Combined associations of the metabolic score for insulin resistance and estimated glucose disposal rate with cardio-renal-metabolic multimorbidity: evidence from two large population studies

Abstract

Objectives

The estimated glucose disposal rate (eGDR) and the metabolic score for insulin resistance (METS-IR) are widely used and reliable clinical indicators of IR. However, how their combined effect influences the risk of cardio-renal-metabolic multimorbidity (CRMM) has not been well characterized. This study sought to evaluate both the individual and synergistic associations of eGDR and METS-IR with CRMM risk.

Methods

Data analyzed in the present study were sourced from the China Health and Retirement Longitudinal Study (CHARLS, 2011–2020). We employed multivariable logistic regression models to examine the relationships of eGDR and METS-IR, both individually and jointly, with the risk of CRMM. Predictive performance was measured via the area under the receiver operating characteristic curve (AUC), net reclassification improvement (NRI), as well as integrated discrimination improvement (IDI). For validation, the main findings were reproduced in an independent population from the National Health and Nutrition Examination Survey (NHANES, 2007–2018).

Results

Among 7,149 participants in the final analytical sample, eGDR was inversely associated with the risk of incident CRMM (hazard ratio [HR] = 0.82, 95% confidence interval [CI]: 0.78-0.84), whereas METS-IR was positively associated with CRMM risk (HR = 1.05, 95% CI: 1.04-1.05). In the joint classification analysis, participants with low eGDR and high METS-IR had a higher risk of incident CRMM than those with high eGDR and low METS-IR (HR = 2.94, 95% CI: 2.47-3.51). The addition of eGDR and METS-IR to the baseline model was associated with statistically significant improvements in predictive performance for CRMM (AUC = 0.662, NRI = 0.427, IDI = 0.037; all P-value < 0.001). Sensitivity analyses yielded generally consistent results.

Conclusions

Higher METS-IR and lower eGDR were associated with an increased risk of incident CRMM, and their joint assessment provided additional risk-related information. Although the combined model showed statistically significant incremental predictive value, its clinical applicability requires further validation.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12872-026-06203-y.

Introduction

Against the background of accelerated global population aging, chronic non-communicable disease multimorbidity has become an increasingly prominent public health issue [1]. Compared with individuals affected by a single chronic condition, those with two or more chronic diseases generally experience poorer prognoses, significantly elevated all-cause mortality, and impose a substantially greater burden on healthcare systems [2]. Cardiovascular disease (CVD), type 2 diabetes mellitus (T2DM), as well as chronic kidney disease (CKD) frequently coexist in clinical settings because they share multiple risk factors and interconnected pathophysiological mechanism [3–5]. This specific pattern of coexisting CVD, CKD, and T2DM is defined as cardio-renal-metabolic multimorbidity (CRMM). Epidemiological evidence indicates that CRMM poses a substantial threat to population health. For example, approximately 30–40% of individuals with T2DM progress to CKD, and the combination of T2DM and CKD synergistically heightens the likelihood of cardiovascular events [6]. When CVD, CKD, and T2DM occur simultaneously, markedly higher risks of major adverse mortality are observed compared with single-disease states or dual comorbid conditions [6]. However, existing studies have largely focused on single diseases or dual comorbidities, while the risk profile and overall health impact of CRMM as an independent and complex multimorbidity phenotype remain insufficiently characterized. Moreover, early identification tools and comprehensive assessment metrics specific to CRMM are lacking in clinical practice. Thus, our study seeks to systematically examine the risk characteristics of CRMM using large-scale population data and to develop a comprehensive evaluation approach applicable to this multimorbidity state, thereby providing evidence to support early identification and risk stratification.

Insulin resistance (IR) refers to a condition where target tissues have reduced sensitivity to insulin, resulting in decreased glucose absorption and use, along with disturbances in glucose and lipid metabolism. Serving as a common pathological basis for CVD, renal dysfunction, and metabolic disorders, IR is key to CRMM onset and advancement [7, 8]. Hyperglycemia and dyslipidemia induced by IR can impair vascular endothelial function and the glomerular filtration barrier, while simultaneously exacerbating inflammation and oxidative damage, promoting CRMM progression [9]. Therefore, the accurate assessment of IR is crucial for elucidating the underlying risk mechanisms of CRMM. While the hyperinsulinemic-euglycemic clamp is the benchmark for IR measurement, its complexity and expense restrict its use in broad studies and everyday practice [10, 11]. In this context, the metabolic score for insulin resistance (METS-IR) stands out as a simple and cost-effective alternative index. METS-IR is calculated from routinely available parameters, including fasting plasma glucose (FPG), triglycerides (TG), body mass index (BMI), and high-density lipoprotein cholesterol (HDL-C), without requiring insulin measurement [12]. One research have suggested that METS-IR was strongly tied to key features of IR, such as ectopic fat deposition, highlighting its sensitivity in detecting early metabolic dysregulation [13]. Furthermore, it also forecasts risks for conditions like T2DM and hyperuricemia [14, 15], and can independently predict both all-cause and cardiovascular-related mortality [13]. Additionally, the estimated glucose disposal rate (eGDR) represents another important surrogate marker of insulin sensitivity. This index is derived from three routine clinical measures: waist circumference, hypertension status, and glycated hemoglobin (HbA1c), offering similar advantages of simplicity and low cost [16]. It quantifies how well insulin promotes whole-body glucose uptake and use, with a decrease in eGDR directly reflecting metabolic dysfunction caused by IR [17]. Research indicated that for every standard deviation rise in eGDR, CVD risk dropped by 16% [18]. Moreover, individuals in the highest eGDR group exhibited a 42% lower cardiovascular risk compared to those in the lowest group [18]. Compared to other indices such as the triglyceride-glucose (TyG) index as well as the homeostasis model assessment of insulin resistance (HOMA-IR), eGDR demonstrates superior performance in predicting all-cause mortality [19]. This suggests that eGDR effectively links IR to multi-system target organ damage. In summary, both METS-IR and eGDR serve as simple, reliable, and cost-effective surrogate markers of IR. They reflect IR-related metabolic abnormalities and are associated with various metabolic diseases and adverse clinical outcomes. However, the utility of these indices for risk assessment in complex CRMM requires further investigation and validation.

Data from two large population-based cohorts were used in this study to investigate the individual and joint associations of METS-IR and eGDR with CRMM risk. We also evaluated whether these indices provided incremental predictive information beyond traditional risk factors. The primary analyses were conducted using data from the China Health and Retirement Longitudinal Study (CHARLS), and supplementary analyses were performed using data from the US National Health and Nutrition Examination Survey (NHANES). In addition, the additive interaction between METS-IR and eGDR was examined to assess whether their joint classification offered additional risk-related information for CRMM.

Methods

Study design and populations

Our analysis drew upon CHARLS data, a nationally representative longitudinal study using multistage stratified sampling. The initial evaluation (Wave 1) in 2011 spanned 28 provinces, 150 districts, and 450 communities in China, recruiting 17,708 middle-aged and elderly individuals. All basic information was obtained using standardized questionnaires. Follow-up surveys occurred every 2–3 years to track health changes, beginning with a baseline assessment in 2011–2012 (Wave 1, response rate 80.5%). Longitudinal follow-up was carried out across four subsequent waves: in 2013 (Wave 2), 2015 (Wave 3), 2018 (Wave 4), and 2020 (Wave 5), with blood specimens collected in Waves 1 and 3. Full methodological details and data acquisition protocols for CHARLS are described in prior publications [20]. Ethical approval was granted by Peking University’s Institutional Review Board (IRB00001052-11015), with all participants providing written informed consent. Detailed information regarding the NHANES was provided in Supplementary Material 1.

This study was based on baseline survey data collected in 2011, with follow-up through 2020. 17,705 subjects were enrolled in Wave 1. First, participants aged younger than 45 years were excluded (n = 381). Second, individuals lacking information on the METS-IR (n = 7,814) or the eGDR (n = 121) were excluded. Subsequently, participants with pre-existing CRMM at baseline were excluded (n = 449). In addition, individuals lacking information on key covariates were further excluded, including smoking status (n = 9), sex (n = 6), low-density lipoprotein cholesterol (LDL-C; n = 14), systolic blood pressure (SBP; n = 69), creatinine (n = 1), and educational level (n = 2). Finally, participants with missing CRMM outcome data during follow-up were excluded (n = 1,690). After these exclusions, a total of 7,149 participants were included in the final analysis (Supplementary Material 2). The corresponding inclusion and exclusion process for the NHANES sample was detailed in Supplementary Material 3.

Definitions of METS-IR and eGDR

The METS-IR was computed as a logarithm-based index incorporating FPG, TG, BMI, and HDL-C, using the following formula [21]: METS-IR = ln[(2 × FPG (mg/dL) + TG (mg/dL))] × BMI (kg/m²) / ln[HDL-C (mg/dL)]

The eGDR value was derived according to a previously validated formula [17]: 21.158 − 0.09 × waist circumference (cm) − 3.407 × hypertension status (yes = 1, no = 0) − 0.551 × glycated hemoglobin (HbA1c, %).

Definition of CRMM

Following an operational definition previously used in the literature [22], CRMM was defined as the coexistence of at least two of the following three major cardio-renal-metabolic conditions: CVD, T2DM, and CKD. In the present study, CRMM was used as a pragmatic composite measure of multimorbidity to reflect the clustering of cardiovascular, renal, and metabolic diseases in middle-aged and older adults, rather than as a fully validated or guideline-defined clinical construct. This definition was not intended to imply that these conditions constitute a single homogeneous disease entity or are equivalent in terms of biological mechanisms, prognostic weight, or clinical implications.

CVD was identified based on self-reported physician diagnoses of cardiovascular conditions, including angina, myocardial infarction, heart failure, coronary heart disease, and stroke. T2DM was defined as meeting any of the following criteria: FPG ≥ 126 mg/dL, HbA1c ≥ 6.5%, random plasma glucose ≥ 200 mg/dL, current use of glucose-lowering medication, or a self-reported physician diagnosis of T2DM. CKD was identified based on a self-reported physician diagnosis at baseline. Participants with two or more of these three conditions were classified as having CRMM.

Covariates

The study accounted for several covariates, including demographic and lifestyle factors such as sex (male/female), age (years), residence (rural/urban), education level (elementary school or below, high school, or college and higher), marital status (married/non-married), smoking status (no/yes), and alcohol consumption (no/yes).

Statistical analyses

In the descriptive analysis, normally distributed continuous variables were expressed as means ± standard deviations (SD) and compared with Student’s t-test, while skewed continuous variables were shown as medians with interquartile ranges (IQR) and compared with the Mann-Whitney U test. Categorical variables were given as counts and percentages and compared with the chi-square (χ²) test.

Cox proportional hazards regression models were used to evaluate the associations of METS-IR, eGDR, and their joint categories with incident CRMM. Hazard ratios (HRs) and 95% confidence intervals (CIs) were reported. Follow-up time was calculated from baseline in 2011 until the occurrence of incident CRMM, loss to follow-up, death, or the end of follow-up in 2020, whichever came first. Additionally, the eGDR and METS-IR were grouped into quartiles (Q1, Q2, Q3, Q4) for further examination. To assess the robustness of the associations, three sequentially adjusted logistic regression models were built. Model 1 was adjusted for age and sex. Model 2 was further adjusted for residence, education level and marital status. Model 3 was fully adjusted for age, sex, residence, education level, marital status, smoking status, and alcohol consumption. Restricted cubic spline (RCS) models were applied to explore potential dose-response and nonlinear relationships between eGDR, METS-IR, and CRMM.

Participants were categorized by their joint status relative to the median values of eGDR and METS-IR, forming four groups: (1) low eGDR and high METS-IR, (2) high eGDR and high METS-IR, (3) low eGDR and low METS-IR, and (4) high eGDR and low METS-IR. The group with low METS-IR and high eGDR served as the reference category to evaluate the associations of the combined exposure groups with CRMM risk. Receiver operating characteristic (ROC) curves were constructed to evaluate the predictive performance of eGDR and METS-IR for CRMM, both separately and jointly, with the area under the curve (AUC) used to assess model discrimination. Based on the combined model, the optimal predicted probability cutoff was further determined using the maximum Youden index, and participants were stratified into relatively higher- and lower-risk groups according to this internally derived cutoff. In addition, a nomogram was constructed to support individualized risk estimation and improve the interpretability of the combined model. Enhancements in predictive ability were further evaluated using the net reclassification improvement (NRI) as well as integrated discrimination improvement (IDI).

Interactions between eGDR and METS-IR on CRMM risk were evaluated on both multiplicative and additive scales. Multiplicative interaction was examined by adding an interaction term between eGDR and METS-IR in multivariable logistic regression models. Additive interaction was evaluated by dichotomizing eGDR and METS-IR and calculating the relative excess risk due to interaction (RERI), attributable proportion due to interaction (AP), and synergy index (SI). A positive additive interaction was defined as RERI > 0, AP > 0, or SI > 1, whereas RERI < 0, AP < 0, and SI < 1 indicated an antagonistic effect. The 95% CIs for additive interaction indices were estimated using the delta method.

Finally, several sensitivity analyses were performed to evaluate the robustness of the observed findings. First, data from NHANES 2007–2018 were used for external validation of the primary findings by examining the associations of eGDR, METS-IR, and their combined exposure with CRMM risk. Second, stratified analyses were conducted to examine potential effect modification by age (< 65 vs. ≥65 years), sex (female vs. male), smoking status (no vs. yes), drinking status (no vs. yes), and residence (rural vs. urban) in the association between the combined eGDR-METS-IR exposure and CRMM risk. Potential interaction effects were assessed by comparing nested models with and without the corresponding interaction terms using likelihood ratio tests. In addition, missing data were addressed using multiple imputation by chained equations (MICE), and the individual and joint associations of eGDR and METS-IR with CRMM were reanalyzed using the imputed dataset. Fine-Gray subdistribution hazards competing risk models were also performed, with incident CRMM defined as the event of interest and all-cause death during follow-up treated as the competing event. Furthermore, to assess the robustness of the results, additional models were constructed by further adjusting for LDL-C, SBP, and creatinine in addition to the original covariates. Finally, to reduce the potential influence of structural overlap between the predictors and the T2DM component of CRMM, participants with diabetes at baseline were excluded, and the associations of eGDR, METS-IR, and their joint exposure with incident CRMM risk were reanalyzed.

All analyses were conducted in R (version 4.1.2), with statistical significance set at a two-tailed P-value < 0.05.

Results

Baseline characteristics

As shown in Table 1, a total of 7,149 participants were included in the final analysis. CRMM was identified in 919 participants, resulting in an incidence of 12.85%, whereas 6,230 participants remained free of CRMM (87.15%). The mean age of the study population was 58.04 ± 8.50 years, including 3,972 women (55.56%) and 3,177 men (44.44%). Compared with participants without CRMM, individuals with CRMM were significantly older and exhibited higher BMI and waist circumference. Significantly higher levels of SBP and diastolic blood pressure (DBP) were observed in the CRMM group. With respect to biochemical parameters, the CRMM group had significantly higher concentrations of creatinine and uric acid, along with higher LDL-C, TG, and FPG. All group differences were statistically significant (all P-value < 0.001).

Table 1.

Baseline characteristics of participants based on CRMM status

Variable	Total	Non-CRMM	CRMM	P-value
Number (%)	7149 (100%)	6230 (87.15%)	919 (12.85%)
Age (years)	58.04 ± 8.50	57.85 ± 8.57	59.33 ± 7.90	< 0.001
BMI (kg/m2)	23.58 ± 3.79	23.38 ± 3.68	24.91 ± 4.21	< 0.001
WC (cm)	84.11 ± 12.58	83.54 ± 12.32	87.99 ± 13.62	< 0.001
SBP (mmHg)	129.23 ± 20.79	128.55 ± 20.66	133.89 ± 21.08	< 0.001
DBP (mmHg)	75.52 ± 11.96	75.15 ± 11.90	78.01 ± 12.05	< 0.001
Creatinine (mg/dl)	0.75 (0.64, 0.87)	0.75 (0.64, 0.87)	0.77 (0.67, 0.89)	< 0.001
SUA (mg/dl)	4.25 (3.55, 5.08)	4.23 (3.54, 5.06)	4.36 (3.63, 5.20)	< 0.001
TC (mg/dl)	190.98 (167.78, 215.34)	190.21 (168.83, 214.18)	196.39 (171.88, 225.00)	< 0.001
HDL-C (mg/dl)	49.48 (40.59, 59.92)	50.06 (40.98, 60.70)	47.17 (38.66, 57.22)	< 0.001
LDL-C (mg/dl)	114.82 (93.94, 137.63)	114.05 (93.94, 136.47)	119.85 (95.49, 143.43)	< 0.001
TG (mg/dl)	104.43 (74.34, 153.10)	102.66 (73.46, 148.68)	122.13 (86.73, 181.43)	< 0.001
Glucose (mg/dl)	101.88 (94.14, 111.96)	101.52 (93.82, 110.52)	107.10 (97.29, 120.06)	< 0.001
Sex (%)				0.29
Female	3972 (55.56)	3446 (55.31)	526 (57.24)
Male	3177 (44.44)	2784 (44.69)	393 (42.76)
Marital status (%)				0.24
Married	6429 (89.93)	5592 (89.76)	837 (91.08)
Non-Married	720 (10.07)	638 (10.24)	82 (8.92)
Education level (%)				0.20
Elementary school and below	4965 (69.45)	4307 (69.13)	658 (71.60)
High school	2099 (29.36)	1851 (29.71)	248 (26.99)
College and higher	85 (1.19)	72 (1.16)	13 (1.41)
Residence (%)				0.14
Rural	4807 (67.24)	4209 (67.56)	598 (65.07)
Urban	2342 (32.76)	2021 (32.44)	321 (34.93)
Smoke (%)				0.52
No	4509 (63.07)	3920 (62.92)	589 (64.09)
Yes	2640 (36.93)	2310 (37.08)	330 (35.91)
Drink (%)				< 0.001
No	4801 (67.16)	4135 (66.37)	666 (72.47)
Yes	2348 (32.84)	2095 (33.63)	253 (27.53)
DM (%)				< 0.001
No	6354 (88.88)	5639 (90.51)	715 (77.80)
Yes	795 (11.12)	591 (9.49)	204 (22.20)
Hypertension (%)				< 0.001
No	4448 (62.22)	4010 (64.37)	438 (47.66)
Yes	2701 (37.78)	2220 (35.63)	481 (52.34)
Dyslipidemia (%)				< 0.001
No	4329 (60.55)	3895 (62.52)	434 (47.23)
Yes	2820 (39.45)	2335 (37.48)	485 (52.77)

Categorical variables are presented as counts (n) and proportions (%), and differences between groups were assessed using weighted chi-square tests. Normally distributed continuous variables were compared using Student’s t-test, whereas non-normally distributed variables were compared using the Mann-Whitney U test

Abbreviations: TG triglycerides, BMI body mass index, WC waist circumference, SUA serum uric acid, TC total cholesterol, HDL-C high density lipoprotein cholesterol, LDL-C low density lipoprotein cholesterol, DM diabetes mellitus, CRMM cardio-renal-metabolic multimorbidity

Bold P-values indicate statistical significance

Association of eGDR and METS-IR with CRMM

The associations of eGDR, METS-IR, and their joint classification with incident CRMM are shown in Table 2. In the fully adjusted model, eGDR was inversely associated with incident CRMM risk (HR = 0.82, 95% CI: 0.78–0.84). When eGDR was analyzed by quartiles, a graded inverse association was observed. Compared with participants in the lowest eGDR quartile, those in higher quartiles had a lower risk of incident CRMM, with the lowest HR observed in the highest quartile (Q4: HR = 0.34, 95% CI: 0.28–0.42).

Table 2.

Individual and joint associations of eGDR and Mets-IR with CRMM

CHARLS
eGDR	Model 1a, HR (95% CI), P-value	Model 2b, HR (95% CI), P-value	Model 3c, HR (95% CI), P-value
Continuous	0.81 (0.79, 0.84) < 0.001	0.81 (0.79, 0.84) < 0.001	0.82 (0.78, 0.84) < 0.001
Quartile 1	Reference	Reference	Reference
Quartile 2	0.58 (0.49, 0.68) < 0.001	0.58 (0.50, 0.69) < 0.001	0.59 (0.50, 0.69) < 0.001
Quartile 3	0.40 (0.33, 0.48) < 0.001	0.40 (0.33, 0.48) < 0.001	0.40 (0.33, 0.48) < 0.001
Quartile 4	0.34 (0.28, 0.41) < 0.001	0.34 (0.28, 0.42) < 0.001	0.34 (0.28, 0.42) < 0.001

Joint Group	Model 1a, HR (95% CI), P -value	Model 2b, HR (95% CI), P -value	Model 3c, HR (95% CI), P -value
Low Mets-IR + High eGDR	Reference	Reference	Reference
Low Mets-IR + Low eGDR	1.64 (1.31, 2.07) < 0.001	1.67 (1.33, 2.09) < 0.001	1.67 (1.33, 2.10) < 0.001
High Mets-IR + High eGDR	1.69 (1.34, 2.13) < 0.001	1.70 (1.34, 2.14) < 0.001	1.67 (1.33, 2.11) < 0.001
High Mets-IR + Low eGDR	2.96 (2.49, 3.52) < 0.001	2.96 (2.49, 3.52) < 0.001	2.94 (2.47, 3.51) < 0.001

Mets-IR	Model 1a, HR (95% CI), P -value	Model 2b, HR (95% CI), P -value	Model 3c, HR (95% CI), P -value
Continuous	1.05 (1.04, 1.05) < 0.001	1.05 (1.04, 1.05) < 0.001	1.05 (1.04, 1.05) < 0.001
Quartile 1	Reference	Reference	Reference
Quartile 2	1.15 (0.92, 1.43) 0.24	1.15 (0.92, 1.43) 0.23	1.14 (0.91, 1.42) 0.26
Quartile 3	1.75 (1.42, 2.15) < 0.001	1.75 (1.42, 2.16) < 0.001	1.74 (1.41, 2.14) < 0.001
Quartile 4	2.92 (2.40, 3.54) < 0.001	2.91 (2.40, 3.54) < 0.001	2.87 (2.36, 3.50) < 0.001

Abbreviations: HR hazard ratio, CRMM cardio-renal-metabolic multimorbidity, eGDR estimated glucose disposal rate, Mets-IR metabolic score of insulin resistance

Model 1^a was adjusted for age and sex; Model 2^b was adjusted for age, sex, residence, education, and marital status; and Model 3^c was adjusted for age, sex, residence, marital status, education level, smoking, and alcohol consumption

Bold P-values indicate statistical significance

METS-IR was positively associated with incident CRMM risk in the fully adjusted model (HR = 1.05, 95% CI: 1.04–1.05). In the quartile-based analysis, participants in the third and fourth METS-IR quartiles had a higher risk of incident CRMM than those in the lowest quartile (Q3: HR = 1.74, 95% CI: 1.41–2.14; Q4: HR = 2.87, 95% CI: 2.36–3.50), whereas the association was not statistically significant for the second quartile (HR = 1.14, 95% CI: 0.91–1.42).

To examine potential nonlinear associations between eGDR, METS-IR, and incident CRMM risk, restricted cubic spline models were fitted (Fig. 1). The RCS analyses suggested an L-shaped nonlinear association between eGDR and incident CRMM risk (P for overall < 0.001; P for nonlinearity < 0.001). In contrast, METS-IR showed an approximately linear association with incident CRMM risk (P for overall < 0.001), with no evidence of nonlinearity (P for nonlinearity > 0.05).

Fig. 1.

Dose-response relationships exist between eGDR and METS-IR and CRMM, (1) A: Model 1 was adjusted for age and sex. Model 2 was further adjusted for age, sex, and residence, education level and marital status. Model 3 was fully adjusted for age, sex, and residence, education level and marital status, smoking status, and alcohol consumption

In the joint classification analysis, participants with low METS-IR and high eGDR were used as the reference group. After full adjustment, low METS-IR combined with low eGDR, high METS-IR combined with high eGDR, and high METS-IR combined with low eGDR were all associated with a higher risk of incident CRMM. The highest risk was observed among participants with both high METS-IR and low eGDR (HR = 2.94, 95% CI: 2.47–3.51).

Predictive performance of eGDR and METS-IR for CRMM risk

The predictive performance of eGDR and METS-IR for CRMM was assessed through ROC curve analysis, NRI, as well as IDI (Fig. 2 and Supplementary Material 4). When added individually to the baseline model, both indices significantly improved discrimination. The inclusion of eGDR increased the AUC (equivalent to the C-index) from 0.573 to 0.651, while METS-IR alone yielded a comparable AUC of 0.645 (P-value < 0.05 for both versus baseline by DeLong’s test). In terms of reclassification, eGDR demonstrated a significant increase in NRI (0.377; 95%CI: 0.309–0.446) and IDI (0.030; 95% CI: 0.026–0.035). METS-IR similarly enhanced reclassification (NRI: 0.396; 95% CI: 0.328–0.465; IDI: 0.025; 95% CI: 0.020–0.029). Notably, the combined model integrating both eGDR and METS-IR demonstrated the most substantial predictive gain. It achieved the highest discriminative ability, with an AUC of 0.662 (95% CI: 0.643–0.681). This combined model also yielded the greatest improvement in reclassification metrics (NRI: 0.427; 95% CI: 0.359–0.496); IDI: 0.037; 95% CI: 0.032–0.043). These findings were consistently replicated in the NHANES data.

Fig. 2.

Receiver operating characteristic (ROC) curves for predicting CMM risk using different models. The basic model was adjusted for age, sex, residence, education level, marital status, smoking status, and alcohol consumption. *Indicates significantly improved predictive performance compared to the basic model (P-value < 0.05) using DeLong’s test

To further improve the interpretability of the combined model, ROC curve analysis was performed to determine the optimal predicted probability cutoff based on the maximum Youden index (Supplementary Material 5). The optimal cutoff for predicting incident CRMM was 0.12, with a sensitivity of 0.65 and a specificity of 0.60. Participants with a predicted probability greater than 0.12 were classified as being at relatively higher risk and had a significantly increased risk of incident CRMM compared with those below this threshold (HR = 2.76, 95% CI: 2.69–3.20).

In addition, a nomogram was constructed based on the combined model to support individualized risk estimation (Supplementary Material 6). The nomogram assigned point values to each predictor according to its regression coefficient, and the total score corresponded to the predicted probability of incident CRMM. The predicted probability cutoff of 0.12, derived from the maximum Youden index, was displayed in the nomogram as an internally derived reference threshold for identifying individuals at relatively higher risk.

Interaction analyses between eGDR and METS-IR

Interaction evaluations were done to assess possible additive and multiplicative effects of eGDR and METS-IR on CRMM. A statistically significant interaction was identified on the additive scale (Table 3 and Supplementary Material 7). In the fully adjusted model, the RERI was 0.75 (95%CI: 0.14–1.28), suggesting that the joint effect of low eGDR and high METS-IR exceeded the sum of their individual effects. Consistently, the AP was 0.23 (95% CI: 0.05–0.39), indicating that approximately 23% of the excess risk of CRMM among individuals jointly exposed to low eGDR and high METS-IR could be attributed to their interaction. Furthermore, the SI of 1.52 (95%CI: 1.04–2.21) provided additional evidence for a positive additive interaction, signifying a synergistic effect. These patterns of significant additive interaction remained robust across models with varying levels of covariate adjustment (Models 1 and 2). On the multiplicative scale, no statistically significant interaction was observed across any of the models. While eGDR and METS-IR do not exhibit a multiplicative interaction, they demonstrate a clear synergistic relationship on the additive scale, underscoring that the joint adverse state of low eGDR and high METS-IR confers a greater-than-additive risk for CRMM. The findings based on NHANES data corroborated these results.

Table 3.

Interaction between eGDR and METS-IR on risks of CRMM

	CHARLS
Interactive indices	Interactive effects (95% CI)
	Model 1	Model 2	Model 3
Multiplicative effect	1.10 (0.80, 1.51)	1.07 (0.78, 1.48)	1.08 (0.78, 1.49)
Additive effect
RERI	0.78 (0.18, 1.31)	0.74 (0.12, 1.28)	0.75 (0.14, 1.28)
AP	0.24 (0.06, 0.39)	0.23 (0.04, 0.38)	0.23 (0.05, 0.39)
SI	1.55 (1.06, 2.26)	1.49 (1.04, 2.14)	1.52 (1.04, 2.21)

Abbreviations: RERI Relative Excess Risk due to Interaction, AP Attributable Proportion due to Interaction, CRMM cardio-renal-metabolic multimorbidity, eGDR estimated glucose disposal rate, Mets-IR metabolic score of insulin resistance

To evaluate whether the additive interaction between eGDR and METS-IR on the risk of CRMM varied across subpopulations, we performed stratified analyses by sex and age groups. As shown in Supplementary Material 8, potential heterogeneity was observed across age strata. Among younger participants (< 60 years), a strong positive additive interaction was evident (RERI = 1.64, 95% CI: 0.82–2.43; AP = 0.47, 95% CI: 0.25–0.64), whereas the interaction was substantially attenuated in older participants (≥ 60 years) (P for interaction = 0.003). This age‑dependent pattern was consistently observed in the NHANES dataset, with younger individuals also showing a larger RERI estimate (16.12 vs. 1.40 in older group), although the three‑way interaction did not reach statistical significance (P-value = 0.054). No apparent heterogeneity was observed by sex (P for interaction = 0.726).

Sensitivity analyses

Sensitivity analyses were carried out to examine the robustness of the study findings. First, stratified analyses were performed to systematically evaluate potential effect modification by age, sex, smoking status, drinking status, as well as residence on the association between the combined eGDR-METS-IR exposure and CRMM risk (Supplementary Material 9). The associations were generally consistent across all subgroups, and no statistically significant interaction was identified between the combined exposure and any of the stratification variables (all P for interaction > 0.05).

Furthermore, the main findings were externally validated using the NHANES data. The baseline characteristics are summarized in Supplementary Material 10. A total of 10,792 participants were included, with a mean age of 46.96 ± 0.28 years; among them, 10,308 participants were free of CRMM, while 484 had CRMM at baseline. The study population comprised 5,291 men (48.97%) and 5,501 women (51.03%). In multivariable logistic regression analyses, eGDR was inversely associated with CRMM risk (Model 3: OR = 0.72, 95% CI: 0.68–0.77), whereas METS-IR was positively associated with CRMM risk (Model 3: OR = 1.04, 95% CI: 1.03–1.06). In the joint exposure analysis, using the low METS-IR and high eGDR group as the reference, subjects with high METS-IR and low eGDR exhibited an increased risk of CRMM. As shown in Table S4, compared with the baseline prediction model (C-index = 0.830), the inclusion of either eGDR or METS-IR significantly improved model performance, as reflected by increases in the C-index, IDI, and NRI (all P-value < 0.001). Notably, the model incorporating both eGDR and METS-IR achieved the highest discriminative ability (C-index = 0.881), with reclassification metrics reaching the maximum or near-maximum levels, indicating that the combined use of these two indices yielded the greatest incremental predictive value. Supplementary Material 11 and 12 demonstrated that a statistically significant additive interaction between eGDR and METS-IR on CRMM risk was observed, whereas no significant multiplicative interaction was identified. In addition, stratified analyses further supported the robustness of the findings, with association patterns highly consistent with those observed in the CHARLS cohort (Supplementary Material 13). Similarly, the sensitivity analysis using multiple imputation by MICE yielded stable results, which were broadly consistent with the primary complete-case analysis (Supplementary Material 14). After further adjustment for LDL-C, SBP, and creatinine on the basis of the original covariates, the associations of eGDR, METS-IR, and their joint exposure with incident CRMM remained generally stable (Supplementary Material 15). Similarly, when Fine-Gray competing risk models were applied with all-cause death during follow-up treated as a competing event, the direction and magnitude of the associations were largely unchanged (Supplementary Material 16). Finally, after excluding participants with diabetes at baseline, the associations of eGDR, METS-IR, and their joint exposure with incident CRMM risk remained broadly consistent with the primary analysis (Supplementary Material 17).

Discussion

The results of the present study demonstrated that elevated METS-IR and reduced eGDR were independently and jointly associated with an increased risk of CRMM. Furthermore, ROC analyses indicated that the inclusion of either METS-IR or eGDR in the basic model significantly improved the predictive performance for CRMM, with further enhancement observed when both indices were incorporated simultaneously, as further supported by improvements in the NRI and IDI. In addition, a positive additive interaction (synergistic effect) between METS-IR and eGDR on CRMM risk was identified. Overall, these results suggested that the combined application of METS-IR and eGDR may improve the early identification and prevention of CRMM. The observed age-dependent heterogeneity in the additive interaction may be governed by distinct pathophysiological mechanisms across different lifespans. In older populations, a “ceiling effect” (or risk saturation) likely operates; the cumulative burden of advanced age, persistent low-grade chronic inflammation, elevated oxidative stress, and polypharmacy already establishes an excessively high baseline risk for CRMM. Consequently, this pre-existing risk saturation leaves narrow statistical and biological margins for the specific synergy between eGDR and METS-IR to manifest. Conversely, younger individuals, who generally present with a much lower baseline risk profile, offer a more sensitive and unmasked clinical substrate to capture such metabolic synergies. When insulin resistance (indexed by high METS-IR) and endothelial dysfunction (indexed by low eGDR) coincide in younger adults, they may trigger a potent “dual-hit” cascade. Furthermore, younger individuals exhibiting this concurrent metabolic-vascular impairment face a substantially prolonged cumulative duration of exposure to these deleterious drivers prior to reaching the typical age of CRMM onset. This protracted, early-life dual-hit exposure may amplify the synergistic damage over time, thereby culminating in a disproportionately higher additive excess risk in the younger population.

Our findings demonstrated a positive association of METS-IR with CRMM risk, whereas a inverse association was observed between eGDR and CRMM risk. Earlier studies have consistently demonstrated that elevated MetS-IR is associated with higher occurrence of hypertension, T2DM, and kidney-related diseases, all of which are considered key components in the development and progression of CRMM [23–26]. For example, a large cross-sectional investigation involving more than 16,000 participants reported that each 1-unit rise in METS-IR was linked to an about 3% rise in hypertension risk [23]. Similarly, a large-scale study among older Chinese adults shown that each 1-unit increase in the METS-IR was linked to a 46% elevated risk of prediabetes and an 80% higher risk of T2DM [24]. In addition, Shen et al. reported that higher METS-IR levels were significantly associated with an increased risk of kidney stones among U.S. adults, particularly in men and individuals with diabetes [25], while a cohort study by Lin et al. further demonstrated that elevated METS-IR levels were linked to higher risk of CKD [26]. Collectively, these findings suggested that METS-IR was key to the initiation and progression of CRMM. In recent years, multiple epidemiological studies have emphasized the prognostic value of eGDR for cardiovascular outcomes. Evidence indicated that among patients with acute ischemic stroke, higher eGDR levels were linked to a 24% greater likelihood of favorable functional outcomes [27]. In the general middle-aged and older population, each 1-unit increase in eGDR was linked to 21.2%, 18.3%, and 39.5% reductions in the risks of future cardiovascular disease, heart disease, and stroke, respectively [28]. Conversely, among subkects with CKM syndrome at stages 0–3, eGDR exhibited a distinct U-shaped association with cardiovascular risk, suggesting that its predictive role may become increasingly complex as disease progresses [29]. Notably, recent studies have further shown that eGDR was closely linked to both the development and prognosis of cardiometabolic diseases, and has been considered to effectively predict incident cardiovascular events and mortality among patients with CKM syndrome, while exhibiting superior predictive performance compared with other insulin resistance-related indices [30, 31]. Against this background, our study further indicated an inverse link between eGDR and the cardiometabolic risk profile, with a clear dose-response relationship, whereby participants in the highest eGDR group exhibited a substantially lower risk than those in the lowest group. These results suggested that eGDR could function as a potential marker for the early identification of individuals at elevated cardiometabolic risk. From a mechanistic perspective, reduced eGDR may reflect the combined effects of long-term poor glycemic control and elevated blood pressure, both of which are well-established risk factors for cardiac and renal damage. The sustained synergistic effects of these factors may further accelerate the progression of cardiometabolic risk over time.

Although METS-IR and eGDR are widely used surrogate markers of IR, their roles in the development of CRMM have not been fully clarified. Several potential mechanistic pathways may underlie these associations, as outlined below. At the metabolic level, insulin resistance as reflected by METS-IR has been shown to inhibit lipoprotein lipase activity, resulting in a “lipid triad” characterized by elevated TG levels, lowered HDL-C, and increased small, dense LDL particles, thereby directly promoting the development of an atherogenic lipid environment [32]. Concurrently, insulin resistance disrupts the PI3K-Akt signaling pathway, leading to impaired endothelial-dependent nitric oxide-mediated vasodilation and subsequent endothelial dysfunction [33, 34]. In parallel, excessive activation of insulin signaling through the MAPK pathway has been implicated in promoting vascular smooth muscle cell proliferation, collagen synthesis, and pro-inflammatory gene expression, collectively accelerating atherosclerotic plaque formation and vascular remodeling [32, 35]. Furthermore, elevated METS-IR has been consistently linked to higher risk of hypertension [36]. Sustained hypertension may induce systemic vascular stiffness and glomerular microvascular damage, thereby increasing the risk of CRMM [36]. A reduced eGDR is primarily characterized by elevated HbA1c levels, suboptimal blood pressure control, and increased adiposity, all of which contribute to the exacerbation of insulin resistance. Visceral adiposity promotes chronic low-grade inflammation and oxidative stress through the release of free fatty acids and pro-inflammatory mediators [37]. Excessive hepatic fat accumulation further aggravates hepatic IR by enhancing gluconeogenesis and impairing insulin clearance [38]. Hypertension may additionally impair vascular endothelial function, thereby compromising insulin transport and its efficient utilization in peripheral tissues [39]. Taken together, METS-IR and eGDR serve as complementary indicators for evaluating both the risk of CRMM onset and its subsequent progression from the perspectives of metabolic dysregulation and vascular homeostasis, respectively.

Strength and limitation

This study demonstrates several notable strengths. First, to our knowledge, the independent and joint associations of METS-IR and eGDR with CRMM risk were systematically examined for the first time, providing novel evidence supporting their synergistic predictive value in CRMM development and progression. Second, the analysis was performed in two large-scale, nationally representative, population-based cohorts, thereby strengthening the robustness and broadened the applicability of the findings. Nevertheless, several limitations merit consideration. First, CRMM ascertainment relied primarily on self-reported physician diagnoses, which may be subject to recall bias or underreporting and may consequently result in outcome misclassification. In addition, a degree of structural overlap may exist between eGDR, METS-IR, and the CRMM outcome. To assess the potential influence of this issue, we conducted a sensitivity analysis excluding participants with diabetes at baseline and reanalyzed the associations of eGDR, METS-IR, and their joint exposure with incident CRMM risk. The results remained generally stable. Nevertheless, CRMM is an inherently heterogeneous composite outcome, and combining CVD, T2DM, and CKD into a single binary endpoint may not fully capture component-specific or combination-specific risks. Future studies with larger sample sizes, more outcome events, and refined outcome definitions are warranted to further evaluate the associations of METS-IR and eGDR with individual CRMM components and distinct disease-combination phenotypes. Furthermore, although the combined model showed a statistically significant improvement in predictive performance compared with the basic model, its absolute discriminatory ability remained limited. Therefore, this improvement should be interpreted as incremental rather than indicating sufficient clinical utility. Future studies are still needed to further confirm the practical value of this combined model in CRMM risk stratification through external validation, calibration assessment, and decision-curve analysis. Finally, although multiple potential confounders were adjusted for in multivariable models, the possibility of residual confounding arising from unmeasured or inadequately measured factors cannot be entirely excluded.

Conclusions

It was demonstrated that elevated METS-IR and lower eGDR were independently as well as jointly linked to higher risk of CRMM, and that the combined use of METS-IR and eGDR significantly enhanced predictive performance for CRMM risk. These findings suggested that the joint assessment of METS-IR and eGDR may facilitate earlier identification and prevention of CRMM.

Abbreviations

eGDR

Estimated glucose disposal rate

METS-IR

Metabolic score for insulin resistance

IR

Insulin resistance

CRMM

Cardio-renal-metabolic multimorbidity

CHARLS

China Health and Retirement Longitudinal Study

AUC

Area under the receiver operating characteristic curve

NRI

Net reclassification improvement

IDI

Integrated discrimination improvement

NHANES

National Health and Nutrition Examination Survey

ORs

Odds ratios

CIs

Confidence intervals

CVD

Cardiovascular disease

CKD

Chronic kidney disease

T2DM

Type 2 diabetes mellitus

BMI

Body mass index

HDL-C

High-density lipoprotein cholesterol

HbA1c

Glycated hemoglobin

TyG

Triglyceride-glucose

HOMA-IR

Homeostasis model assessment of insulin resistance

LDL-C

Low-density lipoprotein cholesterol

SBP

Systolic blood pressure

FPG

Fasting plasma glucose

TG

Triglycerides

SD

Standard deviations

IQR

Interquartile ranges

RCS

Restricted cubic spline

ROC

Receiver operating characteristic

RERI

Relative excess risk due to interaction

SI

Synergy index

Authors' contributions

Fa-Ming Yang, Zhi-Ping Song, and Feng-Ying Qiao conceived and designed the study. Fa-Ming Yang conducted data collection, data analysis, and data interpretation. Fa-Ming Yang, Zhi-Ping Song, and Feng-Ying Qiao contributed to the literature review and data visualization. Fa-Ming Yang and Feng-Ying Qiao drafted the initial manuscript, and all authors critically revised the manuscript. Fa-Ming Yang and Feng-Ying Qiao verified the underlying study data. All authors read and approved the final manuscript. All authors confirm that they had full access to all the data in the study and accept responsibility for the decision to submit the manuscript for publication.

Funding

None.

Data availability

The datasets generated and analyzed during the current study are available from the following sources: CHARLS (China Health and Retirement Longitudinal Study) at http://charls.pku.edu.cn/en, NHANES (National Health and Nutrition Examination Survey) at https://www.cdc.gov/nchs/nhanes/index.htm.

Declarations

The original survey datasets from NHANES and CHARLS are publicly accessible to qualified researchers.

Ethics approval and consent to participate

The China Health and Retirement Longitudinal Study (CHARLS) was approved by the Institutional Review Board of Peking University (IRB00001052-11015), and all participants provided written informed consent. The National Health and Nutrition Examination Survey (NHANES) was approved by the National Center for Health Statistics (NCHS) Research Ethics Review Board, and all participants provided written informed consent. This study used publicly available de-identified data and therefore did not require additional ethical approval.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.