This research is grounded in a retrospective analysis, leveraging a comprehensive patient dataset from the Department of Cardiovascular Medicine at Xuzhou Medical University Affiliated Hospital. The dataset spans records over the last four years, including individuals diagnosed with Coronary Heart Disease (CHD) and Type 2 Diabetes Mellitus (T2D), aiming to develop an intelligent diagnostic model. This model capitalizes on a diverse array of clinical and biochemical indicators for its analysis.

The study categorized examination indicators into clinical symptoms, biochemical markers, and ECG indicators, encompassing variables such as age, gender, duration of diabetes, history of hypertension, lipid profiles, and various ECG abnormalities.

For the biochemical indicator and ECG feature data, since the numerical distribution intervals of multiple indicators vary greatly, the min-max strategy is used for normalization processing. If the original data is distributed in the interval min,max, transform it to the interval min′,max′, the formula is as follows:(1)v′=min′+v−minmax−min(max′−min′).

For clinical status information, the collected indicator information can be structured and quantified to form a standardized numerical vector.

The study adhered to stringent ethical guidelines, with approval from the Medical Ethics Committee of Xuzhou Medical University Affiliated Hospital (Ethical Approval Number: XYFY-2022-0217) and Xuzhou Central Hospital (Ethical Approval Number: XCH-20240202). All patient data were anonymized and analyzed with utmost confidentiality to protect privacy.

The initial patient pool included 471 individuals with CHD, among which 221 were also diagnosed with T2D (T2D-CHD), and 250 had CHD exclusively (CHD-only). Additionally, 228 individuals with T2D but without CHD (T2D-only) were incorporated for comparative analysis. A thorough univariate examination of each clinical and biochemical indicator was conducted to narrow down the extensive list of potential biomarkers to a more focused subset.

In this step, we integrated indicators into a discriminant model based on their individual significance. This process was refined through iterative testing to identify an optimal set of indicators for disease diagnosis. To thoroughly evaluate the impact of these indicator combinations on diagnostic outcomes, we employed several statistical measures: (1)

Logistic Regression Coefficient (B): This metric quantifies the relationship between each independent variable and the outcome, with its sign indicating the direction of correlation. The coefficient is determined as follows:(2)B=∑(xi−X¯)∗(yi−Y¯)∑(xi∗yi).

The neural network classification model, with a fully connected double-hidden-layer architecture, showcases strong self-organizing and nonlinear mapping capabilities, depicted in Figure 1. A dataset of 699 samples—221 T2D-CHD, 250 CHD-only, and 228 T2D-only—with 68.2% for training and the remainder for validation (Table 1), it uses 21 indicators to distinguish between patient groups effectively.

To optimize performance and mitigate overfitting, we employed a 25% Dropout regularization in the second hidden layer and selected cross-entropy loss, ideal for classification due to its precision in assessing output-label discrepancies (Table 2). The Mini-Batch Gradient Descent (MBGD) algorithm facilitated training, focusing on minimizing cross-entropy loss to improve accuracy (Table 3).

Hyperparameter tuning followed a phased strategy, starting with broad adjustments to refine our search for the optimal hyperparameter set. This methodical tuning, alongside performance evaluation of each parameter set, guaranteed enhanced model performance on both training and validation datasets.

The logistic regression classification model, designed to diagnose T2D-CHD, incorporates L2 regularization within a generalized linear regression framework to mitigate overfitting. This model estimates the probability of T2D-CHD occurrence by applying the logistic function to linear combinations of selected indicators, optimizing its coefficients and bias vector through supervised learning. The basic model is:(6)y=L(W⋅X+B),where, the coefficient matrix W and the bias vector B are the parameters to be solved, which are determined by supervised learning on the sample set.

Logistic regression uses the logistic function L to correspond W⋅X+B to the probability p of the occurrence of a hidden state, and then determines the value of the dependent variable based on the size of p and 1−p, that is, whether it is T2D-CHD.

The logistic regression model's evaluation will also comprehensively encompass Accuracy, Recall, Precision, and the F-1 Score. These added metrics, indispensable for evaluating the model's efficacy in accurately diagnosing T2D-CHD cases, will provide a more detailed view of the model's overall diagnostic performance. (1)

Accuracy represents the proportion of true results (both true positives and true negatives) among the total number of cases examined. It is the most intuitive performance measure and it gives an overall effectiveness of the model. Accuracy is calculated as follows:(7)Accuracy=TP+TNTP+TN+FP+FN,Where TP is the number of true positives, TN is the number of true negatives, FP is the number of false positives, and FN is the number of false negatives.

The neural network model was assessed using a test set, with its classification performance depicted in Figure 2. The model distinguished T2D-CHD, CHD-only, and T2D-only groups with notable accuracy, though some outliers were observed. Figure 3 presents ROC curves for each classification indicator, showcasing discriminative capabilities with AUC values of 0.961, 0.964, and 0.977, respectively. Performance metrics, listed in Tables 6, 7, include an accuracy of 90.7%, recall of 90.78%, precision of 90.83%, and an F-1 score of 0.908, highlighting its diagnostic precision.

The logistic regression model, applying the 8 chosen indicators, showed proficiency in disease classification, as detailed in Tables 8, 9. It accurately classified the majority of cases across the three categories, achieving an accuracy of 90.13%, recall of 90.1%, precision of 90.22%, and an F-1 score of 0.9016, demonstrating reliable diagnostic capability.

The external validation of the neural network model, encapsulated in its classification confusion matrix and summarized in Tables 10, 11, confirmed its exceptional capability to accurately differentiate among the three patient categories. The model achieved an external validation accuracy of 90.57%, with closely aligned recall, precision, and F-1 scores of 90.62%, 90.55%, and 0.9058, respectively, affirming its robust performance and wide applicability.

Parallelly, the logistic regression model's external validation, meticulously detailed in Tables 12, 13, illustrated its commendable accuracy and consistency in disease state classification. This model's external validation metrics showcased an overall accuracy of 89.15%, complemented by a recall of 89.23%, precision of 89.12%, and an F-1 score of 0.8917, further reinforcing the diagnostic models’ reliability and effectiveness in a broader clinical context.