  Ambulatory cardiovascular (CV) measurements provide valuable insights into
individuals' health conditions in "real-life," everyday settings. Current
methods of modeling ambulatory CV data do not consider the dynamic
characteristics of the full data set and their relationships with covariates
such as caffeine use and stress. We propose a stochastic differential equation
(SDE) in the form of a dual nonlinear Ornstein--Uhlenbeck (OU) model with
person-specific covariates to capture the morning surge and nighttime dipping
dynamics of ambulatory CV data. To circumvent the data analytic constraint that
empirical measurements are typically collected at irregular and much larger
time intervals than those evaluated in simulation studies of SDEs, we adopt a
Bayesian approach with a regularized Brownian Bridge sampler (RBBS) and an
efficient multiresolution (MR) algorithm to fit the proposed SDE. The MR
algorithm can produce more efficient MCMC samples that is crucial for valid
parameter estimation and inference. Using this model and algorithm to data from
the Duke Behavioral Investigation of Hypertension Study, results indicate that
age, caffeine intake, gender and race have effects on distinct dynamic
characteristics of the participants' CV trajectories.
