHR datasets (Table 3) [33]. These vital signs vary based on medical conditions, sex, age, etc. For example, the blood pressure of an elderly person in a normal case differs from that of a young person in an abnormal case. However, the common normal range has been determined by medical science researchers [35,36,37], as shown in Table 2. We can associate tachycardia and bradycardia with heart rate (HR) and hypotension; blood pressure (BP), tachypnea, and bradypnea with respiratory rate (RR); and hypoxia with blood oxygen saturation (SpO2).

3. Methodology

Through a data agent, our new model takes data from a healthcare dataset stored in the cloud through IoT devices. It then processes the data, divides it depending on the requests of other agents, and sends it to the LR and AE agents. The LR agent evaluates the data quality and confidence in statistical operations; it then processes in parallel with the AE agent, which reduces feature dimensions and sends the compressed data stored in a bottleneck to the HHM agent to enhance its performance. Then, the HMM agent decreases noise, extracts features, performs time modeling, and predicts states. The coordinator agent documents all phases that lead to the final decision. It also uses $R^2$ and risk probability rules for the final clinical status to provide important recommendations and sends notifications to a supervisory agent regarding error or risk states. Finally, the supervisory agent decides when the model must be retrained, corrects the model when it fails, manages policy, and records all decisions. Consequently, the multi-agent system achieves smart integration and makes a final decision in real time. Its components are implemented in parallel (not sequentially when using LR or AE-HMM without MAS), which increases the response time (each LR and AE agent is implemented at the same time); this is very important in real-time decision-making. The agents operate independently, so if one fails (the sub-agent), the others can complete their tasks; without MAS, each individual failure can cause the system to fail entirely, as shown in Figure 4. The steps of multi-agent systems are detailed in Section 3.2. For the model’s practical applicability, two real datasets are used. The first dataset was collected from the MIMIC-II database of the MIT physio bank archive, containing 1023 patient records [48] used by [38] to establish their baselines. Conversely, the EHR dataset was used by [35] to establish their baselines. We used two datasets to compare our model results for better reliability.

Figure 4. PLPF-MAS model diagram.

3.1. Predicting and Labeling Data Using the Passive Features Model (PLPF)

The proposed model predicts the best outcomes from the input data, using LR for linear data. To make real-time decisions, an AE with an HHM compresses the data, extracts important features, and processes it based on time series and MAS.

3.1.1. Linear Regression

LR establishes a relationship between the target variable and one or more independent variables to determine the best model for later use, as shown in Figure 5 and Algorithm 1. In this advanced model, the LR model processes the data in parallel with the AE-HMM model, where the LR model adds a completely independent layer to achieve high reliability by calculating the risk-flag. When the LR model finds the best relationship between the input data (HR, RR, SpO2, and ABP) and the probability of risk, the data is considered accurate when making a final decision. The model then evaluates a linear relationship among current data. LR with a multivariable can be defined as

$$y_{\phi }\left(x\right)={\phi }_0+{\phi }_1{x}_1+{\phi }_2{x}_2+\cdots +{\phi }_n{x}_n+a$$

(1)

where $y_{\phi }\left(x\right)$ is a hypothesis for a linear regression with a multivariable, and ($a$) is the bias. For the convenience of notation, $x_0=1$.

$$x=\left[\begin{array}{c}{x}_0\\ x_1\\ \begin{array}{c}{x}_2\\ ⋮\\ x_n\end{array}\end{array}\right] ϵ R^{n+1} \phi =\left[\begin{array}{c}{\phi }_0\\ {\phi }_1\\ \begin{array}{c}{\phi }_2\\ ⋮\\ {\phi }_n\end{array}\end{array}\right] ϵ R^{n+1}$$

Figure 5. Linear Regression Model with Multivariable Architecture.

Next, we need to find the transform for the $\phi$ matrix: ${\phi }^T= \left[\begin{array}{ccc}{\phi }_0& {\phi }_1& \begin{array}{ccc}{\phi }_2& \dots & {\phi }_n\end{array}\end{array}\right]$:

$$y_{\phi }\left(x\right)={\phi }^{T}x+a$$

(2)

In Equation (2), we multiply the ${\phi }^T$ matrix by the ($x$) matrix to determine the hypothesis for linear regression with a multivariable ($y_{\phi }\left(x\right)$).

The cost function depends on the following equation:

$$f_{\left({\phi }_j\right)}= {\displaystyle \frac{1}{m}}{\sum }_{i=1}^m\left(y_{\phi }\right(x^{\left(i\right)})-y^{\left(i\right)}) x_j^{\left(i\right)} for (j=0\dots n)$$

(3)

where ($n$) is the number of features, $x^{\left(i\right)}$ is the input (features) of the $i^{th}$ training samples, and $x_j^{\left(i\right)}$ is the value of feature $j$ in the $i^{th}$ training samples.

Algorithm 1 Linear Regression

Input: Training data X (features), y (target) Output: Weight vector, w Initialize weights, w, randomly or with zeros. Repeat until convergence:     y_pred = X · w     error = y_pred − y     gradient = X^T · error     w = w − learning_rate ∗ gradient Return w

3.1.2. Autoencoder Model and Hidden Markov Model (AE-HMM)

The HMM model is strong when it deals with short correlations, but it faces challenges when it deals with complex models with noise. To enhance model performance, the AE model can simultaneously process data to decrease noise, extract features, perform time modeling, and predict states by merging these models (AE-HMM).

• Autoencoder Model (AE): This is an unsupervised deep learning technique widely used in data analysis and processing. It is trained to reconstruct the input data, which helps extract important and hidden features. The simple autoencoder goes through several stages: encoding in Equation (4), which teaches it to compress the input; bottlenecking, which stores the encoded representation of the input; and decoding in Equation (5), which teaches it to reconstruct the output from the bottleneck, as shown in Figure 6. Reconstruction loss measures the error between the input and output (Equation (6)).
  

  Figure 6. Autoencoder model architecture.

$$z=f_e(\omega y_t+{\theta }_e)$$

(4)

where ($f_e$) is the activation function of the encoder, ($\omega$) is the prediction weights (predicted by machine learning) in the encoder step, ($y_t$) is the original input feature, (${\theta }_e$) is the theta (often called bias) value predicted via machine learning in the encoder step.

$$y_{de}=f_{de} (\omega z+{\theta }_{de})$$

(5)

where ($f_{de}$) is the activation function of the decoder, ($\omega$) is the prediction weights (predicted by machine learning) in the decoder step, ($z$) is the latent data that is saved in a bottleneck, and (${\theta }_{de}$) is the theta (often called bias) value predicted via machine learning in the decoder step.

Reconstruction loss is calculated using several methods, including mean squared error:

$${MSE}_{AE}={\displaystyle \frac{1}{n}} \sum _{i=1}^n{{{(y}_t}_{\left(i\right)}-{y_{de}}_{\left(i\right)})}^2$$

(6)

where (${MSE}_{AE}$) is the mean square error, ($n$) is the number of data points, ${{(y}_t}_{\left(i\right)}$) is the observed value, and ${y_{de}}_{\left(i\right)}$ is the predicted value.

• Hidden Markov Model (HMM): This is a statistical model within the machine learning framework that creates a relationship between a series of observations and the hidden data. This name was chosen because it is usually applied to systems where the basic processes are hidden or unknown. It tries to understand processes that occur through the effects of a series of variables. It is used either for prediction or classification and consists of two types of data: hidden states, basic variables that generate observed data but cannot be observed directly, and observations, Basic data that can be observed and processed to create a relationship between these data. Two types of probabilities are used: transition probabilities, the probability of moving between different hidden states, as in Equation (7), and emission probabilities, the probability of inferring certain outcomes in hidden cases, as in Equation (8).

The hidden Markov model is used on the latent data resulting from the AE model after it compresses the data and extracts the important features. This is inferred from Equation (4), where the data are stored in the bottleneck ($z$). The difference square between the original and compressed data is also called the loss data ($MSE$), which is calculated from Equation (6). $z$ and $MSE$ are then combined into one variable, $e$. This is calculated using Equation (7) to analyze the temporal relationship with the hidden states (h), which are inferred through the HMM model (Figure 7) and Algorithm 2.

$$e=z+MSE$$

(7)

Figure 7. Hidden Markov model architecture.

The probability distribution of hidden cases ($h_t$) is found according to the following mathematical equation:

$$P\left(h_t|h_{t-1}\right)=H_{ij}$$

(8)

where ($h_t)$ is the current hidden status, ($h_{t-1})$ is the previous hidden state, and ${(H}_{ij})$ is the probability of transition from state ($i$) to state ($j$).

The probability distribution of the observed cases ($e_t$) is found according to the following mathematical equation:

$$P\left(e_t|h_t\right)=A_j\left(e_t\right)$$

(9)

where ($e_t)$ is the observed and reminder data at time ($t$), ($h_t)$ is the hidden data at time ($t$), and ($A_j\left(e_t\right))$ is the observed probability $\left(e_t\right)$ in state ($j$).

We can find the joint probabilities using the following mathematical equation:

$$P\left(e,h\right)=P\left(h_1\right)\prod _{t=2}^{t}P\left(h_t|h_{t-1}\right) \prod _{t=1}^{t}P\left(e_t|h_t\right)$$

(10)

We can find the Log-likelihood loss using the following mathematical equation:

$$L_{HMM}= -\log P(e,h)$$

(11)

where ($L_{HMM}$) is the log-likelihood loss, ($e$) is the sequence of observed data, and ($h$) is the sequence of hidden data.

The Viterbi algorithm is used to sequence the most probable hidden state, which provides the sequence of information. This can be defined by the following equation:

$${\delta }_t\left(j\right)={max}_i \left[{\alpha }_{t-1}\left(i\right)·H_{\mathit{ij}}\right]A_J\left(e_t\right)$$

(12)

The forward–backward algorithm comprises a forward algorithm used to calculate the total probability of sequences, as in Equation (13), and a backward algorithm used to determine the probability of viewing the rest of the information sequence, as in Equation (14).

$${\alpha }_{\left(j\right)}=\left[\sum _i{\alpha }_{t-1}\left(i\right)·H_{\mathit{ij}}\right]A_J\left(e_t\right)$$

(13)

$${\beta }_{\left(t\right)}\left(i\right)={\sum }_j\left[H_{ij}·A_J\left(e_{t+1}\right)·{\beta }_{\left(t+1\right)}\left(j\right)\right]$$

(14)

Algorithm 2 Autoencoder–Hidden Markov Model.

Input: Sequential data X Output: Hidden states sequence and trained AE-HMM  Step 1: Train Autoencoder Initialize encoder and decoder networks. Repeat for several epochs:     z = Encoder(X)     X_reconstructed = Decoder(z)    loss = ReconstructionLoss (X, X_reconstructed)     Update encoder and decoder parameters to minimize loss  Step 2: Train HMM on latent representation     Z = Encoder (X)         # Get latent features Initialize HMM parameters (A: transition, B: emission, π: initial state) Use Baum–Welch algorithm to train HMM on Z Return trained encoder, decoder, and HMM parameters

3.2. Multi-Agent System (MAS)

The multi-agent system merges the models (LR; AE-HMM) to convert the results from models into real-time action. This improves the model response time and provides an important clinical recommendation depending on the PLPF model. It divides the complex task of the model into subtasks and appoints an agent to each subtask. The coordinator agent interacts with all agents to make the final decision as show in Algorithm 3. The suitable agents of the model are determined as follows:

• Data Agent: This is the only source that provides data for the model, which obtains the healthcare dataset previously stored in the cloud. It then processes the data, divides it depending on the requests of other agents, and sends it to the LR and AE agents. It also notifies the agents if the data is ready and notifies the supervisory agents if their connection to the data source fails.
• Linear Regression Agent (LR agent): This is also called a reliability agent. It evaluates the linear relationship quality between the data and the risk-flag. The actions of this agent are divided into several steps, initially taking the data and risk-flag and dividing the data into training and testing sets to avoid bias. Then, it trains the LR model on the training data and ensures that the training process occurs in parallel with AE-HMM model training, followed by the measurement and verification phase. It does so to predict bias in the training model and to calculate the $R^2$ value by comparing it with the threshold value, as in [38]. This is followed by the communication phase, where the agents connect with the coordinator agent. The LR agent interacts with the coordinator agent to obtain recommendations and warnings depending on the $R^2$ value. It also interacts with the supervisory agent to retrain the model (LR) again if the $R^2$ value decreases. Therefore, the LR agent is important in making the final decision by declining weak evidence, thus decreasing the $R^2$ value. When the $R^2$value is compatible with the HMM, the warnings are more reliable.
• Autoencoder Agent (AE agent): This is also called the feature engineering agent. It obtains data from the data agent and then reduces the feature dimensions (ABP, HR, RR, and SpO2) and decreases noise based on the AE model, which acts in two steps: the encoder step, as in Equation (4), which leads to compressed features (z) that are sent to the HHM model to enhance its performance, and the decoder step, as in Equation (5), which leads to decompressed features (y_de) to used it in calculate error value, as in Equation (6). This determines the model’s capability in terms of feature reconstruction, consequently ensuring that the model can reliably reduce feature dimensions sent to the HMM model. Finally, the AE agent connects to the coordination agent and the supervisory agent to simplify the final decision.
• Hidden Markov Model Agent (HMM agent): This is also called the prediction agent. It models time series to predict the feature state of a patient (the probability of a future state of risk). It deals with transition probabilities, as in Equation (7), and emission probabilities, as in Equation (9), providing an accurate description of the data. The HMM agent processes the data with the Baum–Welch algorithm. This trains the model using incoming compressed data from the AE agent. It then calculates the probability of the created data from the training model and the states of the model using the backward–forward algorithm, as in Equations (12) and (13). It predicts the results based on the most likely value of the hidden state, which leads to a sequence of information using the Viterbi algorithm, as in Equation (11). Consequently, the HMM agent connects to the coordinator agent to send its prediction and risk probability values. It also sends the supervisory agent the final state reports (failure/success) to make the final decision.
• Coordinator agent: This documents all phases that lead to the final decision, using $R^2$ and risk probability rules for the final clinical status. It supervises and administers the data transfer agents, provides the notification, and manages the time limits on completing the processes of the other agents. It also applies logical tools to achieve all the conditions in Table 3 to provide important recommendations, and makes the final real-time decisions if the workflow is normal. In error or risk states, the coordinator agent sends a notification to the supervisory agent to fix the problem.
• Supervisory agent: This is the strategic structure of the model. It protects the model from any risk and maintains its stability, performance, and activities. It decides when the model must be retrained, corrects the model when it fails, manages policy, and records all decisions. For example, if the $R^2$ value is suitable, the process is stored in its log; otherwise, it sends a notification to retrain the LR agent.

Algorithm 3 Multi-Agent System (MAS).

Initialize Dataset D, Data Agent Initialize LR Agent Initialize AE Agent Initialize HMM Agent Initialize Coordinator Agent Initialize Supervisory Agent Define Recommendations:      TTHH→“Critical: Tachycardia + Hypotension + Tachypnea + Hypoxia. Immediate intervention.”      BTHH→“Serious: Bradycardia + Hypotension + Tachypnea + Hypoxia. Cardiovascular support required.”      TTTH→“Warning: Tachycardia + Hypertension + Tachypnea + Hypoxia. Monitor BP and provide oxygen.”      THBH→“Danger: Tachycardia + Hypotension + Bradypnea + Hypoxia. Respiratory failure risk.”      NNNN→“Normal: All vitals stable. Continue routine monitoring.”  Data Agent Stage for each raw_sample in D:      x = Data_Agent.preprocess (raw_sample) Training Stage      for each (x, label) in D:      LR_Agent.train (x, label)      latent = AE_Agent.encode (x)      AE_Agent.train (x, latent)      HMM_Agent.train (latent, label) Inference Stage for each x in D:      x_clean = Data_Agent.preprocess (x)      lr_out = LR_Agent.process (x_clean)      latent = AE_Agent.encode (x_clean)      recon = AE_Agent.decode (latent)      hmm_state = HMM_Agent.forward (latent)      message = {“lr”: lr_out, “latent”: latent, “recon”: recon, “hmm”: hmm_state}      predicted_state = Coordinator_Agent.classify (message)      recommendation = Supervisory_Agent.provide_advice (predicted_state, Recommendations)      output predicted_state, recommendation end for

4. Results

This section discusses hardware, simulation, and evaluation metrics for the PLPF model, consisting of LR, AE, and HMM; the model results; and a comparison with previous work.

4.1. Hardware and Simulations

The dataset processing and simulation were performed with the Google Colaboratory (Google Colab) platform, using the Python version 3.12 programming language. The simulation was run on standard hardware, available for free on Google Colab. The hardware comprises an Intel Xeon CPU, 12 GB of system RAM, and a Graphics Processing Unit (GPU) that runs on GPU acceleration (NVIDIA Tesla K80, T4, V100), provided by Colab for free. The effective calculations were performed using Python libraries such as NumPy, TensorFlow, pandas, sklearn, and matplotlib.

4.2. Evaluation Metrics

Automatic evaluation criteria are used to evaluate the performance of the proposed system. The model’s performance can be evaluated using many metrics; this depends on the evaluation parameters, which are true negative (TN), true positive (TP), false positive (FP), and false negative (FN). In this study, the following parameters were used.

4.2.1. LR Agent Evaluation Metrics

The LR agent evaluates the quality of metrics to ensure the model’s reliability. The most important evaluation metric is the R-square ($R^2$), also called the coefficient of determination. This is a statistical measure that represents the proportion of variance between a dependent variable that is explained by one or more independent variables. The agent measures the reliability through the $R^2$ and sends the result to the coordinator agent to provide it with the model’s reliability. When the value is closer to 1, the model has high reliability. When the value is closer to 0, the model has low reliability, or the linear relationship is very weak. The $R^2$ is calculated using the following equation:

$$R^2=1-{\displaystyle \frac{{SS}_r}{{SS}_t}}$$

(15)

where (${SS}_r$) is the residual sum of squares, and (${SS}_t$) is the total sum of squares.

4.2.2. AE Agent Evaluation Metrics

The most important measure used to train and evaluate the performance of the AE model is the mean squared error (MSE), that is, the mean squared difference between the resulting values and the original values, as in Equation (6). A low value for this measure indicates reliability in reducing original feature dimensions and the model’s capabilities in feature reconstruction, and vice versa.

4.2.3. HMM Agent Evaluation Metrics

The HMM agent predicts risk occurrence and focuses on true positive risk predictions, which are measured by the following metrics:

• Sensitivity (Recall): This measures small changes that cause large changes in value and is calculated using the following equation:

  $$Sensitivity \left(Recall\right)={\displaystyle \frac{TP}{TP+FN}}$$

  (16)
• Specificity: This predicts true negativity for all available categories and is calculated using the following equation:

  $$\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}={\displaystyle \frac{TN}{TN+FP}}$$

  (17)
• Accuracy: This is used to measure the percentage of correct predictions relative to the total number of predictions and is calculated using the following equation:

  $$Accuracy={\displaystyle \frac{TP+TN}{TP+FP+TN+FN}}$$

  (18)
• Precision: This finds the true positive ratio of the total positive predictions and is calculated using the following equation:

  $$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{TP}{TP+FP}}$$

  (19)
• F1-Score: This balances both measures and finds the harmonic mean of precision and recall. It is calculated using the following equation:

  $$\mathrm{F}1-\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}={\displaystyle \frac{2\times \mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\times \mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}}$$

  (20)
• AUC-ROC: The model can distinguish between classes represented by the area under the curve, which is calculated using the following equation:

  $$\mathrm{R}\mathrm{O}\mathrm{C}-\mathrm{A}\mathrm{U}\mathrm{C}={\int }_0^{1}TP\left(FP\right)d\left(FP\right)$$

  (21)
• AUC-PR: This is the integral of precision ($P$) with respect to recall ($R$) through the recall range. It is calculated using the following equation:

  $$\mathrm{R}\mathrm{O}\mathrm{C}-\mathrm{P}\mathrm{R}={\int }_0^{1}P\left(R\right)dR$$

  (22)

4.3. Training

The PLPF model uses a multi-agent system consisting of six agents to perform four major stages: data processing, sub-model training (LR, AE, and HMM), merging the results of the coordinator agent, and managing the policies of the supervisory agent. In the data processing stage, the data agent provides vital data by cleaning and extracting the time series. Then, in the sub-model training stage, the LR agent trains the LR model to connect vital values to five clinical states, the AE agent trains the AE model to compress based on reconstruction loss, and the HMM agent uses the compressed data from the AE agent to train time patterns and transitions. Then, the coordinator agent merges the results from those agents to make a final real-time decision, determine clinical states, and obtain recommendations. Finally, the supervisory agent monitors the agent’s performance and sends a warning if any errors or risks are detected.

4.4. PLPF-MAS Model Performance

The multi-agent system achieves high prediction accuracy in clinical states by merging its results with those of the LR and AE-HMM through the coordinator agent. In testing, the model has a strong ability to differentiate between five clinical states (THTH, BHTH, TTTH, BTHH, THBH, and NNNN). The coordinator agent achieves higher accuracy than the agents because it receives its information from three agents. The model achieves an accuracy of 98.4%, a precision of 95.3%, a sensitivity of 99.2%, a specificity of 99.1%, an F1-Score of 97.1%, and an R2 of 98%, and it is comparable to HMM-PCA [38] based on the MIMIC-II dataset, as shown in Table 4.

Table 4. Performance measures of each clinical state using PLPF-MAS and HMM.

Parameter	Method	BHTH	TTTH	THBH	NNNN
Accuracy	HMM	98.07	98.07	97.77	97.77
	PLPF-MAS	98.22	98.32	98.05	98.01
Precision	HMM	92.36	92.36	92.25	92.25
	PLPF-MAS	95.09	95.25	94.95	94.85
Sensitivity	HMM	98.51	98.51	97.03	97.03
	PLPF-MAS	99.15	99.15	98.27	98.36
Specificity	HMM	97.96	97.96	97.96	97.96
	PLPF-MAS	99.02	99.02	99.02	99.02
F1-Score	HMM	95.34	95.34	94.58	94.58
	PLPF-MAS	97.01	96.32	96.05	96.07
R2	HMM	NoN	NoN	NoN	NoN
	PLPF-MAS	98	98	98	98

Furthermore, PLPF-MAS achieves an accuracy of 93%, a precision of 92%, a recall of 94%, an F1-Score of 93%, an AUC-ROC of 94%, and an AUC-PR of 89%, and it is comparable to LSTM [35] based on the EHR dataset, as shown in Table 5. This indicates the PLPF-MAS model outperforms both HMM-PCA and LSTM in accuracy and reliability; the ability to determine normal and abnormal cases and avoid false negatives and false positives; and the ability to separate positive and negative categories.

Table 5. Performance measures using PLPF-MAS and LSTM.

Parameters	PLPF-MAS	LSTM
Accuracy	93%	87%
Precision	92%	89%
Recall	94%	86%
F1-Score	93%	87%
AUC-ROC	94%	92%
AUC-PR	89%	88%

The LR agent checks the data and calculates the $R^2$, which measures data reliability and the interpretability of the statistical samples. $R^2$ = 98% in all clinical cases, indicating that the data agent successfully provides high-quality data and segments data with regularity. In the parallel phase, the AE-HMM agent implements the prediction and classification processes and calculates the evaluation metrics (an accuracy of 98.4%, a precision of 95.3%, a sensitivity of 99.2%, a specificity of 99.1%, an F1-Score of 97.1%). This indicates that the AE agent effectively compresses data and reduces noise, which enhances the HMM agent’s implementation during all clinical cases and leads to good results. The R2 value indicates high-quality statistical data, while the accuracy, precision, sensitivity, specificity, and F1-Score indicate model strength. However, all are important, and they are sent to the coordinator agent for real-time decision-making.

4.5. Model Recommendations

After model training and performance, the coordinator agent merges the results. The HMM agent measures the most important risk probabilities, and the LR agent measures the statistical reliability. This ensures the validity of warnings, decreases false alerts, and detects data skewness. Consequently, the model uses rules to convert these alarms into recommendations. It can also use Prisk and the $R^2$ to give recommendations based on the five clinical states. If Prisk is very low and the $R^2$is very high, the model interprets an NNNN state and recommends the following: Continue routine monitoring. Patient’s vital signs are within normal limits. If Prisk is high, and the $R^2$is high, it interprets a THTH state and recommends the following: Administer IV fluids and monitor blood pressure closely. Consider vasopressors if hypotension persists. If Prisk is very high, and the $R^2$is high, it interprets a BHTH state and recommends the following: Initiate cardiac pacing or atropine administration. Monitor for signs of shock and improve blood pressure. If Prisk is medium to high, and the $R^2$is low, it interprets a TTTH state and recommends the following: Immediately assess airway and breathing. Provide oxygen; consider intubation. Address tachycardia and hypotension with fluids and vasopressors. If Prisk is very high, and the $R^2$is high, it interprets a THBH state and recommends the following: Extremely dangerous/immediate warning (see Table 6).

Table 6. Multi-agent system simulation results.

Index	Test Case	Analyzer Agent Response Time (s)	Recommendation Agent Response Time (s)	Clinical Event Code	Detailed Recommendation
0	Normal Vitals	0.2922	0.2845	NNNN	Continue routine monitoring; patient’s vital signs are within normal limits
1	Tachypnea, Tachycardia, Hypotension	0.1468	0.1555	TTTH	Immediately assess airway and breathing; provide oxygen; consider intubation; address tachycardia and hypotension with fluids and vasopressors
2	Tachycardia, Hypotension	0.2724	0.1199	THTH	Administer IV fluids and monitor blood pressure closely; consider vasopressors if hypotension persists
3	Bradycardia, Hypotension	0.1394	0.2880	BHTH	Initiate cardiac pacing or atropine administration; monitor for signs of shock and improve blood pressure

This indicates that the system can identify cases that need to be monitored, such as TTTH, and cases that require immediate intervention, such as THTH and BHTH. The normal values of the four vital signs (HR, RR, BP, and SpO2) depend on six bio-signals (Table 3) and are used to detect early clinical signs [33]. The normal range is determined by medical science researchers [36,37], as shown in Table 2, which is very important in the healthcare field because prediction results are represented by numerical values [35,38] and must be readable for AI technicians. Therefore, a human doctor cannot understand this prediction result. Consequently, we used MAS to make the result clear to physicians. Our recommendation will help doctors to make final decisions, depending on their experience in the medical field.

4.6. PLPF-MAS Response Time

The PLPF-MAS response time is the period during which new vital sign data are read by the coordinator agent to make a final decision. This interval must be very short (less than 1 s) to ensure the work is performed in real time. It is calculated by adding the time of data retrieval to the longest execution route among parallel agent routes, as defined by the following equation:

$$T_{total}=\mathrm{m}\mathrm{a}\mathrm{x}(T_{AE}+ T_{HMM},T_{LR})$$

(23)

Then, the fusion time and the final format are added. Especially when dealing with healthcare, time reduction is very important in ensuring that any warnings are received accurately. This allows medical staff to intervene in time, as shown in Figure 8.

Figure 8. Multi-agent system response time.

The time of the AE model is about 187 s. The MAS analysis time decreases to 0.2365 s, and the MAS recommendation time decreases to 0.2132 s. This is achieved using Python version 3.12 in Google Colab and an Intel Xeon CPU with 12 GB of system RAM. This reduces the MAS response time, indicating a very strong and efficient model. While the AE-HMM can take time to train and predict, the MAS can provide the user with a very fast response. This indicates that the MAS is suitable for the PLPF model.

Figure 9 shows the response times of AE-HMM and the MAS when dealing with clinical states. The figure indicates that for clinical states and recommendations, the MAS is highly efficient and responsive. This makes it suitable for real-time clinical decision support systems.

Figure 9. Response time of AE-HMM and MAS for individual clinical states.

Through study and comparison with previous works (Table 7), we have created a smart healthcare model characterized by strong flexibility and reliability, an ability to deal with large datasets, and a short response time. It can provide recommendations and warnings regarding risks and predict clinical states with high accuracy.

Table 7. Comparison of PLPF-MAS, HMM, and LSTM results and features.

Features	PLPF-MAS	HMM-PCA	LSTM
Number of bio signals	6	6	6
Vital signs	HR, BP, RR, SPO2	HR, BP, RR, SPO2	HR, BP, RR, SPO2
Clinical event	ANY	ANY	ANY
Number of normal samples	460 in MIMIC-II 1309 in EHR	700 in MIMIC-II Not measured	Not measured 13,535 in EHR
Number of abnormal samples	1960 in MIMIC-II 14,001 in EHR	1720 in MIMIC-II Not measured	Not measured 1775 in EHR
Accuracy	98.4% in MIMIC-II 93% in EHR	97.7% in MIMIC-II Not measured	Not measured 87% in EHR
Early prediction capability	Yes	Yes	Yes
Continuous monitoring support	Yes	Yes	No
Response time	Yes	No	No

5. Discussion

Previous methods face several challenges in analyzing complex medical data in smart healthcare, including the inadequacy of simple linear relationships, difficulty in handling high-dimensional data and noise, and difficulty in capturing nonlinear patterns and latent representations. These methods also have problems in modeling the time evolution of predictions. The new method (PLPF-MAS) represents a robust solution for real-time clinical risk prediction problems. It uses the Google Colab platform to process and simulate the MIMIC-II and EHR datasets using the Python version 3.12 programming language, an Intel Xeon CPU with 12 GB of system RAM, and a Graphics Processing Unit (GPU).

It is distinguished from traditional methods in its advanced system, which combines the activities of several agents and the intelligent distribution of responsibilities among them. The model depends on a linear regression agent to calculate the $R^2$to measure its reliability and reduce false alerts (false positive states), thus increasing its credibility with medical staff. The model also depends on an AE agent to measure its ability to compress data, reduce data noise, reconstruct data, and send compressed data to the HMM agent. This allows it to make predictions and calculate the probability of risk, allowing it to track the transmission of hidden states, as shown in Figure 5. For example, this may involve updating the patient’s state from a normal state to a risk case. In this situation, the coordinator agent detects risk depending on the Prisk and $R^2$values, providing warnings and recommendations based on clinical states. All of these records are sent to the supervisory agent to record all processes and to retrain the model’s management procedures based on risk states. This model’s structure can accurately identify subtle changes or unusual patterns in vital signs over time, enabling early intervention and improved understanding of a patient’s condition. This helps in uncovering subtle stages of disease progression or recovery that may not be apparent in static individual measurements. The model deals with complex data and overcomes the challenges of high-dimensional, noisy, and time-related healthcare data. These features allow the model to make clinical decisions more accurately and successfully clarify recommendations to medical staff.

6. Limitations

The proposed method does not include an analysis of patient demographics, such as age and sex. Furthermore, we did not study the security of the patients’ information against adversarial attacks, which can lead to data theft and alterations. Moreover, we did not study the privacy of the data between various agents in the MAS system. This study did not apply to real-life integration steps in operating systems or the planning of future clinical trials.

7. Conclusions

Previous studies have shown that central processing units (CPUs) experience many challenges in data analysis, specifically in converting data into real-time and reliable decisions for healthcare activities in smart cities. The HMM model has many problems that reduce its effectiveness, such as complex healthcare datasets, the assumption that the current observation depends on the current hidden state only, and observations that are conditionally independent of the hidden states. However, this assumption does not apply to real healthcare data, where prior observations can directly influence subsequent observations. Furthermore, nonlinear relationships are difficult to address, processing complex data is difficult, the number of hidden states is difficult to identify, and there are problems with overfitting and sparsity.

When performing experiments on the same datasets used in other studies, the proposed PLPF-MAS model outperformed the previous methods. This is due to the PLPF-MAS model’s use of a linear regression agent, which helps to address direct linear relationships and to calculate reliable statistics. It then uses an AE agent in parallel with an LR agent, which generates robust, nonlinear feature representations for complex and noisy data. The AE agent-compressed data is then used to model temporal dependencies and to detect hidden states and patterns as inputs to the HMM agent, making it an integrated model that outperforms the HMM alone in analyzing and processing complex healthcare data.

The PLPF-MAS model achieved an accuracy of 98.4%, a precision of 95.3%, a sensitivity of 99.2%, a specificity of 99.1%, an F1-Score of 97.1%, and an $R^2$of 98%. The previous method recorded an accuracy of 97.4%, a precision of 92.36%, a sensitivity of 98.51%, a specificity of 97.96%, and an F1-Score of 95.34%. Furthermore, the PLPF-MAS model uses multiple agents, facilitating task distribution between these agents and making the system more flexible. As such, it is an integrated model that outperforms the LSTM in analyzing and processing complex healthcare data for decision-making. The PLPF-MAS model achieved an accuracy of 93%, a precision of 92%, a recall of 94%, an F1-Score of 93%, an AUC-ROC of 94%, and an AUC-PR of 89%. The previous method recorded an accuracy of 87%, a precision of 89%, a recall of 86%, an F1-Score of 87%, an AUC-ROC of 92%, and an AUC-PR of 88%.

8. Future Work

Our future research will involve hardware that can collect real data from patients and analyze it by using the PLPF MAS model. We will also evaluate the model’s security and privacy regarding information. We will use integrated interpretability techniques, such as Shapley values, to provide interpretations for the decisions of the HMM agent based on compressed data from the AE agent; this will increase the reliability of medical staff regarding the model’s decisions. Our future study will also implement the model using cloud or edge computing.