Many scholars have explored the applications of ML in the healthcare domain. Gilbert et al.⁷ discussed the use of AI and ML in healthcare and highlighted the regulatory challenges associated with adaptive algorithmic model updates. As the performance of ML models in healthcare improved over time, regulatory frameworks gradually shifted toward a dynamic approach. For instance, the Food and Drug Administration (FDA) proposed quality management systems and algorithm change protocols. Similarly, the European Union introduced comparable drafts, although their details remained underdeveloped. These studies suggested that innovative approaches to healthcare must align with novel regulatory methods to simultaneously enhance medical services and ensure patient safety. Syed and Es⁸ noted that the widespread adoption of IoMT devices not only enhanced the quality of healthcare services but also introduced significant challenges related to cybersecurity and data privacy. AI-driven security frameworks, leveraging ML algorithms and anomaly detection techniques, monitored threats in real-time and responded swiftly, thereby improving the cybersecurity of such devices. However, ethical concerns and regulatory implications associated with these technologies required further investigation to balance technological innovation with the protection of patient privacy. Gerke et al.⁹ proposed that a shift from product evaluation to a system-level regulatory perspective was critical for ensuring the safety and efficacy of medical AI/ML devices. However, this shift posed substantial challenges for traditional regulatory bodies. They recommended that regulators adopt a system-level approach to assess the overall safety of AI healthcare products, rather than focusing solely on performance testing. This approach offered new insights into the personalized development of healthcare services and the innovation of legal regulatory frameworks. Shinde and Rajeswari¹⁰ explored the application of ML techniques in health risk prediction, demonstrating their potential in processing electronic health record datasets. ML methods effectively predicted disease risks and provided decision support for physicians. The advantage of this technology lies in its ability to learn from historical data and optimize healthcare resource allocation through automated analysis. However, they emphasized the need for further research on its applicability in real-world scenarios and the associated ethical concerns. Mavrogiorgou et al.¹¹ conducted a comparative study on seven mainstream ML algorithms across various healthcare scenarios. These algorithms included Naïve Bayes, decision trees, and neural networks, among others, and were applied to the prediction of diseases such as stroke, diabetes, and cancer. The study revealed significant differences in algorithm performance across specific scenarios, highlighting the necessity of constructing a tailored algorithm selection framework based on data characteristics and medical requirements. This analysis provided theoretical support for improving the accuracy and reliability of medical AI models. Saranya and Pravin¹² reviewed advancements in ML for disease risk prediction, covering a technical overview, algorithm selection, and future research directions. The study demonstrated that ML remarkably improved the accuracy of medical predictions but faced challenges such as data privacy, algorithm interpretability, and regulatory compliance. This review offered a reference for applying ML in legal risk assessment and optimizing regulatory frameworks.

To sum up, existing literature generally emphasizes the extensive application potential of AI and ML technologies in the medical field, covering multiple aspects such as diagnostic assistance, risk prediction, and resource optimization. However, these studies also reveal the legal, ethical, and regulatory challenges faced in the process of algorithm deployment. On this basis, this study further analyzes the applicability and risk control mechanisms of ML models under the HIPAA regulatory framework. Meanwhile, it attempts to provide empirical evidence and feasible suggestions for the technical supervision of legal risks in internet healthcare through paths such as classification label standardization, model output structure constraints, and the introduction of future interpretability mechanisms.

Experimental design

This study employs an ML-based analytical framework, leveraging data from the HIPAA database to explore how ML technologies can enhance the regulatory capacity for legal risk management in internet healthcare. Specific methods encompass data collection and processing, construction and optimization of ML models, and risk assessment based on evaluation frameworks. The steps are detailed below.

Data collection and processing

The primary data source for this study is the HIPAA database, which contains comprehensive information on medical data privacy protection, including patients’ medical records, insurance details, and related usage data. The data types in the HIPAA database encompass both textual data, such as medical records and personal information, and numerical data, such as treatment costs and medical course details. Structurally, the data includes both structured and unstructured formats, with the latter primarily involving medical texts and images. Due to issues with data quality, such as missing values or noise, essential data preprocessing must be performed prior to analysis to ensure the accuracy of model training and risk assessment results.

Data preprocessing involves several critical steps. First, to eliminate outliers and erroneous data, noise reduction is applied to identify and rectify inconsistencies in the data. Next, considering the potential dimensional inconsistency in numerical data, the z-score normalization method is utilized. Specifically, z-score normalization transforms data into a standard normal distribution with a mean of zero and a standard deviation of one, which can be written as Eq. (1):

\(X\) represents the raw data value; \(\mu\) is the mean of the feature, and \(\sigma\) refers to the standard deviation. Through this standardized method, numerical data can be compared and analyzed on the same scale, which improves the model’s training effect and accuracy.

Furthermore, for textual data, the term frequency-inverse document frequency (TF-IDF) method is used for feature extraction. TF-IDF is a statistical approach to measure the importance of terms within a collection of documents. By calculating the frequency of each term in a document and its distribution across the entire document set, the method evaluates the significance of terms effectively. This approach enables the extraction of meaningful features from large volumes of textual data, providing essential inputs for ML model training. Consequently, the data processing steps establish a more reliable and accurate foundation for subsequent ML model development.

Selection and construction of ML models

This study selects a variety of common ML algorithms for experimental analysis and constructs corresponding models to predict and evaluate legal risks in internet healthcare. The algorithms selected include random forest (RF), support vector machine (SVM), DNN, and extreme gradient boosting (XGBoost).

The RF algorithm. RF is an ensemble learning method based on decision tree construction, which improves classification performance by integrating the prediction results of multiple trees. RF uses bootstrap sampling to randomly select subsets from the data for training, and votes on the predicted results of each tree¹³. Firstly, data cleaning is performed, including denoising and missing value processing, to ensure the quality of the training data. Each tree is trained independently, and the characteristic of RF is to adopt random feature bagging for each tree, rather than using all features¹⁴. This process enhances the diversity of the model and reduces the risk of overfitting. The equation for information gain is as follows:

\(IG(T,A)\) denotes the gain of feature \(A\) on the dataset \(T\); \(H(T)\) represents the entropy of the dataset; \({T}_{v}\) is a subset divided by a value \(\text{v}\) of feature \(A\).

When all trees have completed training, RF integrates the predictions for each tree by voting (for classification tasks) or averaging (for regression tasks) to make a classification decision. The integrated voting is expressed in Eq. (3):

\({y}_{i}\) indicates the prediction for each decision tree, and \(\widehat{y}\) refers to the final prediction.

Compared to traditional single decision trees, RF introduces randomness during the training process, specifically by incorporating randomness when selecting split attributes. This enhances the model’s diversity and robustness. In RF, each decision tree is constructed independently, and the final prediction is determined by voting among the predictions of all decision trees¹⁵. If the model contains n decision trees, each sample will have n prediction results. RF selects the class with the highest number of votes as the final prediction result by aggregating the votes across all trees. The flowchart for generating the forest in the RF algorithm is presented in Fig. 1.

The process of decision-making in the RF algorithm is displayed in Fig. 2.

The flow diagram of decision-making.

The SVM algorithm. SVM is a classification method based on the maximum margin hyperplane. It looks for a hyperplane in the high-dimensional space to separate different classes of samples, and the optimal hyperplane is the plane that maximizes the margin¹⁶.

Data preprocessing: SVM has high requirements for data standardization, and often uses the z-score standardization method to process numerical data. As a result, the data have a distribution with a mean value of 0 and a standard deviation of 1¹⁷.

Finding the hyperplane: Given the training data \(\{({x}_{1},{y}_{1}),\dots ,({x}_{n},{y}_{n})\}\), the SVM finds the optimal hyperplane by solving an optimization problem that aims to maximize the boundary spacing while guaranteeing that all data points are correctly classified. The optimization objectives are:

\(w\) denotes the normal vector of the hyperplane, and the constraint is: \({y}_{i}(w\cdot {x}_{i}+b)\ge 1\).

For nonlinear separable data, SVM utilizes kernel tricks to map the data to a higher-dimensional space to solve nonlinear classification problems. Common kernel functions include linear kernels, Gaussian kernels, and others¹⁸. The Gaussian kernel function is shown in Eq. (5):

\(x\) and \({x}{\prime}\) refer to the input vectors; \(\upsigma\) represents the parameters of the Gaussian kernel.

The DNN algorithm. DNN is a multilayer perceptron (MLP) structure that enables complex pattern learning through multi-layer networks. DNN has powerful capabilities in handling large-scale data and complex nonlinear relationships, particularly suitable for the classification and regression of complex data such as images and speech¹⁹.

Data preprocessing: Similar to SVM, DNN requires high standardization of input data, so z-score standardization is usually performed first. For text data, TF-IDF or word embedding methods are employed.

The DNN architecture is revealed in Fig. 3.

The DNN consists of an input layer, multiple hidden layers, and an output layer. Each layer includes a number of neurons, each connected to all the neurons in the previous layer, and a weighted sum is performed. The output is nonlinearly transformed by activation functions such as ReLU, Sigmoid, etc.²⁰. The neuronal calculation reads:

\({z}^{(l)}\) indicates a linear combination of the \(\text{l}\)-th layer; \({W}^{(l)}\) stands for the weight matrix; \({a}^{(l-1)}\) refers to the activation value of the previous layer; \({b}^{(l)}\) is the bias term; \(\upsigma\) represents the activation function. The cross-entropy loss function is commonly used to evaluate the predictive performance of a model, which is represented by Eq. (8):

\({y}_{i}\) refers to real labels; \({\widehat{y}}_{i}\) is predicted probability.

Selection and construction of XGBoost. XGBoost is an ensemble learning method based on gradient boosting, widely used for classification and regression tasks. It enhances the traditional gradient boosting algorithm by introducing a regularization term to control model complexity and prevent overfitting²¹.

Data preprocessing: Similar to other models, XGBoost requires data standardization and denoising prior to training.

Construction of tree models: XGBoost improves classification accuracy by incrementally building multiple decision trees. Each new tree is trained based on the residuals of the previous model, correcting the errors made in the prior iteration.

The loss function and regularization are expressed by Eq. (9):

\(l({y}_{i},{\widehat{y}}_{i})\) means the target loss; \(\Omega ({f}_{k})\) represents the regularization term.

Performance evaluation metrics

The evaluation metrics for the proposed model in this study include the F1-score, accuracy, precision, and recall. Accuracy measures the proportion of correctly predicted samples out of the total number of samples, and its calculation is defined as follows:

\(TP\) represents the number of positive samples correctly predicted as positive by the model, while \(TN\) denotes the number of negative samples correctly predicted as negative. Moreover, \(FP\) refers to the number of negative samples incorrectly predicted as positive; \(FN\) indicates the number of positive samples incorrectly predicted as negative. Precision measures the proportion of correctly classified positive samples out of the total number of samples predicted as positive by the classifier. The predictive ability of the model is directly proportional to its precision. The equation for precision reads:

The recall measures the ratio between the number of positive samples correctly classified by a classifier and the total number of positive samples. It mainly refers to the proportion of predicted positive text to actual emotional text. The calculation is given in Eq. (12):

Accuracy and recall constitute a pair of interdependent evaluation metrics, with high accuracy often accompanied by low recall, while high recall results in relatively low accuracy, presenting an opposing relationship between the two. The F1 score is the harmonic average of precision and recall, calculated as follows: