We carried out our study by utilizing data from the National Health and Nutrition Examination Survey (NHANES) database available at www.cdc.gov/nchs/nhanes.com. The purpose was to evaluate the health conditions of individuals aged 20 and older in the United States. The data sets were gathered from various states and counties across the nation. These samples were obtained from all NHANES participants from 1999 to 2018 (n = 101306), we excluded participants whom younger than 20 years (n =46235), those missing data for GGT, waist circumference, fasting insulin or fasting glucose (n = 32486), Participants with tested positive or missing data for HBV/HCV infection(n = 632) and heavy alcohol use(n = 6879), participants without NAFLD (n = 9771), those without HbA1c(n = 5), blood pressure data (n = 229), pregnant participants (n = 59) and participants missing data on follow-up information (n = 6) and other covariates data (n = 153). The analysis sample comprised 4861 participants in total. The screening process details were illustrated in Figure 1 .

The diagnosis of NAFLD usually involves detecting liver fat through imaging examinations such as abdominal ultrasound and magnetic resonance imaging. Additionally, we need to exclude other clear factors of liver injury. If necessary, further liver biopsy is also required. These methods require high operational requirements and are costly. Moreover, steatosis can only be detected when the steatosis rate of liver cells exceeds 20%-30%, it has not been widely applied. Therefore, a score for assessing fatty liver disease in the United States population was developed by CE Ruhl (21). Therefore, we used us-FLI≥30 as a criterion for diagnosing NAFLD.

The eGDR (mg/kg/min) was created as a measure of IR and calculated by using the following formula: eGDR = 21.158 − (0.09∗WC) − (3.407∗HT)− (0.551∗HbA1c) [WC = waist circumference (cm), HT = hypertension (yes = 1/no = 0) and HbA1c = HbA1c (%)] (15). In 2008, TyG index was introduced as a reliable and specific predictor of IR. It has been shown to have a good correlation with the hypoglycemic-hyperinsulinemic clamp test and HOMA-IR. The TyG index was calculated as Ln [fasting triglycerides (mg/dL) × Fasting glucose (mg/dL)/2] (22). HOMA-IR is an indicator used to evaluate an individual’s IR level but it is expensive. The HOMA-IR was calculated as fasting insulin (μU/mL) × fasting plasma glucose (mg/dL)/405 (23). We used ePWV to evaluate arterial stiffness. According to the equation, ePWV was calculated from age and mean blood pressure (MBP): 9.587 − 0.402 × age + 4.560 × 10⁻³ × age² − 2.621 × 10⁻⁵ × age² × MBP + 3.176 × 10⁻³× age × MBP − 1.832 × 10⁻² × MBP. MBP was calculated as diastolic blood pressure+0.4 × (systolic blood pressure − diastolic blood pressure) (24).

In this study, we selected covariates related to NAFLD based on previous research. Demographic information was obtained from the NHANES database, which contained data on age (in years), sex (categorized as male or female), racial/ethnic background (including white, black, Mexican and others), educational attainment (categorized as less than high school, high school, and post-high school education). This information was obtained from the NHANES demographic questionnaire. Body mass index (BMI) was calculated by dividing weight [kg] by the square of height [m²]. We obtained smoking status (yes/no) from the questionnaire. Coronary heart disease (CHD) and congestive heart failure (CHF) were diagnosed based on medical history. In addition, we collected glycated hemoglobin (HbA1c) (%), total cholesterol (TC) (mmol/L), triglycerides (TG) from laboratory examination data. We calculated the estimated glomerular filtration rate (eGFR) based on the creatinine data of participants provided by NHANES using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) method (25). Hypertension was diagnosed based on guidelines provided by the Joint National Committee on Prevention, Detection, Evaluation, and Treatment of High Blood Pressure. We applied hypertension assessment criteria: SBP ≥ 140 mmHg or DBP ≥ 90 mmHg and the patients using anti-hypertensive medications for the period of being investigated (26). We applied diabetes evaluation criteria: doctor diagnosis as diabetes, HbA1c ≥ 6.5%, fasting glucose ≥ 7.0mmol/L, random blood glucose ≥ 11.1mmol/L, 2h OGTT blood glucose ≥ 11.1mmol/L, or being treated with diabetes drugs and insulin (27).

To assess the mortality, we paired the National Death Index data with the mortality information for the period ending on December 31, 2019 (https://www.cdc.gov/nchs/data-linkage/mortality.htm). Outcomes were be defined as all-cause and cardiovascular mortality. Causes of death were defined according to the codes of ICD-10. Cardiovascular mortality was defined using ICD-10 codes 100-109,111,113,120-151 (28).

Firstly, we divided the data into four groups according to the quartile of eGDR. Continuous variables were presented as means (95% confidence intervals (CI)) and proportions with their respective 95% CI were employed for categorical variables. In order to ascertain variations between the four groups, the variance analysis or Kruskal–Wallis test were conducted for continuous variables, while chi-square tests were utilized for categorical variables. Statistical significance was considered at P values < 0.05. We excluded other missing variables after obtaining the main data for the study. Due to the small number of missing variables, we excluded them to ensure the objectivity and accuracy of the results. Finally, the analysis sample comprised 4861 participants in total. When conducting various statistical analyses, we adjusted for demographic variables, hematological indicators and medication information which may have an impact on the prognosis of NAFLD patients (29). Next, we conducted weighted linear regression analyses in order to examine the correlation between eGDR and ePWV. Restricted cubic splines are an important tool in statistics used for smooth fitting and modeling of data, as well as analyzing complex relationships between continuous variables. To examine the correlation between eGDR and ePWV, we employed a restricted cubic spline method. In the multivariate cox regression model, other confounding factors are adjusted so that the real effect can be displayed. Therefore, weighted cox regression analyses were used to investigate the relationship between eGDR and all-cause mortality and cardiovascular mortality. We constructed two models: Model I and Model II. Model I was adjusted for age, sex, race. Model II was adjusted for age, sex, race/ethnicity, education levels, smoking, BMI, TC, TG, eGFR, DM, CHD, CHF, hyperlipidemia, anti-diabetic drugs and anti-hyperlipidemic drugs. Results were presented as hazard ratios (HRs) with 95% CIs. Restricted cubic spline method was used for the correlation between eGDR and mortality. To further ensure the robustness and credibility of the results, sensitivity analysis and subgroup analysis have been adopted in many studies (30). Furthermore, different researchers have utilized different approaches for analysis, such as weighted and unweighted methods. NHANES uses complex sampling techniques to enhance the accuracy and relevance of results. However, discrepancies may arise between weighted and unweighted analyses. Therefore, we conducted a sensitivity analysis using unweighted regression to verify our findings. Receiver operating characteristic (ROC) curve chart is a graph used to evaluate the performance of diagnostic systems and find the optimal threshold. Consequently, we used ROC curves to compare the predictive value of the eGDR with the triglyceride-glucose (TyG) index and the homeostasis model assessment of insulin resistance (HOMA-IR) for all-cause and cardiovascular mortality. Finally, we aim to further clarify the relationship between eGDR and NAFLD in different subgroups.

A total of 4.861 participants with NAFLD were involved in the study. As showed in Table 1 , we divided the data into four groups according to the quartile of eGDR. The baseline characteristics of all participants, including age, sex, race, education levels, smoking, BMI, waist circumference, HbA1c, TG, TC, HOMA_IR, TyG, ePWV, eGFR, DM, CHD, CHF, hyperlipidemia, anti-diabetic drugs, anti-hyperlipidemic drugs, all-cause mortality and cardiovascular mortality are presented in Table 1 . Table 1 shows significant differences in clinical characteristics between the four groups. Compared with the lower eGDR group, patients with higher eGDR were younger, higher levels of education, fewer white people. The high eGDR group has fewer smokers, a lower proportion of hyperlipidemia, CHD, CHF and lower use of hypoglycemic and lipid-lowering drugs. Participants with higher eGDR had lower BMI, WC, ePWV, TyG index, HOMA-IR, HbA1c, higher TC and eGFR (P < 0.001). Additionally, both all-cause mortality and cardiovascular mortality significantly decrease as eGDR increases.

In the unadjusted linear regression analysis, we observed a negative correlation between eGDR and ePWV (β=-0.24(-0.26–0.21, P< 0.001). In Model II, eGDR was significantly negatively correlated with ePWV (β=-0.13(-0.14–0.11, P< 0.001). However, TyG index and HOMA-IR showed no significant correlation to arterial stiffness ( Table 2 ). Restricted cubic spline indicated a non-linear inverse relationship between eGDR and ePWV (P for nonlinear < 0.05). As eGDR increases, ePWV decreases more significantly ( Figure 2 ).

1051 all-cause deaths and 283 CVD deaths were showed during the follow-up period. The mortality rate of eGDR group was shown in the Figure 3 . We observed significant differences in mortality between different eGDR groups (all-cause mortality: P <0.001; cardiovascular mortality: P <0.001). The all-cause mortality and cardiovascular mortality rates were significantly decreased in the higher eGDR group.

We also used cox regression model to evaluate the association between eGDR and mortality. Represented as a continuous variable, we observed a negative correlation between eGDR and all-cause mortality with a hazard ratio (HR) of 0.93 (95%CI: 0.89-0.98) and cardiovascular mortality with a hazard ratio (HR) of 0.84 (95%CI: 0.77-0.92). Compared with participants having lowest eGDR, those having highest eGDR had a reduction of 35% (adjusted HR, 0.65; 95% CI, 0.48-0.89) in the risk for all-cause mortality and 65% (adjusted HR, 0.35; 95% CI, 0.19-0.65) in the risk for cardiovascular mortality in Model II ( Table 3 ).

A restricted cubic spline was used to examine the association between eGDR and mortality. The findings indicated a linear inverse relationship between eGDR and mortality (all-cause mortality: P for non-linear=0.34; cardiovascular mortality: P for non-linear=0.69) ( Figure 4 ). As eGDR rose, there was a substantial decrease in the risk of mortality ( Figure 4 ).

Similarly, sensitivity analysis adopting unweighted logistic analysis reveals that the lower risk of mortality was showed in the highest eGDR (all-cause mortality: HR = 0.61, 95%CI: 0.48-0.77; cardiovascular mortality: HR = 0.34, 95%CI: 0.20-0.57) in Model II ( Table 4 ). These results suggest a consistent inverse relationship between eGDR and mortality.

The ROC curves of eGDR, TyG index, and HOMA-IR predicting mortality in NAFLD patients are shown in Table 5 and Figure 5 . Compared with TyG index and HOMA-IR, the eGDR shows excellent predictive value in all-cause mortality (0.588 vs. 0.550 vs. 0.513, P < 0.001) and cardiovascular mortality (0.625 vs. 0.553 vs. 0.537, P < 0.001). In predicting all-cause mortality, its AUC was 0.588 (0.574,0.602) and the optimal cut-off value was 5.95. The sensitivity was 73.64 and the specificity was 53.15. In predicting cardiovascular mortality, its AUC was 0.625 (0.611,0.639) and the optimal cut-off value was 5.70. The sensitivity was 77.00 and the specificity was 54.50.

We conducted subgroup analysis to examine the possible link between eGDR and mortality among diverse subgroups categorized by age, sex, race, BMI, smoking, CHD and hyperlipidemia ( Supplementary Tables S1 , S2 ). For all-cause mortality, eGDR may have interactive effects in different BMI populations ( Figure 6 ). The influence of eGDR on cardiovascular mortality did not vary among the subgroups ( Figure 7 ).