Data were retrospectively collected from coal miners who attended physical examinations at a hospital in North China between October 2021 and January 2022. After excluding incomplete data recorders, attendees younger than 18 years or older than 60 years, and participants with cardiovascular disease, 2,956 participants were included in the study for the prediction model.

All procedures were approved by the Research Ethics Committee of the Second People's Hospital of Shanxi Province and were conducted strictly in accordance with internationally recognized ethical standards for human research. All participants in this survey were aware of the research contents and precautions and participated voluntarily.

A review of the pertinent literature on carotid plaque and an analysis of the accessibility of predictors led to the identification of 27 potential factors: (1) Demographic characteristics: gender, age; (2) Physical examination indicators: height (HT), weight (WT), body mass index (BMI), systolic blood pressure (SBP), diastolic blood pressure (DBP); (3) Laboratory tests: total cholesterol (TC),triglycerides (TG), high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), fasting blood glucose (FBG), alanine aminotransferase (ALT), aspartate aminotransferase (AST), direct bilirubin (DBIL), total bilirubin (TBIL), alkaline phosphatase (ALP), uric acid (UA), platelet count (PLT), white blood cell count (WBC), creatinine (CRE); (4) Lifestyle habits: smoking, alcohol consumption; (5) Occupational factors: years of working experience, exposure to dust (rock dust and coal dust), exposure to hazardous gases (carbon monoxide and hydrogen sulfide); (6) Other indicators: fatty liver disease (FLD).

Cases were defined as whether participants were diagnosed with carotid plaque by carotid ultrasound. The diameters and IMT of the distal common carotid artery, the carotid bulb, and the proximal internal carotid artery were measured within 1–1.5 cm below the level of the bifurcation of the participant's internal and external carotid arteries by an experienced physician to observe the presence of atherosclerotic plaque.

To make full use of the data and evaluate the model's performance, we first randomly divided the dataset into a training set (70%) and a test set (30%), which were used for model training. To ensure the robustness and generalizability of our model, all the data in the training set were utilized in ten-fold cross-validation for model training.

The statistical analyses in this study were conducted using IBM SPSS 26.0. The data, which exhibited a normal distribution, were expressed as “`x ± s”, and t-tests were employed for comparisons between groups. The data, which did not exhibit a normal distribution, were expressed as “[M (P₂₅, P₇₅)]”, and rank-sum tests were employed for comparisons between groups. The data for categorical variables were expressed as percentages, and the Pearson χ² test was employed for comparisons between groups. The level of the test was set at α = 0.05 in this paper. R4.2.3 was employed for the purpose of feature screening, model construction, the generation of nomograms, and the assessment of the effects.

XGBoost, random forest, and LASSO regression were used to select the features from the training set as input variables, and the incidence of carotid artery plaque as the output variable to construct a logistic regression model. Considering the potential multicollinearity among different variables, which may lead to model instability, the study evaluated the features selected by three machine learning algorithms based on correlation statistical charts as part of model selection. The performance of the three models was compared by the area under the ROC curve (AUC), net reclassification index (NRI), and integrated discriminant improvement index (IDI), and ultimately selected the model with the best performance. Subsequently, the optimal model was used to construct a nomogram, which was evaluated using decision curves (DCA) and clinical impact curves (ICI).

A total of 2,956 individuals were included in this study, with a prevalence of carotid plaque of 10.52%. Patients who developed carotid plaque were older and had a higher prevalence in men compared to the no carotid plaque group. They also had higher BMI, systolic blood pressure, diastolic blood pressure, total cholesterol, triglycerides, LDL cholesterol, fasting blood glucose, alkaline phosphatase, white blood cell count, creatinine, years of working experience, a higher prevalence of fatty liver disease, and higher rates of alcohol and smoking. The statistical analysis revealed that there were significant differences in the predictors between healthy individuals and patients with carotid plaque (Table 1). Following the random allocation of the data, a total of 2,069 individuals were included in the training set, with a prevalence of carotid plaque of 10.54% (Supplementary Table S1), and a total of 887 individuals were included in the test set, with a prevalence of carotid plaque of 10.48% (Supplementary Table S2).

The correlation statistics chart in the training set demonstrates a robust correlation between the selected features (Supplementary Figure S1). Consequently, three machine learning algorithms were selected to filter the features and subsequently construct the prediction model.

In the XGBoost algorithm, the hyperparameters of the model are selected through cross-validation and random search. The optimal number of iterations of the model is obtained by monitoring the number of iterations of the model using the test data, thereby preventing overfitting (Supplementary Figure S2). The optimal number of iterations and the optimal hyperparameters of the model were then incorporated into the model. The relative importance of the features was determined by training the model on the training set. Features with the highest feature importance were extracted and plotted on a bar graph (Supplementary Figure S3). The five most important features were selected for the next step of model construction, and the resulting prediction model was named the “XGBoost model”.

In the random forest model, the minimum mean squared error and the Gini coefficient are employed as the pivotal hyperparameters in the training set to filter the features. The relative importance of the features is then plotted (only the top ten features are plotted, Supplementary Figure S4). Subsequently, the intersection of the top ten features is taken as the input variable for logistic regression analysis, and the constructed prediction model is designated as the “RF model”.

Finally, LASSO regression was employed to identify the most pertinent features. In the LASSO regression model, the value of λ was selected through cross-validation, and the maximum penalty parameter λ with the lowest mean square error within one standard deviation was ultimately selected (Supplementary Figure S5). A total of five meaningful variables were obtained under this λ for the subsequent model construction, and the constructed predictive model was designated as the “LASSO model”.

Logistic regression models were constructed using features selected by XGBoost, Random Forest and LASSO regression, respectively. The data from the training and test sets were incorporated into the three models to generate their respective ROC curves (Figure 1). The AUCs of the three models in the training set are 0.846, 0.846 and 0.852, respectively. The AUCs of the three models in the test set are 0.817, 0.815 and 0.817, respectively. The AUCs of the “LASSO model” in the training and test sets are higher than those of the other models, although the differences are relatively minor.

The accuracy of the three models in the training cohort and test sets was evaluated by the net reclassification index (NRI) and the integrated discrimination improvement index (IDI), respectively (Table 2). It can be seen that the accuracy of “XGBoost model” is slightly better than the other models. There was a strong correlation between the characteristics of “RF model” and “LASSO model”, including systolic blood pressure (SBP) and diastolic blood pressure (DBP), total cholesterol (TC) and low-density lipoprotein cholesterol (LDL-C) (Supplementary Figure S1). The inclusion of variables with strong correlations in a predictive model can lead to an increase in the variance of parameter estimates, which in turn reduces predictive accuracy. In severe cases, anomalies may occur in which the predictive model does not reflect the relationship between the input and output variables, but rather their joint influence on the output variables. Therefore, the “XGBoost model” is chosen as the final model in this study, and the formula of the model is shown below:P=e−13.5554+0.1544×Age+0.0349×DBP+0.3557×HDL−C+0.0754×WBC+0.0092×BMI1+e−13.5554+0.1544×Age+0.0349×DBP+0.3557×HDL−C+0.0754×WBC+0.0092×BMI

A forest plot was constructed based on the characteristics of the “XGBoost model” (Figure 2). It was found that age, diastolic blood pressure (DBP), low-density lipoprotein cholesterol (LDL-C), and white blood cell count (WBC) were the risk factors for carotid artery plaques among coal miners, with odds ratios (ORs) greater than 1 and statistically significant differences.

A nomogram was constructed using the features from the XGBoost model to assess the risk of carotid plaque in miners (Figure 3A). Using the first sample in the training set as an example, a nomogram was created to locate the risk score for age (Figure 3B). A straight line was drawn vertically on the “scores” axis to determine how many scores correlate with the risk for age. This process is repeated for each trait, with the sum placed on the “total points” axis. Finally, a straight line is drawn vertically down to give the risk of carotid plaque in miners.

In parallel, the decision curve analysis (DCA) and clinical impact curve (CIC) of the nomogram were plotted on the training and test sets. The prevalence of carotid plaque in miners was found to be approximately 13.06% in the previous study, thus serving as the baseline prevalence of carotid plaque in miners to plot the DCA and CIC. The analysis of the decision curves revealed that the threshold range of the nomogram in the training set was 0.02–0.40, with the highest net gain of 0.88 (Figure 4A). In the test set, the threshold range was 0.03–0.42, with the highest net gain of 0.82 (Figure 4B). The results of the DCA were used to plot clinical impact curves, which were employed to assess the clinical utility of the nomogram. The results of the clinical impact curves demonstrated that the predicted probabilities were in good agreement with the actual probabilities (Figure 5A), and similar results were obtained in the test set (Figure 5B).