The study subjects were female and male participants drawn from the NHANES (13). This study incorporates the populations in the NHANES database from 2007 to 2008, 2009 to 2010, 2011 to 2012, 2013 to 2014, 2015 to 2016, and 2017 to 2018. The NHANES database was a nationwide and ongoing cross-sectional survey conducted among the non-institutionalized US population. The database is publicly available at https://www.cdc.gov/nches/nhanes. The NHANES protocol was approved by the National Center for Health Statistics (NCHS) Research Ethics Review Board. 2007 to 2008, 2009 to 2010, 2011 to 2012, 2013 to 2014, 2015 to 2016, and 2017 to 2018 NHANES cycles were selected, and a total of 59,482 participants were included in the study. We excluded participants with missing HF, TyG index, and covariates. We also excluded uncertain diagnosis of HF. Finally, a total of 13,825 participants were included in the present study. The flowchart of sample selection is shown in Figure 1 .

We used the “MCQ160B” variable from MCQ in the questionnaire to diagnose HF, which asked “Someone ever told you had congestive HF?” Some previous NHANES-based articles have been published (14–16). The demographic information and characteristics, which consist of age, gender, body mass index (BMI), race, education, and income, were obtained by interviewing. The TyG index (17) was calculated by TyG = Ln [fasting TG (mg/dL) ×fasting glucose (mg/dL)/2]. Thus, we included triglyceride and fasting glucose data to calculate the TyG index. The TyG index was divided into four groups, according to the quartiles (Q1: <P25, Q2: P25–P50, Q3: P50–P75, and Q4: P75). Homeostasis Model Assessment of Insulin Resistance (HOMA-IR) (18) was calculated by HOMA-IR = (fasting glucose (mmol/L)×fasting insulin (μU/ml)/22.5).

Covariates included demographic data including age, race, gender, education, and household income level. Personal data included BMI, sex, and age. Age was divided into three groups (20 to 40, 40 to 60, and ≥61), family income level was divided into two groups according to the score of income poverty (low-income families and high-income families), and BMI was divided into three groups (<25.0, 25.0–29.9, and ≥30.0 kg/m²). Education level was divided into three groups based on high school (less than high school, high school, and more than high school), and race was divided into five groups (Mexican, Hispanic, white, black, and others). Individuals were considered to have coronary heart disease if they answered yes to the question “Someone ever told you had coronary heart disease?” Individuals were considered to have angina pectoris if they answered yes to the question “Someone ever told you had angina pectoris?” Individuals were considered to have heart attack if they answered yes to the question “Someone ever told you had heart attack?” Individuals were considered to have stroke if they answered yes to the question “Someone ever told you had stroked?” Type 2 diabetes mellitus (19) was defined as a diagnosed case of diabetes mellitus with insulin or oral hypoglycemic agents and fasting glucose levels above 7.0 mmol/L (126 mg/dL) or glycated hemoglobin A1c (HbA1c) levels above 6.5%.

All statistical analyses were performed using the R software (R version 4.3.1) and SPSS (25.0). NHANES collected data nationally representative through a complex sampling design and the use of sample weights. In this paper, the data are weighted according to the sample weight calculation method recommended by NHANES. The demographic characteristics of the HF and non-HF groups were described by the composition ratio (%), and the weighted χ² test was used to compare the differences between the two groups. Weighted univariate logistic regression analysis calculated the independent risk factors for HF. The TyG index was divided into Q1 to Q4 groups according to quartiles, and the Q1 group was used as the reference group to adjust for potential confounders, including age, sex, BMI, poverty income ratio, education, coronary heart disease, heart attack, stroke, hypertension, and diabetes. A multivariate logistic regression model was used to analyze the relationship between the TyG index and HF risk, and the results were reported as the OR and its 95% confidence interval (95% CI) and p-values. No covariates were adjusted for as indicated in Model 1. Age, sex, and BMI were adjusted in Model 2; coronary heart disease, angina pectoris, heart attack, stroke, and hypertension were adjusted in Model 3. Model 4 was adjusted for all covariates, including age, sex, BMI, coronary heart disease, angina pectoris, heart attack, stroke, hypertension, and diabetes. In addition, we carried out several restricted cubic spline (RCS) analyses to explore the non-linear dose–response relationship between HF and the TyG index in the whole population, and four knots were placed at the 5th, 35th, 65th, and 95th percentiles. ROC (20) curves were used to evaluate the predictive efficacy of TyG on patients with HF. 1 − Specificity is the X axis in the ROC curve plot, and the Y axis represents the sensitivity. The accuracy of index in predicting the HF determines the offline area (AUC) of the ROC curve. p-values <0.05 were considered as statistically significant differences in chi-square test, ANOVA, RCS analyses, and ROC curves.

A total of 13,825 study subjects, namely, 6,651 men and 7,174 women, were included in this study, as shown in Figure 1 . Of the 13,825 subjects, 435 were diagnosed with HF, representing 3.14% of the total population. Compared with non-HF people, the included HF population group had lower education level and income level and higher body mass index (p < 0.001). Male, age, coronary heart disease, heart attack, hypertension, angina pectoris, and stroke were higher among the HF population (p < 0.001). In addition, diabetes incidence was higher among the HF population ( Table 1 ). In terms of laboratory indicators, HF patients had higher levels of triglyceride and fasting plasma glucose. Notably, the HF group exhibited a significantly higher TyG index and HOMA-IR than the non-HF group (8.91 vs. 8.57, p < 0.001 for TyG index; 7.27 vs. 4.01, p < 0.001 for HOMA-IR).

To further investigate the correlation between the TyG index and HF, Table 2 presents the baseline characteristics of the patients divided into quartiles based on the TyG index ( Table 2 ). The TyG index was divided into four groups, namely, ≤8.15, 8.16–8.57, 8.58–9.03, and ≥9.03 in Q1, Q2, Q3, and Q4, respectively. Individuals in Q4 had a higher BMI, with lower education, lower household income level, and more male population. The prevalence of hypertension, coronary artery disease, heart attack, stroke, and angina pectoris had a significant difference (p < 0.001) among Q1, Q2, Q3, and Q4, while Q2 occupied the highest proportion of angina pectoris (18.2%). Individuals in Q2 had a higher risk of stroke than individuals in Q3. Among the patients in the Q4 group, they exhibited a higher incidence of diabetes. With the increase of the TyG index, there was a gradual increase in the incidence of diabetes.

Multiple logistic regression models study the relationship between TyG index levels and HF. The unadjusted model and the adjusted model are shown in Table 3 and Figure 2 . In Model 1, without adjusting for any variables, the OR of HF was increased with a higher TyG index (OR: 1.644, 95% CI 1.451, 1.863, p < 0.001), and the test for trend was statistically significant. After adjusting for age, sex, and BMI, the OR in Model 2 was 1.306. Model 3 was adjusted for coronary artery disease, heart attack, stroke, angina pectoris, and hypertension. We found significant correlation between TyG index levels and HF in Model 2 and Model 3. When the models were further adjusted for all covariates, we found no significant correlation between the TyG index and HF (OR [95% CI] = 1.057 [0.888–1.259], p = 0.531). In addition, we transformed TyG index into categorical variables (Q1, Q2, Q3, and Q4). Compared with the Q1 group, Q2, Q3, and Q4 in Model 1 had increased risk of HF, and the OR (95% CI) values are 1.629 (1.182–2.244), 1.716 (1.249–2.358), and 2.795 (2.081–3.755), respectively. After adjusting for age, sex, and BMI, the OR in Model 2 was 1.077, 0.948, and 1.382 compared with the Q1 group, respectively. After further adjustment for coronary artery disease, heart attack, stroke, angina pectoris, and hypertension, the OR in Model 3 was 1.195, 1.118, and 1.537 compared with the Q1 group, respectively.

The TyG index levels in Model 2 and Model 3 were positively correlated with HF, while there were no statistically significant differences in the Q2 and Q3 group (Model 2: p = 0.657 for the Q2 group, p = 0.747 for the Q3 group; Model 3: p = 0.324 for the Q2 group, p = 0.535 for the Q3 group). After adjusting all covariates, the TyG index was negatively correlated with the risk of HF in Model 4 (OR = 0.970 in the Q2 group; OR = 0.808 in the Q3 group; OR = 0.996 in the Q4 group), while there were no statistically significant differences (p = 0.868 for the Q2 group; p = 0.250 for the Q3 group; p = 0.982 for the Q4 group).

The dose–response relationship between the TyG index and HF was further explored using restricted cubic spline plots ( Figure 3 ), and results are displayed in Figure 3 . We built four restricted cubic spline plots according to Model 1, Model 2, Model 3, and Model 4, and all the curves were J-shaped. Model 1 and Model 3 showed that there was a linear dose–response relationship between TyG and HF (p = 0.686, p = 0.619). However, in Model 2 and Model 4, we found that there was a nonlinear dose–response relationship between TyG and HF (p = 0.004, p = 0.042). The risk of HF increases with rising TyG index. In addition, we also conducted a restricted cubic spline regression model based on the TyG index quartiles. The results showed that there was a linear dose–response relationship between the TyG index and HF risk in Model 1 (p for non-linearity = 0.151), Model 2 (p for non-linearity = 0.081), Model 3 (p for non-linearity = 0.345), and Model 4 (p for non-linearity = 0.297). Figure S1 showed the relationship between TG, fasting glucose and HF risk.

ROC curves were used to evaluate the predictive efficacy of TyG on patients with HF. This area is proportional to the predicted value of the index; the larger the AUC, the higher the predicted value; otherwise, the lower the predicted value is. By drawing the ROC curve, the TyG index (continuous) predicted the area of the ROC curve of 0.602 (95% CI: 0.575–0.629, p < 0.001). The optimal cutoff value was 8.91, suggesting some value for predicting the occurrence of HF when the TyG index is greater than 8.91 ( Figure 4 ). The corresponding sensitivity and specificity were 45.1% and 70.2%, respectively. Statistical significances were found in predicting the area of the ROC curves in Model 1 (AUC: 0.598, 95% CI: 0.571–0.625, p < 0.001), Model 2 (AUC: 0.806, 95% CI: 0.788–0.825, p < 0.001), Model 3 (AUC: 0.885, 95% CI: 0.868–0.903, p < 0.001), and Model 4 (AUC: 0.908, 95% CI: 0.894–0.923, p < 0.001), based on the TyG index quartiles.