Multivariate adaptive regression spline modeling for estimating carotid artery plaque thickness in Chinese men with type 2 diabetes

Abstract

Objective

The incidence of type 2 diabetes continues to increase worldwide, with cardiovascular disease as the leading cause of mortality in this population. Carotid artery plaque thickness serves as a non-invasive marker of atherosclerosis. This study applied multivariate adaptive regression spline analysis to estimate artery plaque thickness using routinely available clinical data in Chinese men with type 2 diabetes.

Methods

In this retrospective cross-sectional study, 648 male patients with type 2 diabetes were analyzed using demographic and biochemical data. Multiple linear regression analysis served as a benchmark comparison. Model performance was evaluated using repeated train–test splits, with hyperparameter tuning conducted exclusively on training data, followed by bootstrap-corrected internal validation. An estimation equation was constructed based on basis functions derived from multivariate adaptive regression spline analysis.

Results

Mean participant age was 63.16 ± 11.78 years, mean diabetes duration was 12.26 ± 7.15 years, mean glycosylated hemoglobin level was 7.76 ± 1.66%, and mean artery plaque thickness was 0.943 ± 0.38 mm. Multivariate adaptive regression spline demonstrated lower prediction errors than multiple linear regression across multiple metrics. Five key predictors were identified, including age, diabetes duration, low-density lipoprotein cholesterol level, microalbumin-to-creatinine ratio, and diastolic blood pressure, each with clinically meaningful threshold effects.

Conclusions

A multivariate adaptive regression spline–based equation incorporating five routinely available clinical variables was developed for estimating arterial plaque thickness. Although multivariate adaptive regression spline outperformed multiple linear regression, the model's modest explanatory power (R² ≈ 0.21) indicates that it should be viewed as a potential screening adjunct rather than a definitive diagnostic tool. External validation in independent and further validation on diverse populations is warranted.

Introduction

The global prevalence of type 2 diabetes (T2D) has increased significantly, representing a pressing public health challenge. In 2017, Khan et al. estimated the global T2D population at approximately 462 million, representing 6.28% of the world's population. ¹ This prevalence increased to approximately 7.08% by 2023, with over 1 million annual deaths attributable to diabetes, making it the 9th leading cause of death worldwide. Similar trends have been observed in Taiwan. In 2021, the diabetes population was estimated at approximately 2 million, representing approximately 9.7% of the total population, with a similar proportion believed to remain undiagnosed. ² Diabetes causes macrovascular and microvascular complications, with arterial changes representing an important pathway. These changes include increased arterial calcification, medial thickening, and accelerated atherosclerosis. ³ Epidemiological data have demonstrated that 47.5% of T2D patients have established cardiovascular disease (CVD) at diagnosis, and CVD is the proximal cause of death in approximately 50% of these patients.^4–6 Thus, the early detection of CVD in T2D patients represents an urgent priority. Several modalities are available for the evaluation of arterial atheroma status; however, the use of non-invasive methods is associated with significant costs. In contrast, carotid artery ultrasonography offers a non-invasive, low-cost method for evaluating arterial condition. ⁷ The Kuopio Ischemic Heart Study has reported that each 0.1-mm increase in common carotid artery plaque thickness (APT) corresponds to an 11% increased risk of myocardial infarction. However, most previous studies have focused on APT and incident CVD events, with little attention directed toward estimating APT without direct imaging.

Insulin resistance plays a key role in atherosclerotic plaque progression and clinical outcomes. In patients with carotid artery stenosis, insulin resistance promotes plaque fissuration and rupture through several mechanisms, including increased inflammatory activity, endothelial dysfunction, and enhanced matrix metalloproteinase expression. These processes contribute to higher rates of adverse cerebrovascular events. A study has demonstrated that insulin resistance is independently associated with unstable plaque morphology and worse clinical outcomes in patients with carotid artery stenosis. ⁸ This underscores the importance of metabolic control beyond glycemic measures alone in preventing atherosclerotic complications.

Many machine learning methods have been employed in medical research but are often “black-box” methods. Multivariate adaptive regression spline (MARS) differs in that it provides explicit equations that clinicians can examine. ⁹ The use of MARS in clinical research is in its early stage; however, results indicate that it frequently outperforms traditional multiple linear regression (MLR) analysis where relationships are nonlinear. The present study applied MARS to build an equation incorporating routinely available data for predicting APT in an ethnic Chinese T2D cohort.

Recent advances in pharmacotherapy have demonstrated plaque-stabilizing effects in patients with T2D. Glucagon-like peptide-1 receptor agonists (GLP-1 RAs) and sodium–glucose co-transporter-2 inhibitors (SGLT-2is) reduce cardiovascular events after acute myocardial infarction through multiple mechanisms, including plaque stabilization. GLP-1 RAs reduce macrophage infiltration, decrease oxidative stress, and increase fibrous cap thickness. SGLT-2is improve endothelial function and reduce inflammation. Their combination therapy may provide additive benefits. One study has shown that patients receiving combination therapy exhibited significantly lower rates of major adverse cardiovascular events compared with those receiving either agent alone, supporting the role of these agents in atherosclerotic plaque stabilization. ¹⁰ Additionally, SGLT-2is have been shown to modulate sympathetic tone. According to a recent study, SGLT-2is reduces sympathetic nervous system overactivity, which is a key driver of hypertension, arrhythmias, and adverse cardiovascular remodeling. ¹¹ This sympathomodulatory effect contributes to their cardiovascular benefits beyond glycemic control.

Materials and methods

Participant and study design

This retrospective cross-sectional study conforms to the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guideline. ¹² The participant selection process is summarized in Figure 1. Data were sourced from the Taiwan MJ Cohort, an ongoing prospective cohort study. ¹³ This cohort represents one of the largest health screening populations in Asia. ¹⁴ Eligible participants were consecutively identified from the Taiwan MJ Health Database. The MJ Health Database includes only participants who provided written informed consent to the MJ Health Research Foundation for future research-based use of anonymized data. All patient data were de-identified and anonymized before analyses. Data access was authorized by the MJ Health Research Foundation (Authorization code: MJHRF2024023A). Any interpretations or conclusions described in this paper are those of the authors alone, and do not represent the views of the MJ Health Research Foundation. The study protocol was approved by the Institutional Review Board of the Tri-Service General Hospital. In total, 1584 T2D patients were initially identified. Following exclusion criteria and removal of missing data, 648 participants were retained. Inclusion criteria included: (a) established T2D; (b) age, 50–75 years; (c) body mass index (BMI), 22–30 kg/m²; (d) glycosylated hemoglobin (HbA1c), 6.5%–10.5%; (e) chronic kidney disease (CKD) stage I–III; and (f) availability of previous carotid ultrasound. Exclusion criteria included missing data for age, sex, BMI, lipid levels, liver enzyme levels, renal function test, blood pressure, or ultrasound measurements. Senior nursing staff recorded medical history, and physical examination was performed following standardized protocols. ¹⁵ BMI was calculated as body weight (kg) divided by the square of the height (m). Blood pressure was measured using standard mercury sphygmomanometers. Blood samples were drawn after 10 h fasting. Fasting plasma glucose (FPG), cholesterol, triglyceride, high-density lipoprotein cholesterol (HDL-C,) and low-density lipoprotein cholesterol (LDL-C) levels were measured using standard enzymatic methods. Urine microalbumin level was determined using turbidimetry. The microalbumin-to-creatinine ratio (MCR) was log-transformed. Estimated glomerular filtration rate (eGFR) was calculated using the Chronic Kidney Disease Epidemiology Collaboration (CKD–EPI) equation. CKD staging was assigned per the Kidney Disease: Improving Global Outcomes (KDIGO) guidelines. ¹⁶

Figure 1.

Participant selection process.

Lifestyle variables, including smoking status, alcohol consumption, and physical activity were not systematically recorded in the MJ Health Database for the study period, and therefore could not be included in the analysis. Participants with missing values in any candidate predictor or outcome variable were excluded prior to model development. Therefore, complete-case analysis was performed, and no imputation procedures were applied.

Quantification of carotid intima-media thickness and plaque

APT measurement was performed using a high-resolution B-mode ultrasound machine. All examinations were performed by an experienced neurologist blinded to clinical data. APT was measured in the common carotid artery. For each segment, the sonographer identified the thickest area of the atherosclerotic plaque. Three measurements were taken, and the average was calculated.

Machine learning modeling: MARS and MLR

To predict APT, we employed MARS and conventional MLR. The validation workflow was designed to ensure that the test set remained completely independent during all tuning procedures, thereby providing unbiased performance estimates. The workflow comprised the following steps:

1. Step 1–Data partitioning and repeated train–test splits. The dataset (N = 648) was randomly partitioned using a repeated 80/20 train–test split strategy conducted 10 times. For each of the 10 iterations, 80% of the data (n = 518) was allocated to the training set and 20% (n = 130) was held out as an independent test set. The test set was not accessed during any subsequent model development or tuning steps within that iteration.

2. Step 2–Hyperparameter tuning within training data. Within each training set, hyperparameter tuning for MARS was performed using a systematic grid search combined with repeated 5-fold cross-validation. Specifically, the training data were further split into five folds; four folds were used for model fitting with a given hyperparameter combination, and the remaining fold was used for validation. This process was repeated five times (5 × 5 cross-validation), and the hyperparameter combination that minimized the cross-validated root mean square error (RMSE) was selected. The hyperparameters tuned included the maximum number of basis functions (nk), degree of interaction (degree), generalized cross-validation (GCV) penalty per knot (penalty), and forward step threshold (thresh). The search ranges and final selected values are detailed in Supplementary Table 1. The held-out test set was never used to guide hyperparameter selection.

3. Step 3–Model fitting and performance evaluation. Using the optimized hyperparameters, the final MARS model was fitted on the entire training set and then evaluated on the independent test set. Performance metrics, including mean absolute percentage error (MAPE), symmetric mean absolute percentage error (SMAPE), and relative absolute error (RAE), were computed on the test set predictions. This entire process (Steps 1–3) was repeated for each of the 10 train–test split iterations. The average and SD of each performance metric across the 10 iterations are reported. The corresponding formulas for MAPE, SMAPE, and RAE are provided in Supplementary Table 2.

4. Step 4–Bootstrap-corrected internal validation. To further correct for potential overfitting and to obtain robust confidence intervals (CIs), we performed bootstrap-corrected internal validation. Using 200 bootstrap resamples drawn with replacement from the full dataset, we computed bias-corrected and accelerated (BCa) 95% CIs for mean absolute error (MAE), RMSE, and R². For each bootstrap sample, the entire modeling pipeline (including hyperparameter tuning via 5 × 5 cross-validation) was repeated to ensure that the uncertainty in model selection was incorporated into the CIs.

5. Step 5–Final model construction. After confirming the stability of the hyperparameters across bootstrap samples, the final MARS model was constructed using the full dataset (N = 648) with the modal hyperparameter values across all iterations. The final model retained 11 basis functions after backward pruning using GCV. ¹⁷ MLR was fitted on the full dataset using ordinary least squares and served as the benchmark comparator.

All analyses were conducted in R version 4.0.5 and RStudio version 1.1.453.^18,19 MARS was implemented with the “earth” R package and “caret” R package.^20,21 MLR was implemented using the “stats” R package. Model performance was evaluated using SMAPE, MAPE, RAE, and RMSE. Statistical significance of the difference between MARS and MLR performance across the 10 test-set iterations was assessed using the Wilcoxon signed-rank test (paired, non-parametric). MARS constructs each basis function as a hinge function, partitioning the predictor space at clinically meaningful thresholds. To evaluate agreement between predicted and observed APT values visually, a Bland–Altman plot was constructed.

Variable importance criteria. Variable importance in the MARS model was assessed using two complementary criteria: (a) number of basis functions contributed by each predictor, reflecting the complexity of its relationship with APT; and (b) reduction in GCV score when the variable was removed from the model, reflecting its marginal contribution to model fit. According to these criteria, age contributed the most basis functions (four); however, diastolic blood pressure (DBP) produced the largest GCV reduction when removed. Thus, age was associated with the largest number of basis functions in this study (as described in the Results section), while DBP was found to be the most important factor (as mentioned in the Discussion section). Both statements are accurate when referring to different importance metrics.

Results

Participant characteristics

Table 1 presents the demographic and clinical characteristics of the 648 male T2D patients. Mean participant age was 63.16 ± 11.78 years, mean diabetes duration was 12.26 ± 7.15 years, mean APT was 0.943 ± 0.38 mm, and mean HbA1c was 7.76% ± 1.66%. Supplementary Table 3 presents the results of simple Pearson correlation analysis between APT and all candidate predictor variables. Among all variables examined, only age (r = 0.228, p < 0.01) and diabetes duration (r = 0.087, p < 0.05) demonstrated statistically significant positive correlations with APT. Notably, traditional cardiovascular risk factors, including lipid profile parameters, blood pressure components, and glycemic measures did not demonstrate significant univariate correlations with APT, underscoring the complexity of atherosclerotic plaque formation.

Table 1.

Demographic data of study participants.

Variable	Mean ± SD
Number	648
Age (years)	63.16 ± 11.78
Duration of diabetes (years)	12.26 ± 7.15
Glycosylated hemoglobin (%)	7.76 ± 1.66
Triglyceride level (mg/dL)	147.94 ± 123.02
High-density lipoprotein cholesterol level (mg/dL)	42.64 ± 11.96
Low-density lipoprotein cholesterol level (mg/dL)	102.75 ± 30.09
Alanine aminotransferase (U/dL)	33.36 ± 26.12
Microalbumin creatinine ratio (mg/g)	129.72 ± 484.41
Fasting plasma insulin level (U/dL)	15.38 ± 15.38
Estimated glomerular filtration rate (mL/min)	79.11 ± 27.47
Systolic blood pressure (mmHg)	130.79 ± 14.47
Diastolic blood pressure (mmHg)	77.05 ± 9.54
Body mass index (kg/m2)	26.39 ± 3.66
Atherosclerotic plaques thickness (mm)	0.943 ± 0.38

Model performance

Table 2 presents the comprehensive average performance metrics across the 10 repeated independent test splits for both modeling approaches. The MARS model demonstrated an average MAPE of 0.1714 ± 0.021, SMAPE of 0.1669 ± 0.018, and RAE of 1.112 ± 0.011. The MLR model yielded slightly higher error rates. The Wilcoxon signed-rank test indicated that MARS significantly outperformed MLR across all three relative error measures (V = 45, p = 0.001953).

Table 2.

Average performance of the multivariate adaptive regression splines and multiple linear regression methods.

Model	MAPE (mean ± SD)	SMAPE (mean ± SD)	RAE (mean ± SD)	MAE (Bootstrap mean, 95% CI)	RMSE (Bootstrap mean, 95% CI)	R2 (Bootstrap mean, 95% CI)
MARS	0.1714 ± 0.021	0.1669 ± 0.018	1.112 ± 0.011	0.0174 (0.0137–0.0233)	0.0342 (0.0202–0.0480)	0.2095 (0.1001–0.3738)
MLR	0.1777 ± 0.019	0.1669 ± 0.015	1.114 ± 0.014	0.0175 (0.0140–0.0230)	0.0364 (0.0216–0.0539)	0.1087 (0.0589–0.1898)

MAPE: mean absolute percentage error; SMAPE: symmetric mean absolute percentage error; RAE: relative absolute error; MAE: mean absolute error; RMSE: root mean square error; CI: confidence interval; MARS: multiple adaptive regression spline, MLR: multiple linear regression.

Table 2 presents the bootstrap-corrected internal validation results. For the MARS model, bootstrap-corrected estimates showed a mean MAE of 0.0174 (95% CI: 0.0137–0.0233), mean RMSE of 0.0342 (95% CI: 0.0202–0.0480), and mean R² of 0.2095 (95% CI: 0.1001–0.3738). For the MLR model, the mean MAE was 0.0175 (95% CI: 0.0140–0.0230), mean RMSE was 0.0364 (95% CI: 0.0216–0.0539), and mean R² was 0.1087 (95% CI: 0.0589–0.1898).

Although MARS outperformed MLR, the modest R² value (approximately 0.21) indicates that the model explains only approximately 21% of the variance in APT. This limited explanatory power suggests that other important predictors—such as medication use, lifestyle factors (smoking status, alcohol consumption, and physical activity), or genetic markers—are not captured in our dataset and that APT is influenced by complex multifactorial processes beyond the examined variables. Consequently, this model should be regarded as an exploratory screening adjunct rather than a definitive predictive instrument.

Basis functions and variable contributions

Table 3 details the 11 basis functions derived from the final MARS model. Age contributed four separate basis functions (knots at 77, 78, 80, and 86 years), indicating a highly nonlinear relationship. Diabetes duration contributed one basis function with a knot at 29 years. LDL-C level contributed one basis function with a knot at 106 mg/dL. The MCR contributed two basis functions (knot at 191 mg/g). DBP contributed three basis functions (knots at 93.5, 95.5, and 98 mmHg), demonstrating complex nonlinear effects.

Table 3.

Basis functions (bi) of the MARS model and their coefficients (ai).

Basis function	Hinge function	Coefficient (ai)
B1	Max (0, Age−77)	0.056775725
B2	Max (0, Age−78)	−0.101183423
B3	Max (0, Age−80)	0.047841700
B4	Max (0, 86−Age)	−0.001005045
B5	Max (0, Duration−29)	0.004804590
B6	Max (0, LDL-C−106)	0.000346232
B7	Max (0, 191−MA)	−0.000093276
B8	Max (0, MA−191)	−0.000016122
B9	Max (0, DBP−93.5)	0.077396100
B10	Max (0, DBP−95.5)	−0.139083780
B11	Max (0, DBP−98)	0.062442092

MAPE, SMAPE, and RAE were averaged across 10 repeated 80/20 train–test splits. MAE, RMSE, and R² are bootstrap-corrected estimates from repeated 5-fold cross-validation (5 × 5), with 95% confidence intervals computed using the percentile method (R = 200). p-values based on Wilcoxon signed-rank test; V = 45, p = 0.001953 for MAPE, SMAPE, and RAE.

MARS: multiple adaptive regression spline; MAPE: mean absolute percentage error; SMAPE: symmetric mean absolute percentage error; RAE: relative absolute error; MAE: mean absolute error; RMSE: root mean square error.

Figures and diagnostic plots

Figure 1 presents the participant selection flowchart, illustrating the stepwise exclusion process from the initial 1584 identified patients to the final analytic cohort of 648 participants. Figure 2 presents the complete equation derived from the MARS model. This equation takes the form of a linear combination of hinge functions and can be readily implemented in standard spreadsheet software. Figure 3 displays the calibration plot. Supplementary Figure 1 illustrates the Bland–Altman plot.

Figure 2.

The equation derived from the multiple adaptive regression splines method.

DD: diabetic duration; LDL-C: low-density lipoprotein cholesterol; MCR: microalbumin-to-creatinine ratio; DBP: diastolic blood pressure.

Figure 3.

Calibration plot showing agreement between predicted and observed atherosclerotic plaque thickness using the MARS model.

MARS: multivariate adaptive regression spline.

Both calibration plot (Figure 3) and Bland–Altman plot (Supplementary Figure 1) suggest larger prediction errors at higher APT values. This heteroscedasticity indicates that the model is less accurate in predicting more severe atherosclerotic plaque thickness. Possible explanations include: (a) fewer patients with high APT values in the dataset, leading to less reliable estimates at the upper range; (b) nonlinear biological mechanisms that become more complex with advanced disease; and (c) unmeasured confounders (e.g. medication intensity, genetic factors, and smoking status) that disproportionately affect patients with greater plaque burden. Future studies with larger sample sizes and oversampling of high-risk patients may improve prediction accuracy in this range.

Discussion

Although many studies have examined the role of APT in predicting CVD, few have attempted to predict APT from routinely available data. The present study addresses this gap using the MARS methodology. Our study identified five key factors determining APT, inducing age, diabetes duration, LDL-C level, MCR, and DBP.

Regarding variable importance, age was associated with the largest number of basis functions (four), reflecting the complexity of the age–APT relationship. However, in terms of marginal contribution to model fit (measured based on GCV reduction), DBP emerged as the most influential predictor. This distinction is important; age demonstrated a more complex nonlinear pattern requiring multiple thresholds, while DBP exerted a stronger overall impact on model accuracy despite being associated with fewer basis functions. Clinically, this suggests that both variables are important but through different mechanisms.

Our primary aim was to demonstrate that MARS offers advantages in capturing nonlinear relationships. Under bootstrap-based internal validation, MLR shows slightly lower MAE and RMSE point estimates. However, CIs overlapped substantially. More importantly, MARS explains substantially more variance in APT (R² = 0.2095 vs. 0.1087). This suggests MARS captures considerably more underlying biological variability. This flexibility allows MARS to model complex biological interactions, such as the accelerating effect of age on APT beyond 80 years, which MLR cannot capture without manual transformation.

Although MARS outperformed MLR, the overall predictive performance remained modest (R² ≈ 0.21). Thus, approximately 79% of the variance in APT was not explained by our model. This finding was expected, considering the cross-sectional study design and the limited set of predictors available. APT is influenced by a wide range of factors, including genetic factors, inflammation, oxidative stress, hemodynamics, cumulative lifetime exposure to risk factors, and behavioral factors such as smoking.^22–24 Our model captures only a fraction of these processes. Therefore, our equation should be viewed as a screening tool to identify patients who may benefit from further evaluation, not as a definitive diagnostic or prognostic instrument. Future studies incorporating additional biomarkers, imaging features, lifestyle variables, and longitudinal data may achieve higher predictive accuracy.

A potential concern is collinearity between age and diabetes duration. Unlike traditional linear regression, MARS selects predictors based on incremental contribution, mitigating redundancy. Both variables were retained with distinct basis functions, suggesting that MARS captured unique information from each.

MARS offers distinct advantages. First, it automatically captures nonlinear relationships without requiring manual specification of transformations or interactions. Second, the variance explained by MARS was approximately double of that explained by MLR, indicating superior capturing of the underlying data structure. Third, MARS provides an explicit, equation-based structure maintaining interpretability, which is essential for clinical translation. Our equation is designed to assist clinicians in evaluating cardiovascular risk. It could help identify T2D patients who might benefit from intensive interventions or further diagnostic workup.

Regarding insulin resistance, although our model did not include direct measures of insulin resistance (e.g. homeostasis model assessment of insulin resistance (HOMA–IR)), the identified predictors, particularly diabetes duration, LDL-C level, and MCR, are closely linked to insulin resistance pathophysiology. Future studies incorporating direct insulin resistance metrics may further improve model performance and mechanistic insights.

Regarding GLP-1 RAs, SGLT-2is, and plaque stabilization, the plaque-stabilizing effects of these agents, along with their combination therapy benefits after acute myocardial infarction, have important implications for our findings. Our cohort was assembled before the widespread use of these agents, and medication data were not available for analyses. Consequently, the model may not fully reflect current treatment paradigms. The sympathomodulatory effects of SGLT-2is may influence DBP, one of our key predictors, suggesting a potential mechanistic link between SGLT-2i use, sympathetic tone reduction, DBP lowering, and subsequent plaque stabilization. Future prospective studies should incorporate detailed medication histories to account for these important therapeutic effects.

Regarding age, simple univariate analysis showed significant positive correlation. However, the MARS model reveals that this relationship is non-uniform. Between the ages of 20 and 70 years, APT increased approximately linearly. After the age of 70 years, particularly beyond 80 years, the relationship changed substantially. Blood pressure influences atheroma formation. Itoh et al. have demonstrated that patients with stage 2 hypertension have a significantly higher percentage of abnormal APT values. ²⁵ In another study involving 311 healthy ethnic Chinese participants, SBP remained positively correlated with APT; however, no such trend was observed for DBP. ²⁶ In the present study, only the association with DBP remained significant and exhibited complex nonlinear threshold effects. Aging contributes to increased APT through multiple mechanisms. One study employed carotid ultrasound to evaluate 352 healthy ethnic Chinese participants and found that atheroma volume values increased across age categories. ²⁷ The systematic review conducted by Munckhof et al. revealed a notably close correlation between age and APT. ²⁸ As captured by the MARS model, the age–APT relationship is distinctly nonlinear. ²⁹ The next most important factor was diabetes duration. The Insulin Resistance Atherosclerosis Study has reported significantly greater APT among populations with established T2D. ³⁰ Microalbuminuria is a well-established diabetic microvascular complication. ³¹ Mykkänen et al. measured APT in 991 non-diabetic and 450 T2D patients. Among patients with diabetes, those with higher MA levels had modestly higher APT. ³² Our MARS model identified a threshold effect at 191 mg/g. LDL-C level is the primary atherogenic lipoprotein.^33,34 In a cohort of 402 healthy ethnic Chinese adults, Yang et al. found that LDL-C level was positively correlated with APT. ³⁵ Another longitudinal study on 207 T2D patients has reported broadly similar findings. ³⁶

Certain study limitations should be carefully considered when interpreting these results.

First, external validation was not performed. Our model has not been externally validated in any independent cohort. The model was developed and internally validated using a single dataset from a Taiwanese health screening population. Performance in independent cohorts—particularly in female patients, non-Chinese populations, primary care settings, or populations with different cardiovascular risk profiles—remains unexplored. Internal validation, even with bootstrap correction, cannot be a substitute for external validation in geographically and demographically distinct populations. External validation is a critical prerequisite before any consideration of clinical implementation.

Second, important confounders were not included in our analyses. Data on smoking status, a major established risk factor for atherosclerosis and carotid plaque progression, was not available in our dataset. Multiple large cohort studies have demonstrated that current and former smoking independently predicts increased carotid intima-media thickness and plaque burden.^22–24 The omission of smoking likely contributes to residual confounding and may partially explain the modest R² value observed. Similarly, data on statin therapy (which lowers LDL-C levels and stabilizes plaque), antihypertensive medications (which affect DBP and SBP), alcohol use, and physical activity levels were unavailable. The absence of these variables limits the interpretability of the identified predictors and may have led to biased effect estimates. Readers should not interpret the selected variables as necessarily the most causally important factors, but rather as the strongest predictors among those available in this dataset.

Third, there could be selection bias from the study population. Participants in the Taiwan MJ Cohort are individuals who voluntarily undergo private health screening, a population that tends to have higher socioeconomic status, better health literacy, and lower prevalence of high-risk behaviors than the general population.^37–39 In Taiwan, socioeconomic disparities in health service utilization are well-documented, with higher-income individuals more likely to access preventive screening and exhibit healthier lifestyle patterns, including lower smoking rates.^38,39 This “healthy user” bias limit the external validity of our model to broader, more diverse populations in Taiwan, particularly those with lower socioeconomic status or higher smoking prevalence. The model's performance in population-based cohorts with more representative risk factor distributions remains unknown.

Fourth, our sample size (N = 648) was modest for machine learning.^40,41 Although research has suggested that a sample size of 200 is sufficient, we acknowledge the potential for overfitting. ⁴² We did not account for confounders such as smoking and medication use. Lifestyle factors such as alcohol and physical activity were not included. The study population was drawn from a private health screening center, introducing “healthy user” bias. We did not directly compare MARS with alternative machine learning approaches. Our cohort only included male participants of Chinese ethnicity. Finally, medication usage and blood glucose control were not directly analyzed.

Fifth, the cross-sectional study design limits causal inference. The identified associations between predictors and APT should not be interpreted as causal relationships. Sixth, we did not formally assess inter-observer variability for APT measurement, although a single experienced neurologist performed all examinations. Seventh, we did not directly compare MARS with other machine learning approaches (e.g. random forests, gradient boosting machines, and neural networks), which might achieve different performance characteristics. Eighth, our cohort consists solely of male participants of Chinese ethnicity aged 50–75 years with a BMI of 22–30 kg/m², limiting generalizability to women, other ethnic groups, and patients outside these anthropometric ranges. Finally, medication usage—including glucose-lowering agents, statins, antihypertensives, and antiplatelet drugs—was not directly analyzed and may substantially modify the relationships between our predictors and APT.

Conclusion

This study suggests that MARS provide a more accurate and clinically interpretable approach for estimating APT in Chinese male patients with T2D compared with traditional MLR. By automatically identifying age, diabetes duration, LDL-C level, MCR, and DBP as influential factors, MARS delivers competitive predictive precision while highlighting biologically meaningful thresholds through its basis function structure. However, the modest explanatory power (R² ≈ 0.21) indicates that much of the variance in APT remains unexplained by the variables available in this study. The derived equation may serve as an exploratory screening tool to support early cardiovascular risk stratification; however, it is not a definitive diagnostic instrument and should not replace direct imaging assessment. These findings suggest the potential of interpretable machine learning techniques to enhance individualized risk assessment beyond what traditional regression approaches can achieve. External validation in independent cohorts that include women and diverse ethnic populations and incorporation of important confounders (smoking status, medication use, and physical activity) are necessary before any clinical application can be considered. Further studies with longitudinal follow-up are warranted to validate and extend these findings.