Cardiovascular disease leads the cause of death worldwide, and several studies have been carried out to understand and explore cardiovascular risk markers in normoglycemic and diabetic populations. In this work, we explore the association structure between hyperglycemic markers and cardiovascular risk markers controlled by triglycerides, body mass index, age, and sex, for the normoglycemic population in The Mexico City Diabetes Study. Understanding the association structure contributes to the assessment of additional cardiovascular risk markers in this low-income urban population with a high prevalence of classic cardiovascular risk biomarkers. The association structure is measured by conditional Kendall’s tau, defined by means of conditional copula functions. The latter are in turn modeled under a fully Bayesian nonparametric approach, which allows the complete shape of the copula function to vary for different values of controlled covariates, which mediate the association.