Complex interaction of waist circumference, cardiometabolic markers, and sex on elderly mortality: a cohort study of 0.4 million UK adults

Abstract

This prospective cohort study included 408,760 older adults to investigate complex interaction between waist circumference (WC), blood glucose (BG) or blood pressure (BP), and sex in relation to elderly mortality. We used Cox regression models incorporating a tensor product interaction function to model joint impacts of WC and four cardiometabolic markers on mortality, and developed a two-dimensional exposure-response function (ERF) to quantify the population adaptability to cardiometabolic dysfunction across different WC levels. The linear and nonlinear effects of BG and BP on mortality varied by WC, with significant synergistic interactions. The two-dimensional ERF quantified variations in excess mortality risk across different WC and cardiometabolic marker combinations. Individuals with higher WC exhibited a forward shift in risk thresholds, indicating reduced adaptability to elevated BG and BP levels. Our findings highlight the need for targeted cardiometabolic health management strategies to enhance adaptability and reduce the burden of cardiometabolic diseases in aging populations.

Introduction

Cardiometabolic diseases—including diabetes, hypertension, and cardiovascular conditions—pose a growing public health challenge among older adults, significantly reducing quality of life and increasing mortality risk^1,2. With the ongoing demographic shift toward an aging global population³, the prevalence and burden of cardiometabolic diseases are expected to rise, highlighting the urgent need for targeted mitigation strategies. While extensive research has explored their risk factors and underlying mechanisms, considerable variability exists in health outcomes among individuals with similar cardiometabolic profiles^4,5. This variability suggests that certain populations may possess differential adaptability or resilience to cardiometabolic dysfunction, which is a critical but often overlooked determinant of health outcomes. Adaptability to cardiometabolic dysfunction refers to the capacity of an individual or population to maintain physiological stability or avoid adverse health outcomes despite the presence of abnormal cardiometabolic markers^6–8. This concept aligns with broader definitions of adaptive capacity or resilience used in public health and environmental health literature^9–11, which describe the ability of physiological systems to adjust to stressors or changing conditions. Population adaptability to cardiometabolic dysfunction varies due to genetic predisposition, physiological compensatory mechanisms, lifestyle behaviors, and socioeconomic and environmental factors^10,12. Understanding why some individuals tolerate cardiometabolic disturbances better than others could enhance risk assessment and inform personalized interventions. However, population adaptability to cardiometabolic dysfunction has been insufficiently characterized in existing research.

Obesity, particularly central obesity, may impair the body’s ability to regulate energy and metabolism, reducing its adaptability to cardiometabolic stress¹³. Waist circumference (WC) is a key measure of central obesity and a well-established predictor of cardiometabolic risk¹⁴. Unlike body mass index (BMI), which may not fully capture fat distribution, WC more accurately reflects visceral fat accumulation—a major driver of cardiometabolic disturbances¹⁵. Central obesity might exacerbate insulin resistance, promote systemic inflammation, and impair vascular function, which could further amplify the risks associated with cardiometabolic dysregulation^4,14. Emerging evidence suggests that WC does more than indicate risk; it may actively modify the effects of dysglycemia and hypertension on health outcomes^14,16–18. Studies have shown that individuals with elevated WC and adverse cardiometabolic markers face a higher risk of negative health outcomes than those with either risk factor alone^4,5,19. This suggests that higher WC may reduce adaptability to metabolic dysfunction, making individuals more vulnerable to adverse outcomes even when typical cardiometabolic biomarkers remain within normal ranges^20,21.

Despite these insights, the role of WC in shaping population adaptability to cardiometabolic dysfunction has not been explicitly modeled in prior studies. Traditional risk assessment frameworks often overlook inter-individual variability in adaptability, potentially underestimating the burden of cardiometabolic diseases in aging populations. Understanding the complex interplay between WC and cardiometabolic markers is essential for refining risk stratification and developing personalized interventions. As a modifiable and easily measured indicator, WC could provide a more nuanced perspective on cardiometabolic disease risk, ultimately informing more effective prevention and management strategies for aging populations.

Using data from the UK Biobank (UKB), a large-scale prospective cohort with extensive health and biomarker data, this study aims to examine the complex interaction between WC, key cardiometabolic markers, and sex in relation to mortality risk in older adults. Elevated blood pressure (BP) and high blood glucose (BG) are widely recognized as core indicators of cardiometabolic health^22,23 and consistently rank among the leading global risk factors for years of life lost⁴. Therefore, this study focuses on cardiometabolic markers related to BG or BP. By developing a two-dimensional exposure-response function (ERF), we estimate the comprehensive mortality risks across different combinations of WC and BG or BP, providing a direct assessment of population adaptability to cardiometabolic dysfunction. Our findings could inform more precise prevention strategies and risk-adapted management approaches, ultimately reducing the burden of cardiometabolic diseases in aging populations.

Results

Population characteristics

A total of 408,760 elderly participants were included in this study, with a median follow-up period of 14.7 years (interquartile range 14.0~15.5). The basic population characteristics are shown in Table 1. The study population had an average age of 56.6 ± 8.1 years, and 219,713 (53.8%) of them are female. During the follow-up period, 31,685 (7.8%) of the participants were deceased. At baseline, the average WC was 90.3 ± 13.5 cm, and 73,659 (33.5%) of the females had a WC exceeding 88 cm and 52,089 (27.6%) males had a WC exceeding 102 cm. The average baseline levels of random BG (RBG), glycated hemoglobin (HbA1c), systolic blood pressure (SBP), and diastolic blood pressure (DBP) were 92.3 ± 22.2 mg/dL, 36.1 ± 6.8 mmol/mol, 139.8 ± 19.7 mmHg, and 82.3 ± 10.7 mmHg, respectively. The deceased population had higher baseline WC, RBG, HbA1c, SBP, and DBP levels.

Table 1.

Basic characteristics of the study population

	All	Survival	Deceased	P
N	408,760	377,075	31,685
Follow-up years, median [interquartile range]	14.7 [14.0, 15.5]	14.9 [14.2, 15.5]	8.7 [5.5, 11.2]	<0.001
WC (cm)	90.3 ± 13.5	89.9 ± 13.3	95.3 ± 14.6	<0.001
WC category (cm)				<0.001
≤88	188,463 (46.1%)	178,156 (47.2%)	10,307 (32.5%)
88~102	148,293 (36.3%)	136,059 (36.1%)	12,234 (38.6%)
102~116	58,254 (14.3%)	51,527 (13.7%)	6727 (21.2%)
>116	13,750 (3.4%)	11,333 (3.0%)	2417 (7.6%)
RBG (mg/dL)	92.3 ± 22.2	91.8 ± 20.9	98.4 ± 33.9	<0.001
HbA1c (mmol/mol)	36.1 ± 6.8	35.9 ± 6.4	38.8 ± 9.7	<0.001
SBP (mmHg)	139.8 ± 19.7	139.4 ± 19.5	144.8 ± 20.7	<0.001
DBP (mmHg)	82.3 ± 10.7	82.3 ± 10.7	82.5 ± 11.3	<0.001
Age	56.6 ± 8.1	56.1 ± 8.1	61.7 ± 6.4	<0.001
Sex				<0.001
Female	219,713 (53.8%)	207,034 (54.9%)	12,679 (40.0%)
Male	189,047 (46.2%)	170,041 (45.1%)	19,006 (60.0%)
Height (cm)	168.6 ± 9.3	168.5 ± 9.3	169.2 ± 9.3	<0.001
Race				<0.001
White	386,876 (94.6%)	356,382 (94.5%)	30,494 (96.2%)
Others	20,068 (4.9%)	19,060 (5.1%)	1008 (3.2%)
Unknown	1816 (0.4%)	1633 (0.4%)	183 (0.6%)
Education				<0.001
Less than high school	97,685 (23.9%)	87,104 (23.1%)	10,581 (33.4%)
High school or equivalent	149,694 (36.6%)	140,497 (37.3%)	9197 (29.0%)
College or above	157,646 (38.6%)	146,195 (38.8%)	11,451 (36.1%)
Unknown	3735 (0.9%)	3279 (0.9%)	456 (1.4%)
Income				<0.001
Less than ￡18,000	79,879 (19.5%)	69,401 (18.4%)	10,478 (33.1%)
￡18,000 to ￡30,999	89,889 (22.0%)	82,436 (21.9%)	7453 (23.5%)
￡31,000 to ￡51,999	92,202 (22.6%)	87,335 (23.2%)	4867 (15.4%)
Greater than ￡52,000	90,793 (22.2%)	87,641 (23.2%)	3152 (9.9%)
Unknown	55,997 (13.7%)	50,262 (13.3%)	5735 (18.1%)
Smoking status				<0.001
Non-smoker	222,177 (54.4%)	210,154 (55.7%)	12,023 (37.9%)
Ex-smoker	141,651 (34.7%)	128,269 (34.0%)	13,382 (42.2%)
Smoker	43,038 (10.5%)	37,017 (9.8%)	6021 (19.0%)
Unknown	1894 (0.5%)	1635 (0.4%)	259 (0.8%)
Drinking status				<0.001
Never	32,412 (7.9%)	28,766 (7.6%)	3646 (11.5%)
<3 times a week	175,270 (42.9%)	160,690 (42.6%)	14,580 (46.0%)
≥3 times a week	200,257 (49.0%)	186,892 (49.6%)	13,365 (42.2%)
Unknown	821 (0.2%)	727 (0.2%)	94 (0.3%)
Physical activity intensity				<0.001
Low	62,394 (15.3%)	56,561 (15.0%)	5833 (18.4%)
Medium	134,560 (32.9%)	124,751 (33.1%)	9809 (31.0%)
High	133,138 (32.6%)	124,288 (33.0%)	8850 (27.9%)
Unknown	78,668 (19.2%)	71,475 (19.0%)	7193 (22.7%)
Hypertension				<0.001
No	279,210 (68.3%)	264,185 (70.1%)	15,025 (47.4%)
Yes	129,550 (31.7%)	112,890 (29.9%)	16,660 (52.6%)
Diabetes				<0.001
No	371,975 (91.0%)	346,804 (92.0%)	25,171 (79.4%)
Yes	36,785 (9.0%)	30,271 (8.0%)	6514 (20.6%)
CVD				<0.001
No	383,046 (93.7%)	358,701 (95.1%)	24,345 (76.8%)
Yes	25,714 (6.3%)	18,374 (4.9%)	7340 (23.2%)

Heterogeneous linear health effects of cardiometabolic markers by WC

We utilized Cox regression models to quantify the sex-specific associations between all-cause mortality and four cardiometabolic markers (Supplementary Fig. S2). In fully-adjusted models, both RBG and HbA1c were positively associated with mortality risk. Each 10 mg/dL increase in RBG was associated with hazard ratios (HRs) of 1.04 (95% CI 1.03, 1.05) in females and 1.04 (95% CI 1.04, 1.05) in males. Similarly, each 10 mmol/mol increase in HbA1c corresponded to HRs of 1.16 (95% CI 1.13, 1.19) in females and 1.09 (95% CI 1.06, 1.13) in males. Regarding BP, SBP was positively associated with mortality in both females (HR 1.01 per 10 mmHg increment, 95% CI 1.00, 1.02) and males (HR 1.01, 95% CI 1.00, 1.01), while a significant association between DBP and mortality was observed only in females (HR 1.01, 95% CI 1.00, 1.03).

The effects of BG and BP on mortality varied by WC category (Fig. 1a), with a significant synergistic interaction observed between WC and all four cardiometabolic markers. Among females, the highest mortality risks were in those with WC > 116 cm, with HRs of 1.06 (95% CI 1.05, 1.07), 1.22 (95% CI 1.19, 1.25), 1.04 (95% CI 1.03, 1.05), and 1.05 (95% CI 1.03, 1.07) for 10-unit increment in RBG, HbA1c, SBP, and DBP, respectively, and the lowest HRs were observed in those with WC ≤ 88 cm, with corresponding values of 1.02 (95% CI 1.01, 1.03), 1.09 (95% CI 1.06, 1.12), 1.00 (95% CI 0.99, 1.01), and 0.98 (95% CI 0.97, 1.00). A similar pattern was observed in males, with the highest HRs among those with WC > 116 cm: 1.06 (95% CI 1.05, 1.06), 1.18 (95% CI 1.15, 1.20), 1.02 (95% CI 1.02, 1.03), and 1.00 (95% CI 0.99, 1.02) for RBG, HbA1c, SBP, and DBP, respectively. The lowest HRs occurred in those with WC between 88 and 102 cm: 1.03 (95% CI 1.02, 1.03), 1.08 (95% CI 1.05, 1.11), 1.00 (95% CI 0.99, 1.01), and 0.96 (95% CI 0.95, 0.97), respectively. Overall, females appeared more susceptible to the adverse effects of elevated cardiometabolic markers on mortality.

Fig. 1. Heterogeneous linear associations between mortality and cardiometabolic markers, by waist circumference and sex.

Panel (a) shows the sex-specific linear associations between mortality and cardiometabolic markers stratified by WC category, demonstrating the linear modifying effect of WC. The association estimates are shown as dots with 95%-confidence-intervals [CI] error-bars. Panel (b) shows the sex-specific linear effect of cardiometabolic markers as a nonlinear function varying with different WC levels (line with 95%-CI ribbon), demonstrating the nonlinear modifying effect of WC. WC indicates waist circumference, RBG random blood glucose, HbA1c glycated hemoglobin, SBP systolic blood pressure, DBP diastolic blood pressure.

We employed a varying-coefficient model to assess the nonlinear modifying effect of WC on the linear associations between mortality and cardiometabolic markers (Fig. 1b). A J-shaped interaction was observed, where the lowest HRs occurred at a WC of 80 cm in females and 90 cm in males. Beyond these thresholds (WC > 80 cm in females and WC > 90 cm in males), the hazardous effects of elevated BG and BP increased sublinearly with WC.

Heterogeneous nonlinear health effects of cardiometabolic markers by WC

Figure 2 and Supplementary Fig. S3 assess the heterogeneity in nonlinear exposure-response relationships between cardiometabolic markers and mortality across different WC categories. Overall, a J-shaped relationship was observed between RBG and mortality, with the lowest HR at a RBG of 90 mg/dL, while HbA1c exhibited a sublinear relationship with mortality. The ERFs of SBP and DBP followed a U-shaped pattern. The lowest HRs were observed at an SBP of 130 mmHg in females and 140 mmHg in males, and at a DBP of 80 mmHg in females and 90 mmHg in males. While the general shape and threshold of these ERFs remained consistent across WC categories, steeper slopes were observed in individuals with higher WC, particularly among females. These results suggest that females with higher WC levels are more vulnerable to the detrimental effects of elevated cardiometabolic markers on mortality.

Fig. 2. Heterogeneous nonlinear associations between mortality and cardiometabolic markers, by waist circumference and sex.

The sex-specific nonlinear effects of cardiometabolic markers stratified by WC are shown as lines with 95%-CI ribbons. WC indicates waist circumference, RBG random blood glucose, HbA1c glycated hemoglobin, SBP systolic blood pressure, DBP diastolic blood pressure.

Joint health effects of WC and cardiometabolic markers

Using a nonlinear tensor product interaction function, we developed a two-dimensional ERF to assess the complex joint effects of WC and cardiometabolic markers on mortality (Fig. 3). The two-dimensional ERF revealed variations in excess mortality risk across different WC and cardiometabolic marker combinations (the participant distributions across different combinations are shown in Supplementary Fig. S4). Notably, lower WC was associated with enhanced physiological adaptability to increases in BG and BP among older adults (aged >40 years), and females with a WC between 70 and 90 cm and males with a WC between 80 and 100 cm showed the lowest HRs of mortality. Specifically, for RBG, individuals with a high WC exhibited a notable forward shift in the risk threshold, indicating greater susceptibility to elevated RBG levels. However, for HbA1c, increased susceptibility to elevated HbA1c levels was observed in individuals with either extremely high or low WC. Regarding BP, significant hazards associated with elevated SBP and DBP were only observed in individuals with a WC exceeding the recommended level (88 cm for females and 102 cm for males). Furthermore, susceptibility to elevated BP increased with WC.

Fig. 3. Joint effects of waist circumference and cardiometabolic markers on mortality, stratified by sex.

The color directly shows sex-specific joint effects of waist circumference (y-axis) and cardiometabolic markers (x-axis), which are estimated using a two-dimensional tensor product interaction function of waist circumference and cardiometabolic markers. WC indicates waist circumference, RBG random blood glucose, HbA1c glycated hemoglobin, SBP systolic blood pressure, DBP diastolic blood pressure.

Discussion

Based on prospective cohort data from 0.4 million older adults across the UK, this study is the first to develop a two-dimensional ERF to characterize the sex-specific joint effects of WC and BG or BP on elderly mortality. This approach directly captures population adaptability to cardiometabolic dysfunction across individuals with varying WC. Our findings suggest that older adults with higher WC exhibit a notable forward shift in the risk threshold, indicating diminished adaptability to cardiometabolic dysfunction. Targeted cardiometabolic health management strategies are needed to enhance adaptability and mitigate the burden of cardiometabolic diseases in aging populations.

Several studies have explored the modifying effect of WC or BMI on the adverse health outcomes related to cardiometabolic dysfunction. For example, based on data from European Medical Information Framework for Alzheimer’s disease (EMIF-AD) 90+ Study, Legdeur et al.²⁴ reported significant synergistic interaction between WC and BP in relation to cognition. A meta-analysis of 14 prospective studies evaluated the combined effects of obesity and cardiometabolic abnormality on CVD, and found that obese individuals (defined by BMI or WC) with cardiometabolic abnormalities were at the highest relative risk for CVD and mortality⁵. A community-based cohort study of 13,251 participants aged over 60 years from China reported that obesity modified the association between glucose metabolic disorder and heart failure²⁵. Our findings align with previous research, demonstrating a long-term synergistic interaction between WC and elevated BG or BP in relation to elderly mortality. However, most prior studies relied on stratified analyses that assume a linear interaction between WC categories and cardiometabolic abnormalities. Using an innovative varying-coefficient regression model and tensor product interaction regression model, this study provides a more precise assessment of the nonlinear interaction between WC and cardiometabolic markers. The derived two-dimensional ERFs fully capture variations in adaptability to BG and BP anomalies across aging populations with different WC levels.

Existing studies have identified several mechanisms underlying this interaction. Excess visceral fat, as indicated by elevated WC, is a key contributor to insulin resistance, glucose intolerance, impaired lipolysis, reduced free fatty acid uptake, inflammatory cytokine secretion, immune cell infiltration, oxidative stress, and neurohormonal dysregulation^25–27. Additionally, accumulating evidence highlights the detrimental impact of excess adiposity and weight gain on central and peripheral hemodynamics, as well as cardiac structure and function²⁷. These processes collectively compromise the cardiometabolic system, leading to endothelial dysfunction and reduced adaptability to elevated cardiometabolic markers. Furthermore, fundamental research suggests that preadipocytes in visceral fat depots have lower adipogenic capacity than those in subcutaneous fat, promoting adipocyte hypertrophy and exacerbating metabolic disturbances²⁵.

Population adaptability to BG or BP abnormalities represents an important yet not sufficiently studied aspect of cardiometabolic health²⁸. While some individuals with elevated BG or high BP remain free of adverse outcomes, others develop diabetes, stroke, or heart failure at relatively lower thresholds. This underscores the need to assess adaptability rather than relying solely on absolute biomarker values. Our study is innovative in being the first to provide a quantitative framework for assessing population adaptability to cardiometabolic dysfunction using a two-dimensional ERF. Our findings carry important implications for public health policy, emphasizing the importance of incorporating population adaptability into cardiometabolic health management strategies, particularly in relation to WC. First, our results indicate that individuals with elevated WC exhibit increased mortality risk even at relatively lower levels of BG or BP, suggesting a downward shift in traditional risk thresholds. This aligns with emerging evidence that some individuals are biologically more vulnerable despite falling below conventional clinical cutoffs. Accordingly, current screening and diagnostic criteria for diabetes and hypertension may need to be refined to incorporate body fat distribution as a modifying factor, thereby enabling more personalized risk stratification. Second, among individuals with high WC, early lifestyle or pharmacological interventions may be warranted even before reaching conventional thresholds for metabolic disorders. This approach contrasts with existing guidelines that typically initiate intervention only upon disease diagnosis and emphasizes the importance of proactive management in vulnerable subgroups. Third, for those with existing cardiometabolic abnormalities, our findings support a dual-targeted strategy: the simultaneous management of both WC and the relevant biomarker (e.g., BG or BP) in clinical and public health settings. This integrated approach could enhance intervention efficacy and reduce long-term risks, complementing ongoing efforts to reduce abdominal obesity by highlighting its role in modifying disease susceptibility. Collectively, these findings contribute to the evolving concept of precision prevention in cardiometabolic health, particularly in aging populations, and underscore the need to move beyond one-size-fits-all risk thresholds toward more nuanced, individualized strategies.

This study has several limitations. First, sample selection bias may affect the generalizability of our findings. The UKB cohort consists primarily of western, white participants, and since WC varies significantly across racial groups, caution is needed when applying our results to other populations. Additionally, as UKB participants are volunteers, the sample may be skewed toward individuals with better health than the general population. Second, mortality risk was estimated based on a single measurement of WC, BG, and BP, which may not fully capture long-term variations and could bias the observed associations. Third, RBG and HbA1C were measured using non-fasting blood samples, making them more susceptible to recent dietary influences and potentially less stable than fasting measurements. Further validation using fasting samples is needed. Fourth, residual confounding is unavoidable. Although we adjusted for multiple potential confounders, factors such as antihypertensive or antidiabetic medication use, dietary habits, and genetic influences were not included in our models. Moreover, lifestyle factors were only assessed at baseline, limiting our ability to account for changes over time. However, using baseline data may help mitigate the risk of reverse causality due to lifestyle modifications following a disease diagnosis.

In conclusion, this large-scale cohort study quantified the complex interaction between WC, BG or BP, and sex in relation to elderly mortality, providing a direct assessment of population adaptability to cardiometabolic dysfunction across individuals with varying WC. Our findings suggest that older adults with higher WC have reduced adaptability to cardiometabolic dysfunction, highlighting the need for targeted cardiometabolic health management strategies to enhance adaptability and reduce the burden of cardiometabolic diseases in aging populations.

Methods

Study design and participants

This cohort study utilized longitudinal data from 408,760 elderly participants extracted from the UKB dataset. The UKB is a large, population-based biomedical database and research resource in the United Kingdom. Established between 2006 and 2010, it recruited over 500,000 participants aged 40–69 years from 22 sites across the UK. The UKB provides comprehensive genetic, lifestyle, and health-related data, including electronic health records, imaging data, biochemical biomarkers, and self-reported questionnaires. Baseline assessments include anthropometric measurements, cognitive function tests, and biological sample collection (e.g., blood, urine, and saliva). As a prospective study, the UKB is linked to national health registries, enabling real-time health monitoring. More details about UKB can be found in the official website (https://www.ukbiobank.ac.uk/) and previous studies^29,30. Informed consent was obtained from all individual participants included UKB cohort, and this study has been conducted using the UK Biobank Resource under application number 90018. The study was approved by the North West Multi-Centre Research Ethics Committee in Haydock, the National Information Governance Board for Health and Social Care in England and Wales, and the Community Health Index Advisory Group in Scotland.

Of the 502,369 participants in UKB, we excluded those (1) without valid information on age, sex, death status, or death date (n = 213), and (2) without baseline measurements for WC, RBG, HbA1c, SBP, and DBP (n = 93,396). This resulted in a final analytical sample of 408,760 participants. The sample selection process is illustrated in Supplementary Fig. S1.

Definitions of health variables

The outcome of this study was participant survival status, obtained from the national central registry system. Each participant was followed from their baseline registration date until either the recorded date of death or the study endpoint in December 2023, whichever came first.

This study analyzed four cardiometabolic markers: RBG, HbA1c, SBP, and DBP. RBG reflects short-term BG metabolism, while HbA1c provides a long-term measure, representing average BG levels over the past two to three months. RBG and HbA1c were measured from non-fasting blood samples collected at recruitment for all 500,000 participants, with a subset of 20,000 undergoing repeat assessments approximately five years later. RBG was analyzed using the hexokinase method, and HbA1c was measured via high-performance liquid chromatography. SBP and DBP were recorded using standardized devices, with the average calculated from two readings taken a few moments apart. WC was also measured by trained fieldworkers for each participant and categorized into four groups based on guideline-recommended thresholds: <88 cm, 88~102 cm, 102~116 cm, and >116 cm¹⁸.

A range of covariates was extracted from the UKB dataset, including: (1) sampling strata; (2) demographic variables such as age, race, education level, income level, and height; (3) lifestyle factors, including smoking history, drinking history, and physical activity status; and (4) comorbidity history, including hypertension, diabetes, and cardiovascular disease (CVD). Detailed definitions of these covariates are provided in Supplementary Table S1.

Statistical analysis

First, we constructed four separate fixed-effects Cox regression models to independently evaluate the associations between each of the four cardiometabolic markers (i.e., RBG, HbA1c, SBP, and DBP) and elderly mortality. The regression models can be parameterized as follows:

$$h\left(t\right)=h_0\left(t\right)exp(\beta x+\mathit{\gamma }\mathit{z}+{\theta }_i),$$

where h(t) denotes the hazard function of mortality for each participant at the follow-up time t, x is the baseline level of cardiometabolic markers (i.e., RBG, HbA1c, SBP, or DBP, respectively), z indicates the covariates set, θ_i is the fixed effect of the sampling site, and β and γ are the corresponding coefficients. Specifically, BP values are strongly associated with participants’ history of hypertension, and BG values are closely linked to diabetes history, raising concerns about multicollinearity. To address this issue, and following the approach used in previous studies^31,32, we included only hypertension history as a covariate in regression models assessing RBG and HbA1c, and only diabetes history in models assessing SBP and DBP. The missing values in the covariates were imputed using multivariate imputation by chained equations approach. HR = exp(β) was used to quantify the associations between cardiometabolic markers and mortality. Sex-specific effects of cardiometabolic markers were estimated using subgroup analysis.

To assess the interaction effect between WC and cardiometabolic markers on elderly mortality, we first evaluated the heterogeneous linear associations between mortality and cardiometabolic markers by WC categories and sex. The HRs were estimated by including an interaction term between WC categories (c) and cardiometabolic markers (c:x) in the regression model as follows:

$$h\left(t\right)=h_0\left(t\right)exp\left[\beta \right(c:x)+\mathit{\gamma }\mathit{z}+{\theta }_i].$$

Using a varying-coefficient model³³, we further assessed the nonlinear modifying effect of WC by parameterizing the linear effect of cardiometabolic markers as a nonlinear function varying with different WC levels. This can be denoted as follows:

$$h\left(t\right)=h_0\left(t\right)exp\left[f\right(\mathit{x|}\mathrm{WC})+\mathit{\gamma }\mathit{z}+{\theta }_i],$$

where f(x | WC) denotes a nonlinear function of the cardiometabolic markers’ effect varying with different WC levels.

Second, previous studies have suggested nonlinear associations between mortality and BG or BP^31,32. We further developed the sex-specific ERFs between mortality and cardiometabolic markers across different WC categories, to assess how the nonlinear associations between mortality and cardiometabolic markers varied by WC. The nonlinear ERFs were estimated using the following equation:

$$h\left(t\right)=h_0\left(t\right)\exp [c:\mathrm{ns}(x,\mathrm{df}=5)+\mathit{\gamma }\mathit{z}+{\theta }_i],$$

where c:ns(x, df=5) denotes an interaction term between WC categories and natural spline function of cardiometabolic markers with five degrees of freedom.

Third, to directly assess the combined effects of WC and cardiometabolic markers on mortality, we developed a two-dimensional ERF. This approach models their joint impact by computing a tensor product interaction function, which offers greater flexibility than simple multiplicative interactions³⁴. Unlike traditional models, tensor product functions allow for nonlinear relationships, making them particularly effective in capturing complex dependencies while remaining interpretable. The two-dimensional ERF enables direct estimation of mortality risk across varying combinations of WC and cardiometabolic markers. The model is specified as follows:

$$h\left(t\right)=h_0\left(t\right)\exp \left[\mathit{te}\right(\mathrm{WC},x)+\mathit{\gamma }\mathit{z}+{\theta }_i],$$

where te(WC, x) denotes a nonlinear tensor product interaction function between WC levels and cardiometabolic markers.

All statistical analyses were conducted using R (version 4.1.3; The R Foundation for Statistical Computing, Vienna, Austria). Statistical inference for the fixed-effects Cox regression model was performed using the R package survival, the natural spline function was developed using the R package splines, and the tensor product interaction function was developed using the R package mgcv.

Author contributions

Jingyi Wu: Conceptualization, Formal analysis, Validation, Writing original draft, Writing – review & editing. Pengfei Li: Conceptualization, Funding acquisition, Supervision, Data curation, Writing – review & editing. Shaomei Shang: Supervision, Writing – review & editing.

Data availability

This research was conducted using the UK Biobank Resource under application number 90018.

Code availability

All analyses were performed using R (version 4.3.3; The R Foundation for Statistical Computing, Vienna, Austria). The R code for data collection and epidemiological analyses is available upon request from the corresponding author.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s44324-025-00075-0.