Extreme value and copula model links blood pressure extremes to BMI

Researchers have developed a new statistical framework that models systolic and diastolic blood pressure together, rather than separately, and links the resulting joint measure to body mass index. The work, published in BMC Medical Research Methodology, combines extreme value theory with mixed copula modeling to capture both the extreme upper tail of blood pressure distributions and the dependence between the two blood pressure components.

The motivation, according to the authors, is that existing approaches often treat systolic blood pressure (SBP) and diastolic blood pressure (DBP) as separate outcomes, or reduce blood pressure to a binary hypertension indicator. Such strategies, they argue, either ignore the inherent physiological correlation between the two measurements or discard clinically relevant continuous information. Mean-based regression, meanwhile, fails to capture the extreme elevations that matter most for cardiovascular risk assessment.

The framework proceeds in stages. First, the marginal distributions of SBP and DBP were fitted using a Lognormal–Generalized Pareto distribution composite model, a construction in which a lognormal body describes the bulk of the distribution while a generalized Pareto tail governs the extreme values. Second, the dependence structure between SBP and DBP was captured using mixed copulas, which allow different dependence patterns to be combined rather than forcing a single copula family. Finally, the resulting joint, continuous blood pressure index was regressed on BMI using weighted least squares.

The data came from 41,451 health examination records collected in Suzhou, China, between 2021 and 2023, stratified by age and sex. Two earlier periods served as temporal reference points: 39,740 records from 2011–2013 and 114,096 records from 2016–2018. The analysis was carried out separately within each age and sex subgroup.

The model comparisons showed that the composite Lognormal–Generalized Pareto model provided a superior fit to the empirical SBP and DBP distributions compared with single parametric distributions across all age and sex subgroups. Mixed copulas likewise outperformed single copulas in capturing the dependence structure in every subgroup examined.

Substantive patterns emerged from the 2021–2023 cohort. Younger and middle-aged adults exhibited strong upper-tail dependence, indicating substantial co-movement of extreme systolic and diastolic values, whereas older adults demonstrated a progressive decoupling of the two measurements. Within the same period, BMI was positively associated with the blood pressure index in nearly all subgroups.

Across the three study periods, both the dependence structures and the BMI coefficients showed heterogeneous and non-monotonic patterns. Significant reductions in the BMI coefficients in 2021–2023 were concentrated primarily among several male age groups. The authors emphasize that these are observational associations from health examination data, and that the age–sex-specific results reveal variation across demographic groups and over time rather than a single uniform trend.

In their conclusion, the authors state that the proposed framework captures marginal tail behavior and joint SBP–DBP dependence and provides a continuous summary of concurrent blood pressure elevation. They suggest that the findings highlight the potential value of incorporating tail and dependence modeling into epidemiological analyses of cardiovascular risk factors.

The team also notes limitations and next steps. The framework was applied to health examination records from a single Chinese city, and the authors call for future research to validate the approach in independent prospective cohorts before broader conclusions can be drawn. The article was published open access on 24 October 2026 as a peer-reviewed, accepted manuscript shared early to provide faster access, with a final version of record to follow.

Subject of Research: A joint extreme value and mixed copula framework for modeling blood pressure extremes and BMI association

Article Title: A joint extreme value and mixed copula framework for modeling blood pressure extremes and BMI association

Article References: Lian, X., Zhu, X., Ling, C., & Bai, L. (2026). A joint extreme value and mixed copula framework for modeling blood pressure extremes and BMI association. BMC Medical Research Methodology. https://doi.org/10.1186/s12874-026-03025-6

Image Credits: AI Generated

DOI: 10.1186/s12874-026-03025-6

Keywords: blood pressure, BMI, extreme value theory, copula models, hypertension, cardiovascular risk, systolic blood pressure, diastolic blood pressure, statistical methods, epidemiology, Suzhou China, joint