2.1 Date Source and Participants

All data utilized in this study were obtained from the National Health and Nutrition Examination Survey (NHANES), an ongoing research program conducted by the National Center for Health Statistics (NCHS). NHANES integrates interviews and physical examinations to assess the health and nutritional status of a nationally representative sample of approximately 5000 individuals annually, providing critical statistics to the Centers for Disease Control and Prevention (CDC) for public health monitoring and policy development [28]. The research protocol of NHANES was approved by the NCHS Ethics Review Board, and all participants provided written informed consent, with NHANES data being publicly accessible and freely available for secondary analysis [29, 30]. Further details about NHANES can be accessed at https://www.cdc.gov/nchs/nhanes/index.htm.

For this study, we included 3632 participants aged ≥ 60 years who completed cognitive function assessments in the NHANES database from 2011 to 2014. After excluding individuals with incomplete cognitive function assessments and missing data for eGDR and covariates, a total of 2370 participants were retained for analysis. The participant selection process is illustrated in Figure 1.

2.2 Cognitive Function Assessment

The cognitive function of participants included in this study was assessed using the Consortium to Establish a Registry for Alzheimer's Disease Word Learning and Recall Module (CERAD), the Animal Fluency Test (AFT), and the Digit Symbol Substitution Test (DSST). The CERAD module consists of three consecutive word learning trials, followed by a delayed word recall test administered after completing the AFT and DSST. Widely utilized in clinical and research settings, CERAD is particularly effective for evaluating cognitive function, with a focus on explicit memory. The CERAD is a comprehensive tool for assessing multiple cognitive domains, including memory, language, visuospatial skills, and executive function, making it particularly valuable for the early diagnosis of dementia by identifying impairments across various cognitive areas [31]. Widely utilized in both clinical and research settings, CERAD is especially effective in evaluating explicit memory, with its Word List Memory Test validated across diverse populations and recognized as a reliable instrument for monitoring cognitive function [32]. The AFT is one of the few neuropsychological assessments that meet the criteria for robust testing and can be fully applied across different linguistic and cultural backgrounds [33]. It evaluates cognitive function by asking participants to name as many animals as possible within 1 min and has proven effective in identifying MCI and Alzheimer's disease (AD) [34]. The DSST is widely used in clinical neuropsychology as an effective and sensitive tool for assessing cognitive impairments, comprehensively measuring processing speed, attention, and executive function by evaluating the speed and accuracy of completing number-symbol matching tasks within a limited time [35]. The results of the DSST provide critical data for clinicians and researchers to identify abnormal changes in cognitive function and monitor the onset and progression of cognitive impairments [36, 37].

Building on previous studies [38, 39], this research established “Cognitive scores” as the measure of participants' cognitive abilities by integrating their CERAD, AFT, and DSST scores, minimizing discrepancies in assessments across different scoring systems, and controlling for extreme values to reduce biases caused by floor or ceiling effects. $$$ \mathrm{Cognitive}\ \mathrm{scores}={\sum}_1^3\left(x-\mathrm{Mean}\right)/\mathrm{SD} $$$, x represents the score of that test, and mean and SD represent the mean and standard deviation of that test, respectively. Given the absence of a gold standard for diagnosing cognitive impairment through cognitive scores, this study defined cognitive impairment as scores below the 25th percentile (P₂₅) of “Cognitive scores” (Cognitive scores P₂₅ = −1.67) [40, 41].

2.3 Assessment of eGDR

The equation for eGDR is defined as: $$$ \mathrm{eGDR}=21.158-0.09\times \mathrm{WC} $$$ $$$ \left(\mathrm{cm}\right)-3.407\times \mathrm{HP}-0.551\times \mathrm{HbA}1\mathrm{c}\ \left(\%\right) $$$ [26], where WC represents waist circumference, HP indicates the presence of hypertension (HP = 1 for hypertensive patients and HP = 0 for non-hypertensive patients), and HbA1c levels are quantified using high-performance liquid chromatography, which utilizes ionic interaction-based separation and photometric detection to measure the stable HbA1c form.

2.4 Covariates

The covariates included in this study were gender (male and female), age, race/ethnicity (Mexican American, other Hispanic, Non-Hispanic White, Non-Hispanic Black, and other races), educational level (less than high school, high school or GED, and more than high school), poverty-income ratio (PIR) (PIR > 4 as high income [42], PIR ≤ 4 as non-high income), and body mass index (BMI) categorized as normal (< 25 kg/m²), overweight (25 to < 30 kg/m²), and obese (≥ 30 kg/m²).

Hypertension was defined as either being diagnosed by a physician or other healthcare professional or currently using antihypertensive medications [43]. Diabetes was defined as being diagnosed by a physician or other healthcare professional, HbA1c levels ≥ 6.5%, fasting plasma glucose (FPG) levels ≥ 7.0 mmol/L after an 8-h fast, 2-h plasma glucose levels ≥ 11.1 mmol/L during an oral glucose tolerance test (OGTT), or current use of glucose-lowering medications or insulin therapy [44]. Stroke was defined as a diagnosis confirmed by a physician or other healthcare professional. Alcohol consumption was categorized into three levels: (1) never: lifetime consumption of < 12 drinks; (2) former: lifetime consumption of ≥ 12 drinks but no drinking in the past year; (3) now: ≥ 12 drinks in the past year. Smoking status was divided into two levels: (1) never: lifetime smoking of ≤ 100 cigarettes; (2) now: lifetime smoking of > 100 cigarettes.

2.5 Statistical Analysis

Participants were classified into four groups based on their eGDR levels. Descriptive statistics for continuous variables are presented as mean ± standard deviation (Mean ± SD), while categorical variables are presented as counts and percentages. Group comparisons for categorical variables were performed using the chi-squared test. For continuous variables, analysis of variance (ANOVA) was used for data that met normality assumptions, while the Kruskal–Wallis test was applied for data that deviated from normality. Detailed results for the normality tests of continuous variables are provided in Table S1. To assess the associations between eGDR levels, eGDR quartiles, and cognitive impairment, multivariable logistic regression models were used. For cognitive scores, multivariable linear regression models were applied. These models were adjusted for potential confounders using three hierarchical approaches: Model 1 (unadjusted), Model 2 (adjusted for age, gender, and race), and Model 3 (adjusted for age, gender, race, education level, income status, alcohol use, smoking status, BMI, and stroke history).

Restricted cubic splines (RCS) were utilized to explore the dose–response relationship between eGDR levels and cognitive impairment. Interaction tests were stratified by age, gender, education level, smoking status, alcohol consumption, stroke history, BMI, and income status. The results were visually presented using forest plots. Additionally, the Boruta algorithm was employed to identify key variables influencing cognitive impairment in this study. Machine learning techniques, including LASSO, XGBoost, and Random Forest, were used to develop and validate predictive models for cognitive impairment based on eGDR levels. The performance of these models was assessed using receiver operating characteristic (ROC) curves and calibration plots, and their clinical utility was further evaluated by decision curve analysis (DCA). Correlation analysis and SHAP (Shapley additive explanations) values were used to assess the relative importance of different IR indices (such as TyG, TG/HDL-C, and METS-IR) in predicting cognitive impairment and to identify key factors influencing cognitive health.

All statistical analyses were performed using EmpowerStats (version 4.1) and R software (version 4.3.3). The odds ratio (OR) with 95% confidence intervals (CI) was reported for the relationship between eGDR and cognitive impairment, while β coefficients with 95% CI were used to quantify the association between eGDR and cognitive scores. A p-value of less than 0.05 was considered statistically significant.

3.1 Population Characteristics

The study included a total of 2370 participants, who were stratified into four groups based on eGDR quartiles: Q1 (−1.45–4.74), Q2 (4.74–6.18), Q3 (6.18–8.55), and Q4 (8.55–12.37). Significant differences in baseline characteristics were observed across the four groups (p < 0.05), as detailed in Table 1. Participants in Q4 were more likely to be high-income, well-educated females under the age of 70, with lower rates of stroke and hypertension, higher cognitive scores, and a decreased prevalence of cognitive impairment compared to participants in Q1.

3.2 Relationship Between eGDR and Cognitive

The associations between eGDR levels, its quartiles, and cognitive outcomes were assessed using multiple linear and logistic regression models (Tables 2 and 3). In the fully adjusted Model 3, eGDR was significantly positively associated with cognitive scores (β = 0.095, 95% CI: 0.053–0.136, p < 0.001), indicating that each 1-unit increase in eGDR corresponded to a 0.095-point improvement in cognitive scores. Quartile analysis further demonstrated significantly higher cognitive scores across all quartiles compared to Q1 (p < 0.05). The most pronounced increase was observed in Q4, with a 0.541-point rise in cognitive scores (β = 0.541, 95% CI: 0.265–0.816, p < 0.001). Similarly, eGDR showed a significant inverse association with the risk of cognitive impairment (OR = 0.925, 95% CI: 0.873–0.980, p < 0.01), indicating a 7.5% reduction in the odds of cognitive impairment for each 1-unit increase in eGDR. Quartile analysis reinforced these findings, with participants in Q4 demonstrating 32.8% lower odds of cognitive impairment compared to those in Q1 (OR = 0.672, 95% CI: 0.457–0.987, p < 0.05).

After adjusting for potential confounders, RCS analysis was performed to evaluate the relationship between eGDR levels and the risk of cognitive impairment. As illustrated in Figure 2, eGDR demonstrated a significant linear inverse association with the risk of cognitive impairment (p for overall < 0.001), with no evidence supporting a nonlinear relationship (p for nonlinearity = 0.139). These results indicate that higher eGDR levels may act as a protective factor against cognitive impairment.

3.3 Interaction test

To assess the reliability of the relationship between eGDR and cognitive impairment, interaction tests were conducted for age, gender, education level, income status (high vs. non-high), alcohol consumption, smoking status, BMI, and history of stroke, as well as for interactions between these factors. The findings (Figure 3) consistently showed a negative association between eGDR and cognitive impairment across all subgroups, with the strongest association observed in overweight women under 70 years old with lower education levels, non-high income, nonsmoking status, and no history of stroke (p < 0.05). No significant interactions were detected across subgroups (p for interaction > 0.05).

3.4 Identification of Key Variables for Cognitive Impairment Using the Boruta Algorithm

In the Boruta algorithm analysis, variables identified in the green zone, including eGDR, were confirmed as significant risk factors, underscoring their critical role in cognitive impairment. Specifically, eGDR emerged as a key risk factor, with its elevated Z-score indicating a substantial contribution to the overall risk profile. In contrast, variables in the red zone, such as smoking status, were classified as non-significant, reflecting their negligible association with the risk of cognitive impairment. For further details, refer to Figure 4.

3.5 Development and Validation of a Machine Learning Prediction Model for eGDR and Cognitive Impairment

Figures 5-7 present the ROC curves (Figures 5-7) and corresponding calibration plots (Figures 5-7) for the LASSO, XGBoost, and Random Forest models in relation to eGDR and cognitive impairment. LASSO was chosen for its capacity to handle high-dimensional data through variable selection, thereby improving model interpretability and reducing the risk of overfitting. XGBoost was selected for its robust predictive performance, particularly its ability to model complex relationships and interactions within the data, as well as its capability to manage missing data and apply regularization to mitigate overfitting. Random Forest was employed due to its ensemble approach, which combines multiple decision trees to minimize variance and enhance the accuracy of predictions, making it highly effective for both categorical and continuous variables. The results indicate that all three machine learning models exhibit ROC curves with an AUC greater than 0.7, and their calibration plots confirm successful model development. Among these, the LASSO model performed the best, with an AUC of 0.778 (Figure 5A), while the Random Forest model demonstrated the most favorable calibration results (Figure 7B). Furthermore, the DCA shown in Figure 8 reveals that the net benefit curves for LASSO, Random Forest, and XGBoost are relatively similar and significantly above the “None” and “All” reference lines. This suggests that these models provide considerable net benefits for clinical decision-making regarding eGDR and cognitive impairment across different threshold probabilities, thereby offering effective decision support.

3.6 Comparison of eGDR With Other IR Indices (TyG, TG/HDL-C, METS-IR) for Predicting Cognitive Impairment

To further analyze the predictive performance of eGDR, TyG, TG/HDL-C, and METS-IR for cognitive impairment, participants with incomplete data on FPG, TG, and HDL-C were excluded to ensure the accuracy of the results. This led to a final sample of 1155 participants. Cognitive impairment was defined based on cognitive scores, with the 25th percentile value (P₂₅ = −1.77) used as the threshold to classify participants into cognitive impairment and non-cognitive impairment groups. Table S2 provides a detailed comparison of demographic characteristics and other relevant variables between the two groups of participants.

Through correlation analysis and SHAP modeling, the relationship between the study variables and cognitive impairment was further explored. Figure 9A presents the correlation analysis between the study variables and cognitive impairment. Among the IR surrogate markers examined, eGDR and TG/HDL-C showed a negative correlation with cognitive impairment, while TyG and METS-IR were positively correlated. The strongest correlation was observed for eGDR. Figure 9B,C show the variable importance for predicting cognitive impairment based on SHAP values. The x-axis in Figure 9B (mean (|SHAP value|)) represents the average absolute SHAP value for each variable, indicating its relative importance in predicting cognitive impairment. The results highlight that, compared to other IR surrogate markers, eGDR holds the highest predictive importance. Figure 9D illustrates a positive correlation between the SHAP values for eGDR, TyG, and METS-IR, except for TG/HDL-C, with eGDR showing the strongest relationship.