This study conducted a prospective analysis with data sourced from the CHARLS. Being a nationwide population-based cohort investigation, CHARLS seeks to evaluate the economic circumstances, social conditions and health conditions among Chinese individuals aged 45 years and older. Baseline data gathering was conducted between June 2011 and March 2012, with a final enrollment of 17,708 participants. The present study adopted data derived from five consecutive follow-up investigations conducted across 2011, 2013, 2015, 2018 and 2020. Following the exclusion of subjects aged below 45 years, individuals lacking relevant data for eGDR or hsCRP, people with pre-existing stroke at the baseline assessment, and respondents without available follow-up data, a total of 8,951 subjects formed the final analytical sample [Supplementary Figure 1].

The covariates considered in this study were collected via the CHARLS questionnaires, including demographic characteristics (age, sex, Ethnicity, place of residence, educational background, marital status, disability status, employment status, health insurance type, smoking and alcohol use behaviors), physical assessments (height, weight, waist circumference), medical conditions (hyperlipidemia, DM, heart disease [HD]), medication utilization (lipid-lowering, glucose-lowering, and antihypertensive agents), lifestyle elements (sleep duration, life satisfaction), and blood biochemical markers. In accordance with established protocols, venous blood specimens were gathered by professionally trained personnel from local CDC, and all collected samples were delivered to a designated central laboratory for standardized testing^[18]. Body mass index (BMI) ≥ 24 kg/m² serves as the diagnostic threshold for overweight^[19].

The baseline exposure variable for this research was defined as eGDR. The eGDR was computed via the formula: eGDR (mg/kg/min) = 21.158 - (0.09 × WC) - (3.407 × hypertension) - (0.551 × HbA1c), where WC denotes waist circumference (cm), and hypertension was coded as 1 for yes and 0 for no. Hypertension was categorized as self-reported physician-diagnosed hypertension, a history of antihypertensive drug use, or systolic/diastolic blood pressure ≥ 140/90 mmHg^[20].

Serum hsCRP was measured by immunoturbidimetric assay at Capital Medical University’s Clinical Laboratory using venous blood samples.

The primary endpoint for this analysis was incident stroke. In this study, we gathered information regarding stroke occurrence via structured questionnaires, asking participants whether they had ever been diagnosed with stroke by a physician, along with the date of diagnosis and current treatment status.

In survival analysis, the time scale was the study observation time. Follow-up began at the baseline survey (2011-2012) and continued until the date of incident stroke diagnosis, death, or the last follow-up survey (up to the 2020 wave), whichever occurred first; participants who did not develop stroke were censored at the time of their last valid follow-up survey.

Prior to analysis, height and weight measurements were screened for data quality. Biologically implausible values—defined as height < 1.2 m (n = 8 participants) or weight < 22.5 kg (n = 1 participant)—were identified as data errors, set to missing, and subsequently handled by multiple imputation together with other incomplete variables. No participants were excluded at this step; therefore, the final analytical sample remained 8,951 participants. Data details regarding incomplete datasets within this research are documented in Supplementary Table 1. To minimize possible confounding bias caused by incomplete data, multiple imputation was employed to replace the missing values. We summarized quantitative continuous indicators in the form of mean ± standard deviation or median (interquartile range), and conducted inter-group comparative analyses with analysis of variance (ANOVA) or the Kruskal-Wallis test where applicable. Categorical variables were expressed as frequencies and percentages, and inter-group variations were examined by chi-square tests. Study participants were stratified into four subgroups according to the median cut-off values of eGDR (9.92 mg/kg/min) and hsCRP (1.03 mg/L). We established cumulative stroke occurrence curves via the Kaplan-Meier approach, and calculated adjusted hazard ratios (HRs) with the group featuring eGDR < 9.92 mg/kg/min combined with hsCRP ≥ 1.03 mg/L as the reference group. In addition, crude event proportions (number of events divided by group size) were reported descriptively for each group. To assess collinearity among variables, tolerance and variance inflation factor (VIF) were calculated, and a correlation matrix was generated. Our analysis revealed that all VIF values fell below 5, thus suggesting the absence of significant multicollinearity [Supplementary Table 2].

Covariates for the multivariable models were prespecified a priori based on clinical knowledge and prior literature on stroke risk factors, including age, sex, education level, marital status, work status, disability, smoking, alcohol consumption, BMI, hyperlipidemia, DM, HD, and the use of lipid-lowering, glucose-lowering, and antihypertensive medications. As a supplementary data-driven check of this prespecified adjustment set, we additionally applied the Boruta algorithm^[21], a random forest-based feature selection method. Cox regression models with proportional hazards assumption were adopted to evaluate the association between combined exposure to eGDR and hsCRP and the onset of stroke. The proportional hazards assumption was assessed using Schoenfeld residuals, supplemented by graphical inspection. Although the global test indicated some deviation (P < 0.001), visual examination of the scaled Schoenfeld residuals for the exposure groups did not reveal any meaningful time-dependent pattern, likely reflecting the large sample size [Supplementary Figure 2]. To address the observed violation, we additionally fitted a Cox model stratified by the covariate(s) that violated the assumption, and the results remained consistent with the primary analysis [Supplementary Table 3]. Restricted cubic splines (RCS) were applied in the complete adjustment model to explore dose-response relationships between eGDR and hsCRP separately and the risk of stroke.

We conducted subgroup analyses to investigate the effect modification of combined eGDR and hsCRP exposure on stroke risk across different populations. To verify the robustness of our results, six sensitivity analyses were executed: (1) rerunning the analyses with the original, non-imputed dataset; (2) excluding participants diagnosed with cancer at baseline; (3) removing those with HD at study entry; (4) developing extended models by sequentially including additional confounders, such as blood biochemical markers; (5) using a clinically accepted hsCRP threshold of 3.0 mg/L recommended by the CDC/AHA^[16] instead of the median-based cutoff, with eGDR dichotomized at its median as in the primary analysis; (6) using the triglyceride-glucose (TyG) index (calculated as ln[triglycerides (mg/dL) × fasting glucose (mg/dL)/2]) combined with hsCRP to examine whether the findings were dependent on the specific eGDR formula. The E-value was calculated to determine the minimum magnitude of association that an unmeasured confounder would need to have with both the exposure and the outcome to fully explain the observed association between combined eGDR and hsCRP exposure and stroke risk^[22].

Receiver operating characteristic (ROC) curves were applied to evaluate the predictive value of eGDR combined with hsCRP for forecasting stroke risk. We evaluated the incremental predictive capacity of the models through the use of the C-statistic, net reclassification improvement (NRI), integrated discrimination improvement (IDI), and likelihood ratio test^[23]. Model performance was further evaluated using calibration plots comparing predicted and Kaplan-Meier-observed 9-year stroke risks across deciles, bootstrap internal validation (500 resamples) with optimism-corrected C-statistics, and decision-curve analysis (DCA) to assess clinical net benefit across threshold probabilities. Mediation analysis was conducted to explore the direct and indirect effects of eGDR and hsCRP on stroke occurrence. We defined dichotomous eGDR as exposure variable X, dichotomous hsCRP as mediator M, and stroke as outcome variable Y within Model 1. In Model 2, the roles of X and M were exchanged for complementary analysis. This method has found widespread application in epidemiological studies to measure mediation impacts^[24]. Formal interaction between low eGDR and high hsCRP was assessed on the multiplicative scale (a product term in the Cox model) and the additive scale, using the relative excess risk due to interaction (RERI), the attributable proportion due to interaction (AP), and the synergy index (SI), with 95%CIs estimated from 1,000 bootstrap resamples.

We performed all statistical computations using R software (version 4.5.1). The main packages used were: mice (version 3.19.0) for multiple imputation, Boruta (version 10.0.0) for feature selection, survival (version 3.8.6) and survminer (version 0.5.2) for Cox proportional hazards regression and Kaplan-Meier analyses, rms (version 8.1.1) for RCS modeling, pROC (version 1.19.0.1) for ROC curve analysis, PredictABEL (version 1.2.4) for NRI and IDI calculations, and mediation (version 4.5.1) for mediation analysis. A two-tailed P value below 0.05 was regarded as the threshold for statistical significance.

Table 1 displays the baseline sociodemographic and clinical characteristics of the 8,951 enrolled subjects. The average age of the total study population was 59.32 ± 9.23 years, with 4,138 men (46.23%) and 4,813 women (53.77%) included. Over the follow-up duration, a total of 815 incident stroke events (9.11%) were documented. Grouping by eGDR and hsCRP levels showed that, relative to the group with high eGDR and low hsCRP, participants in the low eGDR/high hsCRP group tended to be older, had a greater representation of urban residents, and had significantly higher prevalence of non-employment, disability, and obesity. Additionally, a history of hyperlipidemia, DM, and HD was more common in this group. The percentage of participants taking lipid-lowering, antihypertensive, and glucose-lowering agents was also markedly higher, indicating that reduced eGDR in combination with elevated hsCRP collectively signals a clustering of unfavorable metabolic and cardiovascular risk factors.

Based on the algorithm's ranking analysis of variable importance [Figure 1], factors such as ethnicity, residence, life satisfaction, sleep duration, and health insurance were excluded as they did not pass the validation threshold. Ultimately, the algorithm identified a set of 15 variables including age, biological sex, educational attainment, marital status, employment status, tobacco smoking, alcohol intake, disability status, BMI, hyperlipidemia, DM, HD, lipid-lowering agents, glucose-lowering agents, and antihypertensive agents. The variables retained by Boruta were fully consistent with the clinically prespecified covariate set, supporting the appropriateness of the adjustment strategy.

The Kaplan-Meier approach was adopted to explore the association of combined eGDR and hsCRP groups with cumulative stroke incidence [Figure 2]. The results showed that the group with low eGDR combined with high hsCRP had the highest crude event proportion (14.44%), followed by the low eGDR/low hsCRP group (9.90%), the high eGDR/high hsCRP group (7.00%), and the high eGDR/low hsCRP group (4.75%). Intergroup disparities reached statistical significance based on the Log-rank test (P < 0.001), suggesting a progressive increase in stroke risk associated with reduced eGDR concentrations and elevated hsCRP concentrations.

Cox regression models with proportional hazards were employed to evaluate the association between combined eGDR and hsCRP concentrations and the risk of stroke [Table 2]. In the unadjusted model, we took the low eGDR/high hsCRP group (eGDR < 9.92 mg/kg/min; hsCRP ≥ 1.03 mg/L) as the reference, and found that the high eGDR/low hsCRP group had a 69% lower stroke risk (HR = 0.31, 95%CI: 0.25-0.38). After full adjustment for confounding factors (Model 3), the detected risk in the subgroup with high eGDR and low hsCRP was still reduced by 51% (HR = 0.49, 95%CI: 0.39-0.62). Furthermore, both the high eGDR-high hsCRP subgroup and the low eGDR-low hsCRP subgroup also demonstrated reduced risks, with corresponding HRs of 0.68 (95%CI: 0.54-0.85) and 0.74 (95%CI: 0.62-0.89), respectively, indicating a graded joint association of eGDR and hsCRP with stroke risk.

Multiple Cox proportional hazards regression models further estimated the independent associations of eGDR and hsCRP with stroke risk [Table 2]. Following comprehensive adjustment for confounding variables (Model 3), participants with eGDR levels ≥ 9.92 mg/kg/min exhibited a 34% reduction in stroke risk relative to their counterparts with eGDR < 9.92 mg/kg/min (HR = 0.66, 95%CI: 0.55-0.79); in contrast, those with hsCRP concentrations ≥ 1.03 mg/L demonstrated a 38% elevation in stroke risk versus participants with hsCRP < 1.03 mg/L (HR = 1.38, 95%CI: 1.19-1.60). Collectively, these findings indicate that, in contrast to relying on a single biomarker, the integrated evaluation of combined eGDR and hsCRP may allow for more robust stratification for stroke risk. RCS regression models additionally uncovered the dose-response associations between these two factors with stroke risk [Figure 3]. eGDR showed a notable negative linear relationship with the risk of stroke (P for overall < 0.001, P for non-linear = 0.588); conversely, hsCRP exhibited a positive non-linear relationship with stroke risk (P for overall = 0.010, P for non-linear = 0.016).

The results of the subgroup analysis [Table 3] revealed that no significant interactive effects were detected in any subgroup (all P for interaction > 0.05). In the subgroups of participants with HD, DM, or hyperlipidemia, no statistically significant association was observed; however, the estimates in these subgroups were unstable, with wide confidence intervals due to limited sample sizes and event numbers. Therefore, these null findings should be interpreted as inconclusive rather than evidence of no association, and larger studies are needed to clarify the associations in these populations.

To assess the robustness of our main results, we conducted a series of sensitivity analyses [Supplementary Tables 4-7]. After excluding missing data, participants with baseline cancer, and those with baseline HD, followed by additional adjustment for hematological indicators, the HRs for stroke risk in the high eGDR-low hsCRP subgroup relative to the reference group were 0.48 (95%CI: 0.38-0.61), 0.49 (95%CI: 0.39-0.62), 0.49 (95%CI: 0.38-0.63), and 0.51 (95%CI: 0.40-0.65), corresponding to each analysis step, respectively. When hsCRP was dichotomized using the clinically accepted threshold of 3.0 mg/L, the results remained consistent with the primary analysis: the high eGDR/low hsCRP group showed a significantly lower risk after full adjustment (HR = 0.60, 95%CI: 0.47-0.77) [Supplementary Table 8]. Using the TyG index (cutoff 8.61) as an alternative, results were consistent: the high TyG/high hsCRP group had the highest stroke incidence (12.5%), and the low TyG/low hsCRP group had lower adjusted risk (HR = 0.55, 95%CI: 0.44-0.68; Supplementary Table 9), indicating robustness. These findings were in strong agreement with the primary analysis, consistently demonstrating that the joint exposure to low eGDR and elevated hsCRP significantly elevates stroke risk. The E-value obtained from Model 3 was 3.5, suggesting that an unmeasured confounder would need to be associated with both exposure and outcome by a risk ratio of at least 3.5-fold each, above and beyond the measured covariates.

Analysis based on ROC curves was further conducted to assess the predictive value of eGDR combined with hsCRP for stroke risk forecasting [Figure 4]. In the overall population, the predictive utility of eGDR (AUC = 0.648) outperformed that of hsCRP (AUC = 0.587), and the joint use of both biomarkers boosted the AUC to 0.679. Among participants with a history of HD, the predictive utility of hsCRP (AUC = 0.606) was marginally superior to that of eGDR (AUC = 0.595), and the joint model additionally elevated the AUC to 0.661 [Figure 4B]. In the non-HD population, the predictive utility of eGDR (AUC = 0.648) was markedly superior to that of hsCRP (AUC = 0.575), and the joint model yielded the peak predictive performance (AUC = 0.673) [Figure 4C]. Overall, these results indicate that the combined application of eGDR with hsCRP enhances the ability for stratification of stroke risk, and their predictive value exhibits heterogeneity across different population subgroups.

To evaluate the incremental predictive value of each biomarker, hsCRP, eGDR, and their combined application were sequentially added into a basic model. Model improvement was quantified through the C-statistic, NRI, IDI, as well as the likelihood ratio test [Table 4]. For the baseline demographic model, the C-statistic stood at 0.719; when hsCRP was added in isolation, it did not yield a statistically meaningful improvement (C-statistic = 0.726, P = 0.302), whereas the inclusion of eGDR elevated the C-statistic to 0.734 (P = 0.059). When both indicators were added together, the model achieved optimal discriminative ability (C-statistic = 0.739, P = 0.037). Reclassification analysis revealed that the NRI associated with the joint model stood at 0.135, which was markedly greater than the corresponding values for models incorporating only hsCRP (0.121) or only eGDR (0.129) (all P < 0.001). The IDI followed a consistent trend, with the combined model showing the largest improvement (0.004), while the single-indicator models both showed an IDI of 0.002. Subsequent likelihood ratio testing corroborated that the joint model delivered the most pronounced improvement in model goodness-of-fit (Estimate = 38.73, P < 0.001), outperforming models incorporating eGDR alone (Estimate = 21.41, P < 0.001) and hsCRP alone (Estimate = 19.13, P < 0.001). Compared with either single indicator, the combined application of eGDR and hsCRP provided statistically significant, albeit modest, incremental value in predicting stroke risk.

The full combined model was well calibrated, with predicted 9-year stroke risks closely matching observed risks across deciles [Supplementary Figure 3]. Bootstrap internal validation (500 resamples), based on the overall concordance index of the Cox model, yielded an apparent C-statistic of 0.673 and an optimism-corrected C-statistic of 0.665 (optimism = 0.008), suggesting minimal overfitting. DCA showed a net benefit of the combined model over treat-all and treat-none strategies at threshold probabilities of approximately 2%-25%, although the incremental net benefit over the basic model was modest [Supplementary Figure 4].

Mediation analysis uncovered the dynamic interplay between combined eGDR and hsCRP in the pathway linking them to stroke risk [Figure 5]. Our mediation modeling results revealed that hsCRP explained 6.40% of the relationship between eGDR and stroke occurrence (P < 0.001); on the other hand, eGDR explained 4.41% of the relationship between hsCRP and stroke occurrence (P < 0.001). This nearly symmetrical pattern suggests that the statistical associations of each biomarker with stroke are partially captured by the other; however, given the observational design and the dichotomization of the variables, these results should be interpreted as a decomposition of statistical associations rather than evidence of causal or biological pathways.

No significant interaction between low eGDR and high hsCRP was detected on either scale: the multiplicative product term was not significant (P for interaction = 0.811), and additive interaction measures were close to their null values with confidence intervals crossing them (RERI = 0.129, 95%CI: -0.351-0.538; AP = 0.063, 95%CI: -0.172-0.262; SI = 1.141, 95%CI: 0.744-2.156) [Supplementary Table 10], suggesting that the elevated stroke risk in the double-exposed group largely reflects the combined rather than interactive effects of the two biomarkers.