Joint modeling of hypertension and cardiovascular disease among Iranian Hajj pilgrims using Bayesian multivariate generalized linear mixed model

Hypertension (HTN) and cardiovascular disease (CVD) are major contributors to global morbidity and mortality and represent important health concerns during the Hajj pilgrimage, where large numbers of pilgrims are exposed to substantial environmental and physical stress. Despite their close biological relationship and frequent co-occurrence, HTN and CVD have largely been investigated as independent outcomes, potentially overlooking their shared determinants and underlying correlation. Therefore, we jointly modeled these conditions to provide a more comprehensive assessment of cardiovascular risk among Iranian Hajj pilgrims. In this retrospective cross-sectional study, medical records of 478,360 Iranian Hajj pilgrims participating in seven pilgrimage seasons (2013, 2014, 2015, 2017, 2018, 2019, and 2022) were analyzed. A Bayesian multivariate generalized linear mixed model (GLMM) was employed to jointly analyze HTN and CVD, allowing the correlation between these outcomes to be modeled while accounting for geographic clustering among individuals through province-level random intercepts. Associations with demographic and clinical risk factors were estimated using adjusted odds ratios (ORs) and 95% credible intervals (CrIs), and model performance was evaluated using the Deviance Information Criterion (DIC). Spatial analyses were performed to characterize regional variation in disease burden. The prevalence of HTN and CVD was 20.90% and 3.93%, respectively. Among all included pilgrims, the mean age was 54.87 ± 10.92 years, and 49.96% were women. Compared with separate univariate models, the joint Bayesian GLMM demonstrated substantially better model fit (ΔDIC = 51,720.5) and identified a strong residual correlation between HTN and CVD (ρ = 0.75). Age, sex, chronic renal failure, thyroid dysfunction, and diabetes (DM) were significantly associated with both outcomes. Representative estimates from the joint model showed that each additional year of age increased the odds of HTN (OR = 1.14, 95% CrI: 1.13–1.15) and CVD (OR = 1.11, 95% CrI: 1.10–1.11). Women had higher odds of HTN (OR = 2.15, 95% CrI: 1.99–2.32) but lower odds of CVD (OR = 0.80, 95% CrI: 0.76–0.84) compared with men, whereas DM was associated with substantially increased odds of HTN (OR = 9.15, 95% CrI: 7.57–10.95) and CVD (OR = 3.07, 95% CrI: 2.90–3.27). Temporal variation was observed across pilgrimage years, with HTN risk highest in 2018 and lower in 2022 relative to 2013, while CVD risk was also reduced in 2022. Geographic heterogeneity was evident, with HTN prevalence ranging from 13.52% in Qom to 32.39% in East Azerbaijan and CVD prevalence ranging from 1.87% in Esfahan to 8.93% in Ilam. The Bayesian multivariate GLMM provided an informative framework for jointly evaluating correlated HTN and CVD outcomes in a large clustered population. By accounting for the correlation between outcomes and identifying shared determinants, this approach can inform integrated cardiovascular risk assessment, targeted pre-Hajj screening, and region-specific preventive strategies for high-risk pilgrims.