Bivariate semiparametric mixed models to longitudinally measured systolic and diastolic blood pressure of adult diabetic patients

In biomedical research, physicians collect systolic and diastolic blood pressures simultaneously when a patient visits a clinic for treatment and serve as indicators of the patient’s health status. Elevated blood pressure is a common comorbidity in diabetes patients and can increase the risk of developing hypertension over time. The aim of this study was to examine the joint evolution of systolic and diastolic blood pressure and estimate the rate of changes over time. In the analysis of correlated multiple outcomes, multivariate analysis yields satisfactory results compared to univariate analysis. Since the individual and mean profiles of systolic and diastolic blood pressure are nonlinear, we proposed bivariate semiparametric mixed models accounting for the correlation through joint random effects. Smoothing splines and thin-plate splines were specified to capture the nonlinear trends of systolic and diastolic blood pressure overtime and the nonlinear interaction effects between covariates, respectively. The bivariate semiparametric mixed models had a better fit with the data than the parametric counterparts. The study revealed a nonlinear association between weight and age with both systolic and diastolic blood pressure of diabetic patients. The results showed that weight had a more pronounced effect on increasing systolic and diastolic blood pressure in adult diabetic patients. There was a strong association between systolic and diastolic blood pressure, while the rate of change decreases with time. The proposed method may help physicians to monitor the blood pressure of patients regularly and hence to identify periods of changes early and to manage them effectively.