A Stochastic Regression Model for General Trend Analysis of Blood Pressure Data

Abstract

In many biomedical longitudinal studies, the response process may experience natural variation over time, as is the case with systolic and diastolic blood pressures. Depending on what researcher’s interest lies in, one may specify certain disease states of the response process and then try to identify the factors that are associated with the specific transitions among these disease states such as the transition from the state of normal blood pressure to the state of hypertension. But in the setting of continuous response process, the transition among specific disease states are often not as interesting as the general direction and rate of movement because the detailed information about the transitions among states may not provide a summary information about the evolution of the response process. In this talk, I will introduce a multivariate regression model based on Ornstein-Uhlenbeck process for longitudinal data which is capable of providing such general trend information. In addition, our proposed model has also the capacity of assessing the lag effect and the feedback effect simultaneously where the lag effect is closely related to serial correlation for each response process and the feedback effect assesses the mutually dependence among the response processes. An estimating equation approach is proposed to avoid the complicated maximum likelihood estimation that is sensitive to the second moment assumption of our proposed model. The asymptotic property of the estimators was shown and verified by simulation. As an illustration of application for our proposed model, a longitudinal data set on the blood pressures taken from the Cardiovascular Disease Risk Factor Two-township Study (CVDFACTS) was analyzed and will be presented in this talk. Keywords: Markov processes, multivariate Ornstein-Uhlenbeck processes, generalized estimating equations