Development of an optimized risk evaluation system for cardiovascular-kidney-metabolic syndrome-associated coronary heart disease based on tabular prior-data fitted network

Abstract

Background

The innovative concept of cardiovascular-kidney-metabolic (CKM) syndrome and tabular prior-data fitted network (TabPFN) offers opportunities for optimizing coronary heart disease (CHD) risk evaluation. This study compared TabPFN with traditional machine learning (ML) methods in medical small-sample data, aiming to construct and validate a risk model for coronary stenosis in CKM–CHD patients.

Methods

The research strictly adheres to transparent reporting of a multivariable prediction model for individual prognosis or diagnosis + artificial intelligence (TRIPOD + AI). A total of 296 inpatients from the Main Campus of Jiangsu Province Hospital of Chinese Medicine (June 2023–August 2024) and Zidong Branch (June 2024–December 2024) were screened. The data of the Main Campus were randomly divided into a training set (n = 160) and an internal validation set (n = 54) according to a ratio of 3:1, and the data of Zidong Branch were used as an external validation set (n = 82). Integrated least absolute shrinkage and selection operator regression was used to screen risk factors. TabPFN and eight traditional ML algorithms were applied to build models, which were evaluated by common indicators, calibration curves, decision curves, and learning curves. Finally, a local Shiny calculator was built.

Results

Five risk factors were identified: coronary computed tomography angiography, Type 2 diabetes mellitus, triglyceride-glucose index, body mass index, and absolute lymphocyte count. TabPFN outperformed traditional models in small samples, with area under the receiver operating characteristic curve (AUC) values of 0.922 (95% confidence interval [CI]: 0.886–0.958) in the training set, 0.857 (95% CI: 0.733–0.981) in the internal validation set, and 0.815 (95% CI: 0.711–0.918) in the external validation set. The best model reduced the false-negative rate of CCTA by 4.9% (95% CI: 1.9%−8.1%), and a user-friendly Shiny calculator was deployed.

Conclusion

TabPFN shows promise in medical small-sample analysis, and the optimized CKM–CHD risk model offers a certain degree of support for clinical decision-making. However, future larger-sample, multicenter prospective studies are still needed to further optimize the model.

Introduction

In 2023, the American Heart Association (AHA) innovatively proposed cardiovascular-kidney-metabolic (CKM) syndrome in circulation. Based on the shared pathological mechanisms of cardiovascular, renal, and metabolic diseases, it reveals the additive effect of multiorgan comorbidities on mortality risk.^1,2 This concept disrupts the single-disease management paradigm and offers a novel clinical pathway for the prevention and treatment of coronary heart disease (CHD). According to the China Hypertension Survey, the proportion of CKM 1–4 patients among Chinese adults reached 81.2% during 2012–2015. ³ Its high incidence highlights the urgency of life-cycle risk screening and early intervention.

CKM is characterized by a constellation of risk factors, encompassing metabolic abnormality-related factors such as obesity, insulin resistance (IR), and Type 2 diabetes mellitus; cardiovascular risk-related factors such as hypertension and arteriosclerosis; and kidney damage-related factors such as microalbuminuria. These factors form a vicious cycle through shared pathophysiological mechanisms, including inflammatory responses, oxidative stress, and endothelial dysfunction, thereby significantly increasing the risk of disease progression.

In the field of CKM, prevention and treatment of cardiovascular disease (CVD) has always been the core focus. CHD is pathologically characterized by coronary stenosis due to atherosclerosis, with severe stenosis defined as left main artery narrowing >50% or other coronary arteries ≥70%. ⁴ While coronary computed tomography angiography (CCTA) has enhanced stenosis detection rates, the issues of false-positive and false-negative results remain substantial. In addition, the progressive advancement of medical laboratory technology and the gradual exploration of risk factors have driven the evolution of clinical diagnosis toward “multidimensional data integration,” posing significant challenges to clinicians’ expertise.

With the vigorous development of machine learning (ML) technology, more and more new technologies continue to emerge, providing theoretical support for the comprehensive application of high-dimensional clinical data and the construction of models. Traditional ML models encounter challenges such as overfitting and complex parameter tuning in medical small-sample scenarios. However, tabular prior-data fitted network (TabPFN) technology, published in Nature in 2025, provides a novel solution for small-sample learning, featuring advantages such as parameter-free operation, noise resistance, and efficient inference. ⁵

As an emerging clinical concept, CKM syndrome remains in the research improvement stage. There is an urgent need to develop a CHD risk model tailored to the characteristics of the Chinese CKM population. ⁶ This study leverages the innovative framework of CKM syndrome, integrates the latest small-sample ML technology with multidimensional data, and focuses on risk prediction for severe coronary stenosis in CKM–CHD. By fusing multimodal data, the study aims to alleviate the medical burden and provide quantitative support for CHD diagnosis, treatment decision-making, and chronic disease management. The overall flow of this study is shown in Figure 1.

Figure 1.

Overview of the whole process. The structural concept of TabPFN is derived from references. ⁵

TabPFN: tabular prior-data fitted network.

Source: reproduced with permission from the authors based on study data.

Data and methods

Research subject

Patients with CKM who were treated at the Department of Cardiovascular Medicine of Jiangsu Province Hospital of Chinese Medicine: the Main Campus (June 2023 to August 2024) and Zidong Branch (June 2024 to December 2024) were included in this study. The screening of research subjects strictly adhered to the inclusion and exclusion criteria.

Inclusion and exclusion criteria

Inclusion criteria

(a) Age ≥ 18 years and meeting the diagnostic criteria of CKM syndrome; (b) hospitalized for coronary angiography (CAG); (c) having CCTA data within 3 months prior to CAG.

Exclusion criteria

(a) Presence of serious autoimmune diseases, blood system diseases, chronic infections, and other underlying diseases; (b) patients with a confirmed diagnosis of malignancy; (c) patients with a history of myocardial infarction, or those who have undergone coronary stent implantation or coronary artery bypass grafting; (d) combined with severe cardiomyopathy, heart valve disease, or acute complications; (e) with alcohol or drug abuse behavior, or suffering from uncontrollable mental illness; (f) pregnant or lactating women; (g) missing key information in the electronic medical record, or the crucial part cannot be supplemented and improved after verification; (h) other potential factors determined by the investigator that may affect the study results.

Diagnostic criteria

CKM diagnostic criteria

According to the AHA stage definition of CKM, ¹ patients who met at least one of the following conditions were included: (a) presence of excessive or dysfunctional adipose tissue (BMI ≥ 23 kg/m², 5.6 mmol/L ≤ fasting blood glucose ≤ 6.9 mmol/L or 5.7% ≤ Hemoglobin A1c ≤ 6.4%); (b) individuals with metabolic risk factors (triglyceride ≥ 1.5 mmol/L, hypertension, metabolic syndrome, diabetes) or chronic kidney disease; (c) combined with subclinical CVD; and (d) combined with clinical CVD.

Classification of CCTA

According to the coronary artery disease-reporting and data system (CAD-RADS) classification standard jointly issued by the Society for Cardiovascular Computed Tomography, the American College of Radiology, and the North American Society of Cardiovascular Imaging in 2016, ⁷ the degree of CCTA stenosis was categorized into two groups: (a) nonsevere stenosis: CAD-RADS classification of 3 or lower; (b) severe stenosis: CAD-RADS classification higher than 3.​

Classification of CAG

According to the Chinese Guidelines for the Diagnosis and Management of Patients with Chronic Coronary Syndrome ⁸ and the CAD-RADS classification criteria, the degree of stenosis in the largest cross-section of the lumen (excluding coronary muscle bridge lesions) was classified into two categories: (a) nonsevere stenosis: the maximum degree of coronary stenosis was <70%; (b) severe stenosis: maximum coronary artery stenosis ≥70% or left main artery stenosis >50%.

Sample size estimation formula

The sample size calculation for this study was based on the events per variable (EPV) principle, ⁹ and the formula for determining the minimum required sample size for the training set is as follows:

$$\mathrm{Sample}\mathrm{size}\mathrm{required}\mathrm{for}\mathrm{training}\mathrm{set}={\displaystyle \frac{\mathrm{Number}\mathrm{of}\mathrm{included}\mathrm{factors}\times \mathrm{EPV}}{\mathrm{Number}\mathrm{of}\mathrm{positive}\mathrm{events}/\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{training}\mathrm{set}}.}$$

Data collection and processing

Collection and blinding method

The electronic medical record system was employed to collect the clinical data of the included patients, encompassing general information, clinical indicators, and coronary stenosis indicators. During the study, the patient's name, contact information, home address and other privacy information were blocked, and the study ID number was used instead. All objective data originated from the electronic medical record systems of the Main Campus and Zidong Branch of Jiangsu Province Hospital of Chinese Medicine. In addition, this study collected risk factors and outcome variables separately, thus achieving blinding through data isolation. Strict quality control measures were implemented for the preliminary study design, on-site data collection, and subsequent data management.

Calculation formula

(a) ASI = (TC - HDL-C)/HDL-C; (b) UHR = SUA/HDL-C; (c) TyG = ln(TG[mg/dl]×FBG[mg/dl]/2); (d) NLR = neutrophil count/lymphocyte count; (e) SHR = FBG/(1.59×HbA1c - 2.59); (f) NHHR = non-HDL-C/HDL-C

Processing methods

Upon completion of data collection, the data were cleaned to remove duplicate and incorrect information, and the multiple imputation method in R language was applied to supplement missing values. In cases where the number of sample outcomes was unbalanced, the synthetic minority oversampling technique (SMOTE) algorithm was utilized for sample balancing. The eligible data were then converted and standardized to conform to the data types required for model input (including gender, CCTA results, CAG results, etc.), ensuring consistency across different feature dimensions.

Model construction

Partitioning datasets

In this study, the data from the main campus were subjected to stratified sampling according to the dependent variable and randomly divided into a training set and an internal validation set at a ratio of 3:1. The external validation set consisted of data from Zidong Branch to ensure its temporal and spatial independence. The training set was utilized to screen factors, optimize hyperparameters, and fit the model; the internal validation set was employed to verify the model's reproducibility; and the external validation set was used to assess the model's stability and generalization ability.​

Screening risk factors

1. Literature review method: A database search was conducted for relevant literature on the risk factors of coronary artery stenosis, covering China National Knowledge Infrastructure (CNKI), Chongqing VIP Database (CQVIP), Wanfang, PubMed, and Web of Science. Through comprehensive literature analysis, the current status and the latest advancements in the field were summarized, and factors with potential diagnostic value were initially screened out.

2. Experts interview method: The factors initially obtained through the literature review method were evaluated and supplemented by three senior medical experts in the industry to further assess the clinical practicability of these factors.

3. Integrated least absolute shrinkage and selection operator (LASSO) regression method: To eliminate the impact of seed number manipulation, ¹⁰ this study employed integrated LASSO regression to enhance the stability of variable screening via bootstrap and multiple repeated cross-validation. The high-dimensional processing capability of the regularization method was harnessed to effectively remove unnecessary features, prevent model overfitting, and render the model more concise and efficient.

Hyperparameter optimization and model construction

Nine ML technologies, including the latest TabPFN and eight traditional ML techniques (DT, RF, XGBoost, SVM, SNN, LR, LightGBM, and KNN), were employed to build the CKM–CHD optimized evaluation model using R language.

In this study, TabPFN was developed using the Python architecture, and its corresponding R language package has not been released. To ensure the consistency of analysis and comparison, a Python environment configuration script was written in R language, and the interactive operation between the two was achieved through the reticulate package. The relevant code can be found in the Supplementary Material.

Regarding hyperparameter optimization, TabPFN can achieve good performance without hyperparameter tuning. The remaining algorithms employed grid search. Following five-fold cross-validation, the parameters were ranked in descending order of the area under the receiver operating characteristic curve (AUC) to screen and obtain the hyperparameters that optimize model performance, while minimizing the impact of overfitting during the final model training.

Model screening, validation, and evaluation

This study evaluated the performance of each model using a dual evaluation system comprising internal and external validation sets. First, within the R language computing framework, core indicators such as accuracy, kappa consistency coefficient, Matthews correlation coefficient, precision, recall, F1 score, and AUC of different models in the dual validation sets were quantitatively analyzed, and their comprehensive diagnostic efficacies for severe coronary stenosis were compared. Second, the calibration accuracy and clinical applicability of the models were assessed by plotting calibration curves and decision curves to carry out multidimensional screening. Finally, for the best model, the receiver operating characteristic (ROC) curve, learning curve, and confusion matrix were further plotted to thoroughly analyze its diagnostic efficacy, training stability, and cross-dataset generalization ability, thereby providing a solid foundation for the clinical application of the model.

Model presentation

The optimal approach for the visual presentation of the best model, such as a nomogram, scoring system, or calculator, was selected to facilitate clinical application.

Statistical analysis

In this study, a double-check mechanism was employed to ensure data accuracy, and the original data were synchronously entered into Excel 2016 software to construct a structured database. During the data analysis and model-building processes, Statistical Product and Service Solutions (SPSS) 25.0 was comprehensively utilized for traditional statistical analysis, while Python 3.7.3 and R 4.3.2 were employed to establish the ML model framework, enabling the comprehensive analysis of data preprocessing, statistical inference, model construction, and validation.

1. Quantitative data: When conforming to a normal distribution, data were presented as (mean ± SD); when not normally distributed, they were presented as M (Q1, Q3). If the dataset satisfied the assumptions of independence, normality, and homogeneity of variance simultaneously, the two-independent-sample t-test was applied; otherwise, the Wilcoxon rank-sum test was utilized.

2. Qualitative data: Data were presented as Cases (%), and analyzed using the chi-square test. A p-value < .05 was considered statistically significant.

Ethical design

This study adhered to the Declaration of Helsinki and relevant regulations of the World Medical Assembly. As it was a retrospective study involving only data and no biological samples, obtaining exemption from informed consent would not pose physical, mental, or social risks to patients, nor would it involve privacy or commercial interests. Thus, it was exempted upon approval by the ethics committee. The study was approved as a clinical research project by Jiangsu Province Hospital of Chinese Medicine and received ethical approval from the Ethics Committee of the Affiliated Hospital of Nanjing University of Chinese Medicine (YJZ202547).

Results

Comparison of clinical data

A total of 296 patients were ultimately included in this study. Specifically, CKM patients from the Main Campus of Jiangsu Province Hospital of Chinese Medicine between June 2023 and August 2024 were randomly divided into a training set (160 cases) and an internal validation set (54 cases) via 3:1 stratified sampling. From June 2024 to December 2024, CKM patients from Zidong Branch were selected as the external validation set (82 cases). The baseline data comparison of patients from the two sections is presented in Table 1. Notably, significant statistical differences (p < .05) were observed in CCTA, Age, DBP, LDL-C, eGFR, and SHR.

Table 1.

Comparison of general information.

Variable	Abbreviation	Main campus (N = 214)	Zidong branch (N = 82)	χ²/Z	p
Stenosis status
Coronary angiography, cases (%)	CAG	152 (71.0)	53 (64.6)	1.138	.286
Coronary computed tomography angiography, cases (%)	CCTA	152 (71.0)	48 (58.5)	4.221	.040
Characteristic
Age, year, M (Q1, Q3)	Age	66.00 (58.00, 73.00)	62.00 (57.00, 70.00)	−2.166	.030
Male, cases (%)	Gender	136 (63.6)	59 (72.0)	1.861	.173
Pulse, beats/min, M (Q1, Q3)	P	75.00 (68.00, 84.25)	78.00 (70.75, 84.25)	−1.395	.163
Systolic blood pressure, mmHg, M (Q1, Q3)	SBP	134.00 (122.75, 146.25)	135.00 (124.75, 148.00)	−1.040	.298
Diastolic blood pressure, mmHg, M (Q1, Q3)	DBP	80.00 (73.00, 89.00)	86.50 (77.00, 94.00)	−3.545	<.001
Electrocardiogram ST-T changes, cases (%)	ECG	145 (67.8)	52 (63.4)	0.502	.479
Past history
Smoking history, cases (%)	Smoking Hx	74 (34.6)	36 (43.9)	2.207	.137
Drinking history, cases (%)	Drinking Hx	57 (26.6)	27 (32.9)	1.154	.283
Family history, cases (%)	Family Hx	45 (21.0)	21 (25.6)	0.718	.397
Duration of hypertension, year, M (Q1, Q3)	HTN	5.00 (0.50, 10.00)	5.50 (0, 15.85)	−0.605	.545
Duration of diabetes, year, M (Q1, Q3)	T2DM	0 (0, 1)	0 (0, 2)	−0.723	.470
Blood lipids
Total cholesterol, mmol/L, M (Q1, Q3)	TC	3.73 (3.20, 4.70)	3.94 (3.31, 4.70)	−0.711	.477
Triglyceride, mmol/L, M (Q1, Q3)	TG	1.38 (0.99, 1.95)	1.49 (0.99, 1.96)	−0.529	.597
High-density lipoprotein cholesterol, mmol/L, M (Q1, Q3)	HDL-C	1.02 (0.89, 1.20)	1.03 (0.84, 1.22)	−0.049	.961
Low-density lipoprotein cholesterol, mmol/L, M (Q1, Q3)	LDL-C	1.94 (1.58, 2.64)	2.29 (1.73, 3.11)	−2.910	.004
Arterial stiffiness index ≥4, cases (%)	ASI	31 (14.5)	19 (23.2)	3.185	.074
Non-HDL-C to HDL-C ratio, M (Q1, Q3)	NHHR	2.71 (2.01, 3.48)	2.75 (2.07, 3.90)	−0.829	.407
Kidney function
Estimated glomerular filtration Rate, mL/(min·1.73 m²), M (Q1, Q3)	eGFR	89.00 (78.00, 98.00)	94.00 (85.75, 103.00)	−2.476	.013
Serum creatinine, μmol/L, M (Q1, Q3)	SCR	73.05 (61.80, 82.48)	70.50 (55.75, 80.25)	−1.485	.138
Serum uric acid, μmol/L, M (Q1, Q3)	SUA	343.50 (274.75, 386.75)	339.50 (288.00, 401.50)	−0.824	.410
Uric-acid to HDL-C ratio, M (Q1, Q3)	UHR	318.05 (240.41, 430.02)	336.08 (253.27, 427.82)	−0.617	.537
Metabolic state
Hemoglobin A1c, %, M (Q1, Q3)	HbA1c	6.20 (5.80, 6.80)	6.10 (5.70, 6.80)	−0.983	.326
Fasting blood glucose, mmol/L, M (Q1, Q3)	FBG	5.00 (4.42, 6.08)	5.32 (4.67, 6.41)	−1.952	.051
Body mass index, kg/m², M (Q1, Q3)	BMI	25.13 (23.05, 27.35)	25.25 (23.76, 27.26)	−0.668	.504
Stress hyperglycemia ratio, M (Q1, Q3)	SHR	0.69 (0.63, 0.78)	0.75 (0.69, 0.81)	−3.285	.001
Triglyceride-glucose index >9.04, cases (%)	TyG	60 (28.0)	26 (31.7)	0.387	.534
Complete blood count
Leukocyte count, 10^9/L, M (Q1, Q3)	WBC	6.25 (5.31, 7.40)	6.12 (4.94, 7.26)	−1.372	.170
Neutrophil count, 10^9/L, M (Q1, Q3)	ANC	3.90 (3.02, 4.88)	3.50 (2.74, 4.53)	−1.844	.065
Lymphocyte count, 10^9/L, M (Q1, Q3)	ALC	1.69 (1.30, 2.13)	1.75 (1.38, 2.12)	−0.633	.527
Neutrophil-to-lymphocyte ratio, M (Q1, Q3)	NLR	2.25 (1.64, 3.22)	1.96 (1.50, 3.15)	−1.504	.132

In the training set, the proportion of outcome categories was approximately severe stenosis: nonsevere stenosis = 2.48:1, indicating a mild imbalance. The SMOTE algorithm was employed to balance the samples, enabling the model to enhance its recognition of minority classes without compromising data information. Using the DMwR package in R language, the specific parameter settings are as follows: k = 5, perc. over = 100, perc. under = 0. Following data balancing, the training set consisted of 206 cases, with the proportion of outcome categories adjusted to severe stenosis: nonsevere stenosis = 1.24:1.

Screening of risk factors

A total of 31 risk factors were initially identified through the comprehensive literature review and experts interview. Subsequently, the integrated LASSO regression method was applied, with 500 bootstrap samples and a variable selection frequency threshold of 0.95. Taking into account both model simplicity and accuracy, and integrating clinical practice insights with regression analysis results, five factors were ultimately selected: coronary computed tomography angiography (CCTA), Type 2 diabetes mellitus (T2DM), triglyceride-glucose index (TyG), body mass index (BMI), and absolute lymphocyte count (ALC). The variable coding rules and selection frequencies for the integrated LASSO regression variables are presented in Figure 2.

Figure 2.

Frequencies and coding rules for the selection of integrated LASSO regression variables. Introduction: The horizontal axis represents the frequency of variable selection after 500 LASSO regression samples; the vertical axis represents different variables and their encoding rules; distinguish different variable types by using bar chart colors; the red dashed line represents the selection threshold.

LASSO: least absolute shrinkage and selection operator.

Source: reproduced with permission from the authors based on study data.

Further analysis of risk factors

The heatmap of Spearman correlation analysis among variables is depicted in Figure 3(a). The correlation coefficients of all risk factors were <0.2 (excluding self-correlation and correlation with CAG), suggesting that the collinearity of variables selected by LASSO was extremely low, thereby indicating high model stability. Moreover, this outcome implied that the information contributed by each factor was independent yet complementary. Therefore, this study integrated “Coronary imaging features + Immune status + Metabolic indicators” for multidimensional diagnosis, endowing the model with clinical innovativeness.

Figure 3.

Further analysis of risk factors. Introduction: In figure (a), the color and size of the color block in the bottom left corner visually represent the Spearman correlation analysis coefficient values; Figures (b) and (c) show the distribution ratios of CCTA and TyG under different categories of CAG, while Figures (d), (e), and (f) show the distribution of ALC, T2DM, and BMI under different categories of CAG. It can be seen that the values or proportions of these predictive factors are higher in the severe stenosis group defined by CAG than in the nonsevere group.

ALC: absolute lymphocyte count; BMI: body mass index; CAG: coronary angiography; CCTA: computed tomography angiography; TyG: triglyceride-glucose index.

Source: reproduced with permission from the authors based on study data.

To further investigate the distribution of the five risk factors across different CAG outcomes, stacked bar charts and rain-cloud plots were generated based on varying data types, as illustrated in Figure 3(b) to (f). As a coronary imaging feature, CCTA exhibited significant disparities across different CAG outcomes, demonstrating its high diagnostic value (true-positive rate: 84.9%). However, it also had a notable missed diagnosis rate (15.1%), suggesting potential for further optimization. The values or proportions of other factors (TyG, ALC, T2DM, and BMI) in the CAG-defined severe stenosis group were consistently higher than those in the nonsevere group (as indicated by the median, interquartile range), indicating their utility in risk assessment.

Sample size estimation

In this study, five risk factors were ultimately incorporated. A total of 160 patients were included in the training set, including 114 patients with positive events. Therefore, the positive event rate in the training set was 114/160 = 71.25%. To enhance the model's robustness, an EPV value of 20 was adopted. Based on the EPV principle, the required sample size for the training set was calculated as: (number of included factors × EPV)/(positive event rate in the training set) ≈ 140, so the estimated sample size meets the requirements.

Hyperparameter optimization and modeling

Nine ML techniques were employed in R language to construct the CKM–CHD model. With the exception of TabPFN, hyperparameter optimization was performed for the remaining models, and the results are presented in Table 2. The models were then constructed using the optimal parameters respectively.

Table 2.

Table of model parameters.

Model name	Abbreviation	Parameters
Decision tree	DT	engine = “rpart,” cost complexity = 0.00488, tree depth = 6, min n = 6
Random forest	RF	engine = “randomForest,” mtry = 2, trees = 500, min n = 20
Extreme gradient boosting	XGBoost	engine = “xgboost,” mtry = 2, trees = 1000, min n = 8, tree depth =3, learn rate =0.00172, loss reduction = 0.926, sample size =0.981, stop iter = 25
Support vector machine	SVM	engine = “kernlab,” cost =32, rbf sigma = 0.00316
Shallow neural network	SNN	engine = “nnet,” hidden units = 15, penalty =1, epochs = 150
Logistic regression	LR	engine = “glm"
Light gradient boosting machine	LightGBM	engine = “lightgbm,” tree depth = 1, trees = 221, learn rate =0.0740, mtry = 5, min n = 5, loss reduction = 0.0219
K-nearest neighbor	KNN	engine = “kknn,” neighbors = 5, weight func = “rectangular,” dist power = 2
Tabular prior-data fitted network	TabPFN	N_ensemble_configurations = 64L, device = “cpu"

Model screening and verification

Dual evaluation, screening, and validation were conducted using internal and external validation sets. The performance indicators of different models in the internal and external validation sets are presented in Figure 4(a) and (d), and the Supplementary Materials. Among these, the indicators of RF, LR, KNN, SNN, and TabPFN were notably high and stable. In Figure 4(b) and (e), the calibration curves of KNN, LightGBM, LR, RF, XGBoost, and TabPFN were close to the ideal prediction curve, indicating a high degree of calibration. In Figure 4(c) and (f), LR, LightGBM, and TabPFN demonstrated higher net benefit values throughout the decision curves, suggesting stronger clinical applicability.

Figure 4.

Multidimensional screening of different models. Introduction: Figures (a) and (d) show the performance indicators of different models in the internal and external validation sets, respectively. TabPFN maintains an overall high level and has the highest recall rate; Figures (b) and (e) show the calibration curves, and the closer they are to the black diagonal line, the higher the calibration degree of the model; Figures (c) and (f) show clinical decision curves, all located to the right of the black dashed line and above the black solid line, indicating higher clinical applicability.

TabPFN: tabular prior-data fitted network.

Source: reproduced with permission from the authors based on study data.

Considering clinical practice, the misdiagnosis of severe coronary stenosis entails significant medical risks, potentially delaying treatment and endangering patients’ lives. Consequently, the recall rate should be prioritized over the precision rate. TabPFN exhibited the highest recall rate in both internal and external validation sets, with all its indicators demonstrating stability. Following the comprehensive multidimensional screening process, TabPFN was identified as the best evaluation model.

Generalization evaluation of the best model

To evaluate the real-world generalization efficacy of TabPFN model, its discrimination and learning capability were assessed. Figure 5(a) depicts the ROC curves of the model across the training, internal validation, and external validation sets, with AUC values exceeding 0.8, indicative of robust discrimination and stability. The learning curve, presented in Figure 5(b), illustrates that as the training set sample size increased, the model's AUC on the external validation set progressively rose and stabilized above 0.80, demonstrating strong data fitting and generalization performance. Figure 5(c) and (d) present the confusion matrices of the best model and CCTA diagnosis for all patients. Based on the paired design, McNemar test was used for the diagnosis results of CCTA and CKM–CHD model (p = 0.004). The result showed that there were statistical differences between the two diagnostic methods. Bootstrap was used to sample 500 times in all the population in this study. Compared to CCTA alone, the best model reduced the missed diagnosis rate (false-negative rate) by 4.9% (95% confidence interval [CI]: 1.9%–8.1%). These results indicate that the TabPFN model, integrating “Coronary imaging features + Immune status + Metabolic indicators,” achieves dual optimization of diagnostic accuracy and clinical utility, holding significant value for noninvasive decision-making.

Figure 5.

Evaluation of TabPFN model generalization. Introduction: Figure (a) shows the ROC curves of the TabPFN model in the training set, internal validation set, and external validation set; Figure (b) shows the learning curve. As the sample size of the training set increases on the x-axis, the AUC value of the TabPFN model in the external validation set tends to stabilize and remains above 0.80; Figures (c) and (d) are confusion matrices, which intuitively reflect the predicted and true distributions of the diagnostic model and CCTA in different classifications of CAG.

ROC: receiver operating characteristic; AUC: area under the receiver operating characteristic curve; CAG: coronary angiography; CCTA: computed tomography angiography; TabPFN: tabular prior-data fitted network.

Source: reproduced with permission from the authors based on study data.

Model interpretation and application

Numerous prior studies have employed SHapley Additive exPlanations (SHAP) analysis to elucidate variable importance in ML models.^11,12 However, SHAP relies on local linearity assumptions and feature independence, whereas TabPFN is an ensemble model with inherent feature interactions. This methodological mismatch results in computationally inefficient and interpretively inaccurate outcomes. Consequently, this study adopted permutation feature importance analysis, as shown in Figure 6(a), which ranked the variables by importance as follows: CCTA > ALC > T2DM > BMI > TyG.

Figure 6.

Model interpretation and local shiny calculator construction. Introduction: Figure (a) shows the importance analysis of permutation features, and the lengths of different bar graphs reflect the influence of this factor on the diagnostic model. Figure (b) is a grouped accumulated local effect plot, categorized by TyG. Figures (c) to (e) are univariate accumulated local effect plots. The abscissa (x-axis) represents different variables, while the ordinate (y-axis) reflects the net impact of changes in feature values on the model's prediction results. Figure (f) shows the initial interface of the local Shiny calculator; Figures (g) to (i) show the diagnostic result interface, with green, orange, and red representing different degrees of illness.

TyG: triglyceride-glucose index.

Source: reproduced with permission from the authors based on study data.

To further interpret the model, accumulated local effect (ALE) plots were generated. Given the well-established consistency and complementary roles of TyG and BMI in clinical practice, a stratified ALE plot was employed to dissect the net impact of BMI on the model's predicted outcomes. As shown in Figure (b), stratify according to the TyG level. Specifically, in the population with lower TyG values, BMI exhibited a negative correlation with the model-predicted risk of coronary artery stenosis. In contrast, among individuals with higher TyG levels, a bidirectional association was observed between BMI and predicted coronary stenosis risk: both low and high BMI were associated with an elevated risk of coronary artery stenosis. This finding delineates the interplay between the TyG index and BMI at a more granular level. Meanwhile, Figures (c) to (e) depict the univariate ALE curves for T2DM, CCTA, and ALC, respectively. Among these variables, T2DM and CCTA were positively correlated with the predicted risk of coronary artery stenosis. Notably, ALC displayed a “U-shaped” relationship with the predicted risk, indicating that both abnormally low and high ALC levels were linked to increased risk.

Finally, a user-friendly local Shiny calculator was developed based on the TabPFN model to support clinical decision-making. Figure 6(f) depicts the interface, featuring input fields on the left and detailed guidelines on the right. Figure 6(g) to (i) illustrates the risk stratification output, color-coded into green (low risk), orange (medium risk), and red (high risk), each accompanied by evidence-based clinical recommendations.

Discussion

Status of CKM–CHD

The complications of CKM syndrome form a vicious cycle. Their main hazards include: first, the exacerbation of IR, which promotes the occurrence and development of diabetes and its microvascular complications (such as retinopathy and neuropathy); second, the acceleration of atherosclerosis, which significantly increases the risk of myocardial infarction, heart failure, and stroke; and finally, the progressive decline in renal function, which can eventually lead to end-stage renal disease. These systems interact with each other, collectively resulting in extremely high all-cause mortality and disability rates. Among these, the hazards of CVD are particularly prominent. According to the 2017 Global Burden of Disease Study report, approximately 31.8% of global population deaths are attributed to CVD. ¹³ Coronary atherosclerotic heart disease has emerged as one of the primary threats to the health of the Chinese population.^14,15 The innovative concept of CKM syndrome provides a systematic framework for explaining the disease progression from a risk-free state to severe clinical CVD. This theoretical framework facilitates early comprehensive management of multiple risk factors in CKM patients, thereby mitigating the risk of CVD. In recent years, research in this field has made significant strides. Explorations into pathological mechanisms have continued to deepen, while the development of prevention and control strategies has steadily advanced. Meanwhile, innovative research findings have emerged in an unceasing stream.^16–20

Currently, the cross-integration of medical big data and ML is deepening steadily. ML's strengths have become increasingly prominent, particularly in efficiently mining hidden data patterns, accurately processing multidimensional information, and enabling autonomous learning of complex features. This has emerged as a crucial pillar for constructing a modern disease prevention and control system. Within the innovative theoretical framework of CKM syndrome, the AHA has proposed the development of novel risk prediction algorithms. ²¹ The American Heart Association predicting risk of CVD events (PREVENT) model, released in 2024, incorporates enhanced modules for renal and metabolic function, along with key indicators such as urinary albumin/creatinine ratio and hemoglobin A1c (HbA1c). This advancement further refines the risk stratification framework for patients with CKM syndrome. ²²

Notably, China is a country with a population exceeding 1.4 billion. It exhibits distinct baseline population characteristics compared to other regions worldwide, including demographic traits, comorbidity distributions, and ranges of laboratory indicators. Given that the PREVENT model was developed based on an American population cohort, its applicability in the Chinese population still requires clinical validation. Therefore, the construction of a CKM–CHD risk model tailored to the disease characteristics of CKM patients in Asian populations has become an urgent research priority.

With the rapid advancements in artificial intelligence (AI) technology in recent years, model-building methodologies have exhibited a diversified trend. In January 2025, TabPFN proposed by Hollmann's team in Nature has garnered significant academic attention. ⁵ Designed based on transformer architecture, this small-to-medium table data foundational model achieves efficient prediction through a context-learning mechanism and synthetic data pretraining strategy. Medical research, constrained by legal and ethical frameworks, encounters unique challenges in data acquisition, analysis, and application. Notably, small-sample datasets constitute a substantial proportion of medical research data, aligning closely with TabPFN's technical advantages. As a cutting-edge ML technology of 2025, TabPFN offers a novel solution to traditional small-sample learning challenges. It showcases distinct strengths including automatic hyperparameter optimization, noise-robust processing, and ultraefficient reasoning. Naturally, TabPFN has certain limitations. It relies on synthetic data for pretraining, and its practical application may be constrained by distribution discrepancies between the pretraining domain and real-world medical scenarios. Additionally, the technology still has limitations in scaling feature dimensions and sample sizes. However, taken together, TabPFN remains a promising research frontier with broad prospects in the medical field.

Analysis of risk factors

Through comprehensive literature review, experts interview, and integrated LASSO regression analysis, this study ultimately identified five key factors: CCTA, ALC, T2DM, BMI, and TyG. Subsequent Spearman correlation and distribution analysis revealed negligible multivariate collinearity, indicating that these factors provide independent yet complementary information. Notably, their distributions showed certain differences in different outcomes of CAG, which can assist in judging the relevant risks.

Current noninvasive assessment of coronary stenosis in CHD mainly relies on CCTA. However, this approach is constrained by calcified plaques, vascular hypoperfusion, and imaging artifacts. In this cohort, it results in misdiagnosis and missed diagnosis rates of 31.4% and 15.1%, respectively. While partly attributable to hospitalization selection bias, these findings highlight the need for CCTA optimization. The multidimensional CKM–CHD model developed herein achieved a 4.9% reduction in missed diagnosis, demonstrating the optimization of diagnostic accuracy. From the perspective of clinical doctors, this ensures timely intervention for high-risk patients and avoiding delayed vascular reconstruction or acute coronary syndrome. Faced with the large sample size of CHD patients today, these improvements can further boost physicians’ confidence in decision-making for complex cases. They also help optimize medical quality and the utilization of medical resources.

The pathogenesis of atherosclerosis is fundamentally driven by chronic vascular wall inflammation. In this process, lymphocytes participate in disease progression through immune regulation, cytokine secretion, and modulation of lipid metabolism. As a key marker of immune system homeostasis, ALC has been demonstrated to independently correlate with adverse cardiovascular outcomes under acute stress conditions.^23,24 Notably, unlike the stress-induced lymphopenia observed in acute coronary syndrome, stenosis progression in CHD is characterized by lymphocyte activation triggered by persistent antigen exposure. This study observed elevated ALC in the CAG-defined severe stenosis group, suggesting that chronic inflammation-driven adaptive immune responses may serve as a pivotal factor in disease exacerbation. This phenomenon may obscure imbalances in key lymphocyte subsets, such as the expansion of CD4 + CD28null T cells ²⁵ and depletion of regulatory T cells. ²⁶

As a core surrogate marker of IR, TyG index serves as an efficient and cost-effective tool for IR assessment by integrating lipid and glucose metabolism parameters. Emerging evidence has established its robust association with the pathogenesis, progression, and prognosis of T2DM and CHD, garnering significant attention from the global researchers. A population-based studies has demonstrated that diabetic patients with elevated TyG levels (>9.04) exhibit an increased risk of all-cause mortality. ²⁷ Concurrently, the TyG index has been linked to poor clinical outcomes in premature coronary artery disease (CAD), ²⁸ major adverse cardiovascular events, ²⁹ and increased stroke incidence. ³⁰ Additionally, a finding from the Gold-Health cohort reveals that TyG independently predicts CAD in older adults with CKM Stages 0–3. ³¹

Following integrated LASSO regression screening, TyG was incorporated into the CKM–CHD optimized diagnostic model construction framework. However, permutation feature importance analysis revealed that TyG still ranked lowest among the variables. This finding indicates that its contribution to the model's overall predictive performance remains relatively limited. Within the ML paradigm, variable importance scores carry greater decision-making value than traditional statistical significance tests. This allows for the inclusion of variables that exhibit “weak single-factor correlation yet significant combinatorial effects.” Based on TyG's formula and in-depth analysis, we hypothesize that the widespread use of lipid-lowering drugs by outpatient patients may be one of the main reasons for this phenomenon. With the growing recognition of dyslipidemia's association with CHD, statins, fibrates, and niacin have been widely administered in outpatient settings. These agents rapidly normalize lipid profiles, thereby interfering with TyG's predictive efficacy in a model built from inpatient data. To fully exploit TyG's clinical potential, we recommends that future research incorporate weighted analyses of lipid-lowering drug variables, including medication status (use/nonuse), drug class, and dosage. Notably, the retrospective design of this study presented challenges in comprehensively documenting patients’ medication histories. This limitation is planned to be addressed in upcoming prospective multicenter investigations.

TyG and BMI exhibit remarkable consistency and complementarity in clinical applications. The TyG-BMI composite index, derived from these two parameters, has also emerged as a promising biomarker in current research. It has demonstrated promising utility in risk assessment for metabolic dysfunction-associated steatotic liver disease, ³² stroke in older adults,^33,34 frailty, ³⁵ and prediction of CAD severity. ³⁶ Additionally, studies have confirmed its positive association with increased CVD incidence in patients with CKM Stages 0–3. ³⁷

Clinical symptom inquiry traditionally holds a pivotal role in coronary risk assessment. Chest tightness and chest pain are the most prevalent symptoms among CKM–CHD patients. Careful interrogation of their timing, location, nature, severity, precipitating factors, and relief patterns is critical for evaluating coronary stenosis. However, symptom expression is significantly influenced by many factors such as patients and doctors, so this study did not include relevant symptoms. Traditional Chinese medicine (TCM) factors, including syndrome types and elements, offer a multidimensional approach to capturing the overall patient state, potentially enhancing model accuracy. For instance, one subproject of this study incorporated four TCM syndrome elements: phlegm (Tan), hematoma (Yu), stagnation (Zhi), and deficiency (Xu). It then used LightGBM to develop an integrated traditional Chinese and Western medicine diagnostic model, which achieved an AUC of 0.897 (95% CI: 0.818–0.975) in the external validation set. ³⁸ Nevertheless, discrimination of syndrome types and elements requires experienced TCM practitioners to apply standardized scoring scales, imposing practical limitations on its broad implementation.

Result analysis

This study enrolled 296 patients across two independent districts, undertaking the construction, feature screening, internal/external validation, and clinical application evaluation of the CKM–CHD diagnostic model. The SMOTE algorithm was utilized to address data imbalance, yet the synthetic data it generates may still introduce potential biases. While rigorous management has effectively mitigated such risks, the generalizability of the model could still be impacted to a certain extent. Baseline data analysis via Wilcoxon rank-sum test and chi-square test revealed statistically significant interdistrict differences in CCTA, age, DBP, LDL-C, eGFR, and SHR (p < .05). This cross-center data diversity affords a natural stress-testing scenario for evaluating the model's external generalization capability. Evaluating model performance in heterogeneous datasets effectively assesses its robustness across clinical settings, providing high-level evidence-based support for multicenter implementation of the diagnostic model. Five risk factors were identified through comprehensive literature review, experts interview, and integrated LASSO regression analysis: CCTA, T2DM, TyG, BMI, and ALC.

Nine ML techniques were comprehensively employed for constructing the CKM–CHD optimized evaluation model, including TabPFN and eight traditional methods: DT, RF, XGBoost, SVM, SNN, LR, LightGBM, and KNN. Through multidimensional comparisons of model effectiveness, encompassing discrimination, calibration, and clinical utility, the results demonstrated that the TabPFN model excelled across all evaluation metrics. Notably, the model exhibited robust stability and generalization capability in external validation, establishing its status as the best evaluation model. Specifically, first, TabPFN demonstrates significantly faster training speed compared to traditional ML methods, leveraging its advantage of eliminating the need for hyperparameter optimization. Second, in terms of model performance, TabPFN achieved higher recall rates in both the internal and external validation sets of this study. This characteristic is more aligned with clinical medical practice, thereby further reducing the rate of misdiagnosis and medical risks. Finally, according to research by the developers of the TabPFN algorithm, it is suitable for medium and small-sample datasets, which makes it highly compatible with the field of medical research. These findings fully demonstrate that TabPFN confers significant advantages over traditional ML models in small-sample medical data, holding substantial clinical utility and broad potential.

In terms of specific performance indicators, the TabPFN model achieved AUC values of 0.922 (95% CI: 0.886–0.958), 0.857 (95% CI: 0.733–0.981), and 0.815 (95% CI: 0.711–0.918) in the training set, internal validation set, and external validation set, respectively. Moreover, the application of this model greatly reduced the missed diagnosis rate of CCTA by 4.9% (95% CI: 1.9%–8.1%). Permutation feature importance analysis ranked the key decision-driving factors as follows: CCTA > ALC > T2DM > BMI > TyG. To facilitate clinical translation, a TabPFN-based local Shiny calculator was developed with a user-friendly interface. This tool provides clinicians with convenient decision support, enabling accurate diagnosis of CKM–CHD.

Strengths and limitations

The strengths of this study are: (a) Technological innovation: The study demonstrates innovative application of the latest TabPFN algorithm in small-sample medical data analysis. Cross-language integration of Python and R programming environments was employed to validate the technology's unique advantages in handling complex medical datasets. The impact of this work is not limited to the medical field, and there is room for optimization in interdisciplinary fields such as paleontology, ³⁹ engineering, ⁴⁰ fluid dynamics, ⁴¹ and others that have previously studied ML. (b) Rigorous research design: The research strictly adheres to transparent reporting of a multivariable prediction model for individual prognosis or diagnosis + artificial intelligence (TRIPOD + AI), ⁴² establishing a comprehensive framework from data preprocessing and risk factors screening to model construction and multilevel validation. This systematic approach ensures scientific rigor. (c) Clinical translation value: By integrating multidimensional data, the study breaks through traditional diagnostic paradigms, improving the accuracy of noninvasive coronary assessment. The developed local Shiny calculator facilitates clinical translation, providing feasible decision support for CKM–CHD.

There are still some limitations in this study: (a) Technical aspects: The current web calculator is limited to local deployment due to virtual environment configuration issues in R-Python integration, precluding publication via shinyapps.io. Future plans include API-based model deployment to enable network-wide accessibility. (b) Sample aspects: the model's generalization and migration ability require validation in larger cohorts. In the future, we plan to expand the sample size and conduct a prospective multicenter study to enhance the applicability of this model across diverse patient populations.

Conclusions

This study innovatively applied TabPFN to multidimensional small-sample clinical datasets, successfully constructing an optimized risk evaluation model for coronary stenosis in CKM–CHD. This not only confirms that TabPFN holds certain advantages in analyzing small-sample medical data but also establishes an evidence-based foundation for the clinical translation of this technology. Moving forward, further in-depth research in this field is warranted. Furthermore, by integrating multidimensional information including coronary imaging, immune status, and metabolic indicators, the model enhances the accuracy of noninvasive coronary stenosis assessment. This achievement holds substantial clinical significance for guiding the diagnosis and management of CHD.