This study utilized data from the NHANES (https://www.cdc.gov/nchs/nhanes/). NHANES employs a multistage probability sampling design and integrates interviews, physical examinations, and laboratory tests to generate comprehensive and representative health and nutrition data. All analyses adhered to NHANES-recommended protocols, incorporating sampling weights to account for the survey’s complex design and mitigate non-response bias. Rigorous quality control measures were implemented throughout the survey process to ensure data accuracy and reliability. The initial sample included 10,175 participants. After applying the inclusion and exclusion criteria, the final analysis sample consisted of 2,811 participants aged 40 years or older ( Figure 1 ). Participants were excluded for the following reasons: 6,360 individuals were under the age of 40, as AAC-24 data are only available for participants aged 40 years or older, ensuring consistency with NHANES data availability. Additionally, 675 participants were excluded due to missing or incomplete AAC-24 scores, while 125 individuals were excluded due to the absence of AIP data. Lastly, 204 participants were excluded because of missing information on key covariates, including education level, marital status, smoking status, alcohol drinking status, hypertension, high cholesterol, or diabetes status. While excluding participants with incomplete data may introduce selection bias and limit generalizability, sensitivity analyses using multiple imputation (MI) were performed to evaluate the impact of missing data and ensure the robustness of the findings.

The NHANES study protocol was approved by the Ethics Review Board of the National Center for Health Statistics (NCHS). All participants provided written informed consent before enrollment.

The primary exposure variable, AIP, was calculated from blood samples using the formula log10 (triglycerides/HDL-C) (22). Participants were stratified into quartiles based on AIP distribution: Q1 (-0.682 to -0.153), Q2 (0.154 to 0.392), Q3 (0.393 to 0.650), and Q4 (0.651 to 2.169). Quartiles were determined using a data-driven statistical approach by ranking AIP values from lowest to highest and dividing them into four equal-sized groups. This approach minimizes bias from arbitrary cutoffs and is widely applied in epidemiological research (23), enhancing the robustness of the analysis and facilitating the examination of associations between AIP and AAC risk. AAC was assessed using lateral spine images obtained via dual-energy X-ray absorptiometry (DXA, Densitometer Discovery A, Hologic, Marlborough, MA, USA) and lateral spine vertebral scans conducted at NHANES mobile examination centers. AAC was scored using the AAC-24 and AAC-8 methods (Kauppila score) (24). An AAC-24 score >0 was used to define AAC, while severe AAC (SAAC) was defined as AAC-24 ≥6, consistent with thresholds established in previous studies (25, 26). The cutoff was selected due to its clinical relevance and its strong association with elevated cardiovascular risk, as reported in prior studies (27). Furthermore, sensitivity analysis included the AAC-8 score and severe AAC (AAC-8 ≥ 3) (28, 29). Details of AAC measurement protocols are available at https://wwwn.cdc.gov/Nchs/Nhanes/2013-2014/DXXAAC_H.htm.

Potential confounders were identified through a literature review and included demographic variables (age, gender, race, degree of education, marital status, and poverty income ratio (PIR)), lifestyle factors (such as drinking alcohol and smoking), physical examination data (waist circumference, body mass index (BMI), systolic blood pressure (SBP), diastolic blood pressure (DBP)), biochemical markers (total cholesterol (TC), HDL-C, triglycerides (TG), total protein, albumin, aspartate aminotransferase (AST), alanine aminotransferase (ALT), serum calcium, serum phosphorus, serum creatinine, estimated glomerular filtration rate (eGFR), total bilirubin, serum uric acid, total 25-hydroxyvitamin D), and comorbidities (hypertension, high cholesterol, diabetes). Standardized household questionnaires were used to collect demographic data and traits. The categories for race and ethnicity were Other Hispanic, Mexican American, Non-Hispanic White, Non-Hispanic Black, and Other. Education level was classified as below high school, high school or equivalent, or college or above. Unmarried and married were the two categories for marital status. Drinkers were defined as those who claimed to have had at least 12 alcoholic drinks in a given year. If an individual had smoked 100 cigarettes or more during their lifetime, they were considered smokers. Having a medical diagnosis of hypertension, taking medication for hypertension, or having an average systolic blood pressure of at least 140 mmHg and/or a diastolic blood pressure of at least 90 mmHg were all considered to be indicators of hypertension (30). TC ≥ 240 mg/dL during fasting or while using lipid-lowering medications was considered high cholesterol (31). The criteria for diabetes were hemoglobin A1c value ≥ 6.5%, a fasting plasma glucose value ≥ 126 mg/dL, or a 2-hour plasma glucose value ≥ 200 mg/dL, in addition to a diagnosis of diabetes or the use of hypoglycemic medications (32). Four continuous blood pressure readings were taken. The average of four blood pressure readings was used to define SBP and DBP in this study. Every participant was required to supply an immediate venous blood sample overnight. Body mass index (BMI) was calculated as weight (kg) divided by height squared (m). The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was the method used to determine the glomerular filtration rate (eGFR) (33). The study variables’ comprehensive measurement procedures are accessible to the general public at www.cdc.gov/nchs/nhanes/.

Following the NHANES analysis guidelines, survey-weighted means (95% CIs) were used to describe continuous variables, while survey-weighted percentages with 95% CIs were used for categorical variables. AIP was analyzed both as a continuous variable and as a categorical variable (quartiles, with the first quartile serving as the reference). Group differences were assessed using weighted chi-square tests for categorical variables and weighted logistic regression models for continuous variables. The relationship between AIP and AAC was examined using multivariable logistic regression models. The selection of potential covariates for the multivariable regression models was based on the following criteria: (1) relevant demographic characteristics, including factors such as age, gender, and race, which have been shown to influence both AIP and AAC in prior studies; (2) variables shown to affect AIP and/or AAC in previous studies (34, 35), ensuring that known cardiovascular risk factors were considered in the models; (3) variables whose inclusion resulted in a change of more than 10% in the coefficients of the basic model, in accordance with the STROBE statement (36), the basic model changes by more than 10% after the introduction of covariates; (4) other variables based on clinical experience, including factors that could influence the outcomes but were not captured in the previous categories. The selection process aimed to control for confounding by incorporating these factors, ensuring that the estimated relationship between AIP and AAC was not biased by external influences. Furthermore, model validation was conducted through sensitivity analyses to ensure robustness. Collinearity among independent variables was assessed using variance inflation factors (VIFs), with a VIF > 10 indicating significant multicollinearity that could compromise regression stability. Model 1 represented the unadjusted data. In Model 2, the data were adjusted for age, gender, and race. In Model 3, results were adjusted for age, gender, race, education level, marital status, smoking status, alcohol drinking status, waist circumference, BMI, PIR, total cholesterol, triglycerides, hemoglobin A1c, albumin, total bilirubin, AST, ALT, blood urea nitrogen, serum creatinine, eGFR, serum calcium, serum phosphorus, total protein, serum uric acid, total 25-hydroxyvitamin D, hypertension, high cholesterol, and diabetes status. To assess potential non-linear relationships between AIP and AAC, restricted cubic spline (RCS) analyses were conducted with four knots placed at 0.15, 0.35, 0.65, and 0.95. These placements were based on data-driven criteria and prior recommendations to capture non-linear trends while minimizing overfitting (37). Non-linearity was evaluated using the Wald test. A P-value for non-linearity < 0.05 was considered evidence of a non-linear association, whereas a P-value ≥ 0.05 indicated the absence of significant non-linearity.

Furthermore, stratified analyses were conducted to evaluate effect modification by variables such as gender, age, BMI, eGFR, alcohol drinking status, smoking status, and the presence of hypertension and diabetes. All covariates were adjusted except for the stratification variable itself. Interaction tests were performed by including interaction terms between AIP and the stratification variables in the regression models. Interaction p-values were reported to assess subgroup differences.

To validate the findings, sensitivity analyses were conducted using the AAC-8 scoring system and MI methods. Covariates with missing values included education level, marital status, smoking status, alcohol drinking status, hypertension, high cholesterol, or diabetes status. MI with chained equations was used to address missing data, with five imputations performed for each missing value. The imputation model included all covariates and variables potentially predicting missingness. Results from complete-case analyses were compared with those obtained from the imputed dataset to evaluate the impact of missing data on study conclusions. All statistical analyses were performed using R (version 4.2.0, R Foundation) and EmpowerStats (X&Y Solutions, Inc., Boston, MA). A two-sided p-value < 0.05 was considered statistically significant.

The weighted baseline characteristics of all participants are presented in Table 1 . The mean age of the participants was 57.74 ± 11.51 years, with 48.22% being male. The overall mean AIP was 0.40 ± 0.36, and the quartile ranges were as follows: Q1 (-0.682, -0.153), Q2 (0.154, 0.392), Q3 (0.393, 0.650), and Q4 (0.651, 2.169). Notably, participants in the highest AIP quartile (Q4) were more likely to be male and of Mexican American ethnicity and had lower education levels compared to those in lower quartiles (P < 0.05). Q4 participants also exhibited higher rates of hypertension, diabetes, and hypercholesterolemia (all P < 0.05), indicating a greater burden of cardiovascular risk factors. Q4 participants exhibited significantly higher levels of multiple metabolic markers, including waist circumference, BMI, TG, HbA1c, ALT, and serum creatinine (all P < 0.05). These abnormalities, closely associated with arterial calcification, may illuminate potential mechanisms linking higher AIP to AAC. Furthermore, participants in the Q4 group had significantly higher levels of total 25-hydroxyvitamin D, which may reflect metabolic dysfunction and an increased risk of AAC in this group. Overall, individuals with higher AIP not only exhibited higher cardiovascular risk factors but also had a higher prevalence of AAC and higher AAC-24 scores, further supporting the potential role of AIP as a marker for AAC risk.

The VIFs for all covariates included in the multivariable regression models were calculated to assess potential collinearity. The VIF values for all variables were below 10, with the highest being 5.8 for waist circumference ( Supplementary Table S1 ). This indicates that no significant multicollinearity was present among the selected variables, and all selected covariates were retained for the final analysis. Among all participants, AIP showed a strong positive association with AAC, with each 1% increase in AIP linked to a 31% (OR = 1.31, 95% CI: 1.05–1.64) and 144% (OR = 2.44, 95% CI: 1.38–4.32) increase in AAC risk in unadjusted and fully adjusted models, respectively. Quartile analyses confirmed this trend, with participants in higher AIP quartiles exhibiting significantly elevated AAC risks compared to Q1 (p for trend < 0.003). However, multivariable linear analysis revealed no significant difference between AIP and AAC-24 score or the risk of SAAC after adjusting for covariates ( Table 2 ).

Further sex differences were found in the relationships between AIP and AAC-24 score, the risk of AAC, and SAAC among men and women, as shown in Tables 3 and 4 . Sex-stratified analyses revealed no significant association between AIP and AAC outcomes in men ( Table 3 ). In contrast, women demonstrated a positive association, with AIP linked to higher AAC-24 scores and increased AAC and SAAC risks in both unadjusted and adjusted models ( Table 4 ). The AAC-24 score was 1.2 units higher in the unadjusted model (β = 1.20, 95% CI: 0.67, 1.74) and 0.90 units higher in the fully adjusted model (β = 0.90, 95% CI: 0.22, 1.58) for every one-unit (1%) increase in AIP. Additionally, compared with those of Q1, the AAC-24 score of Q2, Q3, and Q4 were 0.41, 0.53, and 0.91 units higher with fully adjusted β (95% CI) values of 0.41 (-0.04, 0.87), 0.53 (0.04, 1.03), and 0.91 (0.31, 1.51), respectively (P for trend = 0.003). Regarding the association between AIP and the risk of AAC, for each unit (1%) increase in AIP in the unadjusted model, AAC risk increased by 95% (OR = 1.95, 95% CI: 1, 40, 2.72) and by 301% in the fully adjusted model (OR = 4.01, 95% CI: 1.65, 9.74). Participants in Q2, Q3, and Q4 of the AIP demonstrated a significant increase in the risk of AAC when compared to those in Q1, with unadjusted ORs (95% CIs) of 1.59 (1.16, 2.17), 1.81 (1.32, 2.48), and 1.95 (1.40, 2.71), (p for trend < 0.001), respectively. In Model 3, this trend persisted to be significant, with Q1 of AIP as the reference. The fully adjusted ORs and 95% CIs of the Q2, Q3, and Q4 categories were 1.61 (1.11, 2.33), 2.01 (1.30, 3.13), and 2.26 (1.16, 4.40), respectively (P for trend = 0.003). Furthermore, we also observed similar results regarding the association between AIP and the risk of SAAC. There was a 143% increase in the risk of SAAC for every unit (1 percent) increase in AIP (OR = 2.43, 95% CI: 1.52, 3.86) in the unadjusted model and in the fully adjusted model by 837% (OR = 9.37, 95% CI: 2.37, 37.03). Participants in Q2, Q3, and Q4 of AIP demonstrated a statistically significant increase in relative risk for developing SAAC when compared to those in Q1, with unadjusted ORs (95% CIs) of 1.85 (1.15, 2.99), 1.80 (1.10, 2.93), and 2.74 (1.69, 4.42), respectively (p for trend < 0.001). This trend remained significant in Model 3. The fully adjusted ORs and 95% CIs of the Q2, Q3, and Q4 categories were 2.10 (1.16, 3.80), 2.48 (1.24, 4.95), and 5.54 (2.05, 14.96), (p for trend = 0.002).

We used logistic regression models to perform RCS in order to further investigate the possibility of nonlinearity between the AIP index and AAC. As shown in Figures 2 – 4 , an RCS model is used for the dose-response analysis. After adjusting for several potential covariates in Model 3, this model demonstrated that there was no significant evidence for a non-linear relationship between AIP and the risk of AAC in all participants (P for nonlinearity = 0.755). This suggests that the association between AIP and AAC can be adequately described using a linear model within the observed data range. Similarly, no evidence of nonlinearity was observed between AIP and AAC outcomes in either sex (P for nonlinearity > 0.5). The P value indicates that no significant evidence supports a non-linear relationship. However, this does not confirm linearity, and further analysis is needed to clarify the association.

Significant interactions were observed between AIP and gender (P for interaction = 0.039) and AIP and smoking status (P for interaction = 0.005) for the AAC-24 score. Similarly, interactions between AIP and gender (P for interaction = 0.001) and AIP and smoking status (P for interaction = 0.035) were significant for the risk of severe AAC. These findings suggest potential effect modification by these factors, warranting further investigation. Full results are provided in Supplementary Figures S1 , S2 , and S3 .

Sensitivity analyses using AAC-8 scores yielded consistent results, confirming the robustness of the findings. Detailed results are provided in Supplementary Tables S2 - S4 . Among females, the AAC-8 score increased by 0.33 units for every unit increase in AIP (β=0.33, 95% CI: 0.07, 0.58) in Model 3. Furthermore, compared with that of the lowest quartile, the AAC-8 score increased by 0.32 units for every unit increase in AIP (β=0.32, 95% CI: 0.10, 0.55) in Model 3. There was a 477% higher risk of severe AAC (OR=5.47, 95% CI: 1.36, 21.92) for every unit increase in AIP in Model 3 when defining an AAC-8 score of 3 or higher than SAAC. Furthermore, individuals in the highest quartile of the AIP group had a 338% higher risk of SAAC compared to those in the lowest quartile (OR=3.88, 95% CI: 1.40, 10.74) (P for trend=0.016). Likewise, no difference was found in males, regardless of whether AIP was considered as a continuous variable or as a categorical variable of AAC-8 score (P for trend = 0.671) or the risk of SAAC (AAC-8 score ≥3) (P for trend=0.389).

To further validate the results, we conducted MI. The distribution of baseline characteristics for imputed data is shown in Supplementary Table S5 . Sensitivity analysis demonstrated consistent results for the association between AIP and AAC-24 score in the fully adjusted model among females (β = 1.02, 95% CI: 0.44, 1.60, P = 0.001), as well as for the risk of AAC (OR = 2.38, 95% CI: 1.24, 4.59, P = 0.009) and SAAC (OR = 6.17, 95% CI = 2.29, 16.65, P < 0.001) (see Supplementary Table S6 ). No significant differences were found among male participants.