This study utilizes data from two national cohort studies: the China Health and Retirement Longitudinal Study (CHARLS) and the National Health and Nutrition Examination Survey (NHANES).

CHARLS Cohort: CHARLS is a national, population-based cohort study initiated in 2011. It collects data biennially from Chinese adults across various regions. The study employs rigorous stratified sampling to recruit participants, and the data collected covers demographic characteristics, medical history, and lifestyle factors. Baseline data were gathered in 2011, with follow-up data collected through 2018. The study adheres to the principles of the Declaration of Helsinki and was approved by the Ethics Committee of Peking University (approval number: IRB00001052-11015) (25, 26).

NHANES Cohort: NHANES is a major health and nutrition survey conducted by the U.S. National Center for Health Statistics (NCHS). The NHANES study protocol was approved by the NCHS Institutional Review Board, and all participants provided informed consent. This cohort includes demographic, socioeconomic, health-related, and medical information, with data collected between 2011 and 2018. All information from NHANES is publicly available, and no additional ethical approval is required for its use.

Both studies follow ethical research standards, and detailed inclusion and exclusion criteria for both cohorts are depicted in Figure 1.

Depressive symptoms in CHARLS were assessed using the 10-item Center for Epidemiologic Studies Depression Scale (CESD-10). The scale consists of 10 questions, with a total score range from 0 to 30. A score of ≥12 is defined as “positive for depressive symptoms,” indicating clinically significant depression. In the NHANES database, the Patient Health Questionnaire-9 (PHQ-9) was used to assess depression. A score below 10 indicates no depression, while a score of 10 or higher indicates depression. The PHQ-9 is considered the most reliable screening tool for depression (27), with a sensitivity and specificity of 88% for detecting major depression at a cutoff of 10 (28).

The specific method for calculating TyG-BMI in this study is defined as follows: the TyG-BMI formula is TyGBMI = TyG × BMI, where TyG = ln [FPG (mg/dL) × TG (mg/dL) / 2], and BMI = weight / height² (kg/m²) (18, 19).

The key diagnostic criterion for stroke in the CHARLS cohort is self-reported stroke, confirmed by a physician’s diagnosis, with the specific question posed to participants: “Has a doctor ever told you that you had a stroke?” In this cohort, participants with a prior history of stroke were excluded during the baseline survey in 2011 to ensure that only individuals without a history of stroke were included. All exposure variables (such as blood lipids and blood glucose) were measured at baseline (2011) or the first follow-up survey (2013). Stroke events strictly occurred after the measurement of exposures, ensuring the “exposure → outcome” temporal sequence. Follow-up intervals were 2 years, and new stroke events were anchored to specific months and years using the “date of first diagnosis.” Stroke events were monitored through follow-up surveys conducted in 2013, 2015, and 2018, where participants were again asked about their stroke history, and the date of their first stroke diagnosis was recorded (accurate to the month and year). If participants were lost to follow-up or deceased, information on stroke events was supplemented by responses from family members or relevant death certificates. Participants with a history of stroke at baseline, missing key variables, or lost to follow-up were excluded from the analysis.

On the other hand, the NHANES cohort adopts a cross-sectional approach for stroke diagnosis. Stroke was diagnosed through self-report with the question: “Has a doctor ever told you that you had a stroke?” Only participants reporting a stroke within the past year were included in the analysis, excluding those with a long-term stroke history to reduce recall bias. Additionally, stroke-related deaths between 2011 and 2018 were cross-validated with the National Death Index (NDI) using ICD-10 codes (I60–I69). Regarding the temporal sequence of exposure and outcome assessment, stroke status and biomarkers (e.g., blood lipids) were measured within the same survey cycle in the NHANES cohort. However, due to the lack of strict follow-up data in the NHANES cohort, weighted multivariable logistic regression was employed to calculate odds ratios (ORs) for this cohort in order to minimize biases between the two databases. The analysis was adjusted for geographic and population representation biases using complex sampling weights. Participants reporting a stroke occurring more than 1 year ago or missing key variables were excluded from the analysis.

The following covariates were included: (i) categorical variables: marriage, gender, home address, education, smoking, alcohol consumption, hypertension, use of antihypertensive medication, diabetes mellitus, use of hypoglycaemic medication; (ii) continuous variables: age, waist circumference, systolic blood pressure (SBP), diastolic blood pressure (DBP), fasting glucose (Glu), serum high-density lipoprotein cholesterol (HDL), serum low-density lipoprotein cholesterol (HDL), serum low-density lipoprotein (LDL), serum total cholesterol (TC), serum triglycerides (TG), and C-reactive protein (CRP).

The CHARLS project team employed a computer-assisted personal interview system for household surveys (29). The questionnaires covered demographic characteristics, health status, functional ability, diagnosed chronic diseases, and health-related behaviors. Interviewers also measured participants’ height, weight, and blood pressure, among other physiological indicators. Blood samples were collected by trained nurses, who obtained fasting venous blood samples from each participant. The samples underwent a complete blood count within 1–2 h of collection, followed by centrifugation to separate plasma from red blood cells. The samples were then aliquoted and stored at −20°C to ensure safe transportation. Ultimately, all blood samples were sent to the Chinese Center for Disease Control and Prevention for in-depth analysis (29).

The NHANES database used a multi-module design (questionnaires, physical exams, and laboratory tests) to collect data on gender, age, blood pressure, and blood samples. Standardized procedures were employed to ensure the quality of the data. Blood samples were processed, stored, and transported to the University of Minnesota in Minneapolis for analysis (30).

Statistical analyses were performed using R software (version 4.4.3) and SPSS software (version 26.0), with statistical significance defined as a two-tailed p-value < 0.05. The baseline characteristics were categorized based on the median of TyG-BMI and the prevalence of depression, with group comparisons for baseline characteristics. Continuous variables were expressed as medians (interquartile range) or means (standard deviation, SD), while categorical variables were described by percentages and frequencies. Differences between TyG-BMI groups were assessed using the χ² test, and differences in continuous variables were evaluated through analysis of variance and the Kruskal-Wallis H test.

To explore the relationships between TyG-BMI, depression, and stroke risk, multivariate logistic regression analyses were conducted. Three models were constructed: Model 1: unadjusted; Model 2: adjusted for age, sex, marriage, education level, smoking status, drinking, hypertension and diabetes; Model 3: further adjusted for Waist, SBP, DBP, Glu, HDL, LDL, TC, TG and CRP.

In order to address potential heterogeneity between the CHARLS and NHANES cohorts, meta-regression analysis was incorporated to assess and adjust for differences across the two cohorts, thereby enhancing the robustness of the results.

Furthermore, to examine the interaction between TyG-BMI and depression in relation to stroke risk, the study employed additional models to calculate the Excess Relative Hazard Ratio (RERI), the interaction attribution ratio (AP), and the interaction index (S), which allow for a more accurate representation of the synergistic effects between TyG-BMI and depression.

To assess the potential non-linear relationship between TyG-BMI, depression, and stroke risk, Restricted Cubic Splines (RCS) were applied in the analysis. This approach allowed us to model and examine the dose–response relationship more effectively. We also conducted a validation process using two separate datasets: CHARLS as the training set and NHANES as the testing set. This approach helped assess the external validity of the model developed on the CHARLS cohort, ensuring that the findings could be generalized to an independent dataset.

In addition, a mediation effect analysis was conducted to explore the potential indirect effects of TyG-BMI and depression on stroke risk through intermediary variables, such as metabolic factors and inflammatory markers. This analysis allowed us to better understand the pathways through which TyG-BMI and depression may interact and contribute to stroke risk. Mediation analysis was performed using the appropriate statistical models, and the results were adjusted for confounding factors to ensure the validity of the findings.

Subgroup analyses were conducted based on age, gender, hypertension, diabetes, smoking, and alcohol consumption status using stratified logistic regression models. Interaction effects were assessed using likelihood ratio tests for models with and without interaction terms.

A total of 24,171 participants (CHARLS: 6,417; NHANES: 17,754) were included in the analysis. The clinical baseline characteristics of both groups are summarized in Table 1. Supplementary Tables S1, S2 present the clinical baseline characteristics of participants from the CHARLS and NHANES, respectively.

The baseline characteristic tables highlight the distribution differences across the four subgroups defined by TyG-BMI level and depression status. Participants in Group 4 (TyG-BMI ≥ median & Depression) tended to be older, predominantly male, and had the highest prevalence of diabetes (23.78%), hypertension (48.91%), and stroke (6.04%).

Table 2 shows the association between TyG-BMI, depression, and stroke. In the unadjusted model (Model 1), Group 2 (TyG-BMI ≥ median and no depression) exhibited a 64.4% increased risk of stroke compared to the normal Group 1 (TyG-BMI < median and no depression) (unadjusted OR 1.644, 95% CI 1.077–2.311, p < 0.001). Group 3 (TyG-BMI < median and depression) showed a 22.1% increase in stroke risk (OR 1.221, 95% CI 1.123–1.318, p < 0.001). Group 4 (TyG-BMI ≥ median and depression) demonstrated a 94.6% increase in stroke risk (OR 1.946, 95% CI 1.133–2.762, p < 0.001).

After adjusting for potential confounders (Models 2 and 3), the results remained significant. In the fully adjusted Model 3, the stroke risk for Group 2 increased by 73.0% (adjusted OR [aOR] 1.730, 95% CI 1.163–2.297, p = 0.002). The stroke risk for Group 3 increased by 16.0% (aOR 1.160, 95% CI 1.043–1.277, p = 0.002). Group 4 showed a 131.5% increase in stroke risk (aOR 2.310, 95% CI 1.503–3.126, p < 0.001). These results remain valid in the separate analyses of the CHARLS and NHANES cohorts (Table 2).

Figure 2 displays the Kaplan–Meier curve of cumulative stroke incidence in the study population. The results from both the CHARLS and NHANES databases indicate that Group 4 (TyG-BMI ≥ median & Depression) had the highest stroke incidence.

When TyG-BMI was analyzed as a continuous variable, a linear positive correlation between TyG-BMI combined with depression and stroke risk was observed (RCS regression, non-linear p-value = 0.384; Figure 3A). Figures 3B,C also show that TyG-BMI combined with depression is positively correlated with stroke risk in both the CHARLS (Figure 3B) and NHANES (Figure 3C) in separate analyses Supplementary Table S3 highlights the heterogeneity issues within the CHARLS and NHANES cohorts through meta-regression analysis, with urban–rural residence and race showing the most significant impact on the outcomes. Supplementary Table S4 quantifies the additive interaction between TyG-BMI and depression, revealing that high TyG-BMI without depression (RERI = 1.823, AP = 0.475, S = 1.935), normal TyG-BMI with depression (RERI = 1.156, AP = 0.387, S = 1.455), and the coexposure to high TyG-BMI and depression (RERI = 2.734, AP = 0.623, S = 2.208) all demonstrate significant additive interactions. Notably, the coexposure of high TyG-BMI and depression shows a supra-additive effect, indicating that comorbid metabolic dysfunction and depression significantly elevate stroke risk beyond their individual contributions.

As shown in Table 3, in the subgroup analysis, the association between TyG-BMI, depression, and stroke risk was not influenced by gender, age, smoking status, alcohol consumption, or diabetes status in any pre-specified or exploratory subgroup. Specifically, the interaction between these variables and TyG-BMI combined with depression was not statistically significant (interaction p-value>0.05). However, we observed that in populations aged<60, those who had never smoked or had quit smoking, those who had never consumed alcohol, and those without diabetes, the stroke risk in Group 4 was significantly higher (p < 0.05). In contrast, the interaction between hypertension and TyG-BMI combined with depression was statistically significant (interaction p-value<0.05). Specifically, in individuals without hypertension, the risk of stroke was 2.34 times higher in those with elevated TyG-BMI and depression compared to those without both conditions. This result remained consistent in separate analyses of the CHARLS and NHANES databases (Supplementary Tables S5, S6).

Table 4 presents the results of the bidirectional mediation model, analyzing the interactive mechanism between TyG-BMI and depression on stroke risk (adjusting for confounding factors such as age, gender, marital status, education level, smoking, alcohol consumption, hypertension, diabetes, Waist, SBP, DBP, Glu, HDL, LDL, TC, TG and CRP). The results showed that when depression was treated as a mediator, the total effect of TyG-BMI on stroke was −207.36 (95% CI: −310.22, −18.28; p < 0.001), the indirect effect was 4.97 (95% CI: −3.69, 17.51; p = 0.387), and the direct effect was −212.33 (95% CI: −306.53, −35.79; p < 0.001), with the mediation effect accounting for 3.12% (p = 0.431). When TyG-BMI was treated as a mediator, the total effect of depression on stroke was −51.44 (95% CI: −167.70, −2.13; p = 0.036), the indirect effect was 12.57 (95% CI: 2.45, 23.58; p < 0.001), and the direct effect was −64.01 (95% CI, −170.15, −25.71; p < 0.001), with the mediation effect accounting for 15.5% (p = 0.235).

To explore the predictive outcome of the TyG-BMI combined with depression on stroke occurrence, we further developed a predictive model, using the CHARLS database as the internal testing set and the NHANES database as the external validation set. This model demonstrated robust discriminatory power in both internal and external validation cohorts. As shown in Figure 4A, in the CHARLS internal testing cohort (n = 6,417), the AUC was 0.85 (95% CI: 0.82–0.88; p < 0.001), with sensitivity and specificity of 75% at a 1-specificity = 0.25 cutoff. As illustrated in Figure 4B, in the NHANES external validation cohort (n = 17,754), the model’s generalizability was confirmed, yielding an AUC of 0.82 (95% CI: 0.80–0.84; p < 0.001). Calibration analysis demonstrated a high concordance between the predicted probability of stroke occurrence and the observed incidence, with a mean absolute error of 0.026. The Hosmer-Lemeshow test revealed no significant deviation (p = 0.194), as shown in Figure 4C. The bias-corrected calibration curve closely aligned with the ideal line, further supporting the clinical reliability of the model.