The retrospective dataset was extracted from the electronic healthcare records of the health management center of the Third Xiangya Hospital. The records collected spanned from 2015 to 2021 and constituted the original set. The dataset consisted of 77,191 physical examinees who underwent a brachial-ankle pulse wave velocity (baPWV) test at the health management center. The exclusion criteria were as follows: (1) individuals who were unable to sign informed consent; (2) patients with a diagnosis of end-stage renal disease and aortopathy. Samples with massive missing data or excessive outliers whose irrationality was justified by the clinician were deleted, resulting in a final dataset of 77,134 individuals. All participants signed the informed consent form. The study was conducted in accordance with the Declaration of Helsinki and approved by the Ethics Committee of the Third Xiangya Hospital (No 2020-S609).

The dataset included a total of 82 features, which encompassed various types of information. These features included physical examination measurements such as body mass index (BMI), waist circumference (WC), and systolic/diastolic blood pressure (SBP/DBP). Laboratory indicators were also present in the dataset and included measurements such as fasting blood sugar (FBS), lipid profile, and renal function markers. Additionally, questionnaire information was collected, including previous diagnoses of diseases, lifestyle factors (diet preference, smoking, alcohol consumption, exercise habits, working and sedentary time, and sleep status), and health literacy regarding basic medical knowledge. For specific definitions within the dataset, alcohol consumption was defined as consuming more than 50 g of alcohol per week. The current smoking status was defined as smoking more than one cigarette per day. The baPWV measurements were obtained using a non-invasive measurement system called VP-2000 manufactured by Colin Co Ltd., Komaki, Japan. Trained medical staff performed the measurements in a room after the subjects had rested in a supine position for 10 min. Four pneumatic cuffs were attached to the bilateral arms and ankles to obtain pulse waves. The baPWV was automatically calculated using the formula (La-Lb)/Tba, where La represents the distance between the heart and ankle, Lb represents the distance between the heart and brachium, and Tba represents the time difference between the initial increase in the brachial waveform and that in the ankle waveform. Elevated arterial stiffness (EAS) was considered as baPWV≥1,400 cm/s (20).

Nineteen features in the original dataset are related to detailed questions about smoking, drinking, exercising, and work intensity, including types and frequency. To reduce the redundancy of the data, these data are not included in the analysis for now. If factors such as smoking and drinking prove important in later analyses, this part of the data will be specifically analyzed. However, since factors such as smoking and drinking were not considered highly important in subsequent analyses, no further specific analysis was conducted on these questions. If a sample has more than 30% of its variables missing, then the sample is deleted. Therefore, a total of 57 samples were deleted. For the remaining missing data, single-value imputation was used to handle features. Ultimately, 63 features and 77,134 samples were retained. The entire dataset was randomly divided into a training set (70%, 53,993 samples) and a test set (30%, 23,141 samples). In the test set, there were 13,600 samples for the non-EAS category and 9,541 samples for the EAS category.

Continuous measurement data conforming to the normal distribution were expressed as mean ± standard deviation, otherwise, the quartile was adopted, and the difference between categorical features was calculated using the chi-squared test. The difference of p < 0.05 on both sides was considered statistically significant.

In the field of machine learning, feature selection can eliminate irrelevant or redundant features, thereby reducing the number of features, improving model accuracy, and reducing runtime. Feature selection methods are mainly divided into three categories: filter, embedded, and wrapper methods.

Filter method: Features that did not show significant differences across categories meant they had no use for the prediction target and would be deleted.

Embedded: The features were input into the Lasso model for training after the filter method. The L1 regularization parameters were tuned using 10-fold cross-validation, and the coefficient would be shrunken to zero if their features were not important.

Wrapper: After filtering through Lasso regression, if there were still quite a number of features left, the wrapper method could be used for further selection. The working principle of recursive feature elimination (RFE) is to recursively remove features and build a model on the remaining features (in this case, the Lightweight Gradient Elevator (LGBM) is chosen), thereby determining which combinations of features contribute more significantly to the prediction results. Regarding the choice of the number of features, as we continuously increase the number of features, the AUC score of RFE-LGBM gradually increases and tends to stabilize. When the number of features reaches N, the AUC score reaches its maximum value. Adding more features will not enhance the model’s predictive capability, so ultimately, N features are determined for model building through RFE-LGBM.

Based on the common usage and the situation of data being selected at each step, we ultimately employed these three methods.

Four machine learning algorithms (logistic regression [LR], random forest [RF], extreme gradient boosting [XGBoost], and light gradient boosting machine [LightGBM]) were used to develop predictive models on the training data. Weights of different classes were assigned by setting parameters in the trained models to deal with data imbalance. The parameters of LR, RF, and LightGBM models were class_weight = “balanced,” and XGBoost’s was scale_pos_weight = “ratio of majority and minority class.” As to the other parameters that required adjustment, grid searching was adopted in the LR model and the Bayesian Optimization Algorithm was applied to the RF, XGBoost, and LightGBM models. To assess the model’s optimization and improve its generalization ability, 10-fold cross-validation was performed. The model’s performance was evaluated by calculating the accuracy, sensitivity, and specificity, and the distinguishing abilities of the risk assessment model were evaluated with the area under the receiver operator characteristic (AUC). The overview of the proposed ML algorithms is shown in Figure 1.

Shapley additive explanations (SHAP) value was defined as the average marginal contribution of a feature value across all possible feature coalitions. It provides insights into the influence of each feature on individual samples, showcasing both positive and negative effects.

ML was implemented in Python (v 3.6) using the sklearn (v. 0.24.1) and XGBoost (v. 1.3.3) packages. Bayesian optimization based on the TPE toolbox (bayes_opt v. 1.2.0) was used to tune hyperparameters for learning algorithms when the best combination of parameters yielded a low model performance. SHAP (V 0.41.0) was for explainable ML.

A total of 77,134 subjects were included, with a mean age of 48.6 ± 11.4 years, and 54.9 ± 10.6 years in subjects with EAS. The sample prevalence of EAS was 40.8%. Significant differences (p < 0.01) were observed in age, BMI, WC, SBP/DBP, indicators concerning renal function, FBS, total cholesterol (TC), triglyceride (TG), high−/low-density lipoprotein cholesterol (HDL-c/LDL-c) (Table 1), sex, history of cardiovascular diseases, smoking, exercise, work intensity, sedentary time, sleeping quality and time, 16 items of dietary habits, 9 items of negative emotions, and 12 items of health literacy (Table 2) between EAS and non-EAS.

Three health literacy items (active in the acquisition of medical knowledge and awareness of normal pulse rate/total cholesterol) with no statistical difference were removed from further analysis, and 60 features were input for subsequent feature selection.

The Lasso regression ranked the features based on their parameter values, and the bottom 25 features (Figure 2A) were visually observed. Subsequently, 21 features with zero parameter values were deleted, including LDL-c, history of other cardiovascular diseases (excluding hypertension and diabetes), awareness of normal salt intake/FBS/TG values, sunlight exposure, lack of enthusiasm, impatience, difficulty concentrating, nervousness, upset, meals on time, gluttony, frequency of consumption of eggs, vegetables, fat, animal offal, coffee, sugary drinks, sedentary duration, and dinner party.

The 39 reserved features were considered too much, and we adopted the LGBM model to train them further. With each addition, AUC scores for the test set were recorded. As depicted in Figure 2B, there was a discernible decrease in the score as we integrated 23 features one by one; continuous feature addition not only raised computational costs but also failed to enhance model performance. Consequently, we discarded the 16 non-contributory features. The remaining 23 significant features were sex, age, history of hypertension, SBP, DBP, BMI, WC, TC, TG, HDL-c, FBS, serum uric acid, serum creatinine, urea nitrogen, exercise, awareness of normal BP, the consumption frequency of items such as fruit, milk, bean products, alcohol, and smoking, work intensity, and irritableness. An important observation was the strong linear correlation between BMI and WC (r = 0.86) and between SBP and DBP (r = 0.78) (Supplementary Figure 1). For efficiency, we retained only WC and SBP, leading to a final 21 features for ML evaluation. It is noteworthy that we also developed a model that prioritizes features that are cost-effective and easily obtainable. Therefore, lab indicators were omitted, leaving us with 14 salient features.

The performance of four classifiers—logistic regression (LR), random forest (RF), XGBoost, and LightGBM—across the training and test sets is detailed in Table 3 (for the 14-feature model) and Supplementary Table 1 (for the 21-feature model). Intriguingly, the incorporation of laboratory indicators in the 21-feature models resulted in only marginal improvements in performance compared to the 14-feature models. For instance, the AUC test scores showed negligible differences: LR (0.8746 vs. 0.8706), RF (0.8697 vs. 0.8695), XGBoost (0.8754 vs. 0.8710), and LGBM (0.8732 vs. 0.8702). This increment came at a significant cost to the testers, suggesting that classifiers with only 14 features are more suitable for broad public applications. In terms of overall performance, the XGBoost model modestly outshone the other classifiers in multiple metrics, including accuracy (0.7878), sensitivity (0.78), specificity (0.73), and AUC (0.8710) on the test set.

Feature importance was assessed in the XGBoost model, and the top 10 most influential features were identified as SBP, age, history of hypertension, FBS, TG, sex, smoking, fruit consumption, awareness of normal BP, and exercise, as shown in Figure 3. Figure 4 visually presents the SHAP values corresponding to the 14 most important features. The x-axis represents the SHAP values, while the y-axis lists the features; each dot symbolizes a sample. The color scale varies from low (blue) to high (red), indicating the feature values. A positive SHAP value indicates contributing to EAS formation, whereas a negative value suggests inhibition. The top 5 features in terms of importance were SBP, age, WC, history of hypertension, and sex.

Our study is not free from limitations. First, given its cross-sectional design, it is not possible to infer causal relationships from the data. However, previous studies had established definite causality that we could follow. Our initial intention for the research was to assess the current status of arterial aging, thus making the study design reasonable. Second, the standards for evaluating certain lifestyle factors, such as fruit and bean consumption or exercise habits, were not unified and objectively quantified. This could potentially decrease the prediction’s precision. Finally, since the study relies on data from physical examinations conducted in China, there may be restrictions on the applicability of the results to other ethnicities or cultures.