Bayesian analysis of ambulatory blood pressure dynamics with application to irregularly spaced sparse data

Abstract

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.

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects

“…More difficult, but also gaining traction, are methods for fitting nonlinear ODEs and SDEs (e.g., Chow, Lu, Sherwood, & Zhu, 2016, 1; Chow, Ferrer, & Nesselroade, 2007; Lu, Chow, Sherwood, & Zhu, 2015, 3; Molenaar & Newell, 2003; Singer, 2002, 2003). In the present article, we are restricting ourselves to two-stage approaches that facilitate the building and refinement of linear and nonlinear ODEs.…”

Whats for dynr: A Package for Linear and Nonlinear Dynamic Modeling in R

“…Currently dynr only allows nonlinearity in the dynamics but not the measurement model to capitalize on the availability of a Gaussian approximate log-likelihood function for fast parameter estimation. Future extensions will incorporate Markov chain Monte Carlo (MCMC) techniques (Chow et al, 2011;Durbin and Koopman, 2001;Kim and Nelson, 1999;Lu et al, 2015) and pertinent frequentist-based estimation techniques (Fahrmeir and Tutz, 1994) to accommodate a broader class of measurement models consisting of nonlinear functions and non-Gaussian densities. In addition, several other extensions are being pursued and implemented in the dynr package.…”

A Latent Gaussian process model for analysing intensive longitudinal data

“…In addition, all the SDE‐based continuous‐time latent curve models fall into this framework, when the noise component of the SDE is assumed to be Gaussian. For example, Lu et al () assume the dynamic latent trait to follow the Ornstein–Uhlenbeck process (Uhlenbeck & Ornstein, ). This process is a Gaussian process described by an SDE with Gaussian noise.…”

“…Such models are usually known as the latent variable‐autoregressive latent trajectory models (Bianconcini & Bollen, ) or dynamic structural equation models (Asparouhov, Hamaker, & Muthén, ). The continuous‐time models typically assume that the dynamic latent traits follow a stochastic differential equation (SDE; Oud & Jansen, ; Voelkle, Oud, Davidov, & Schmidt, ; Lu, Chow, Sherwood, & Zhu, ). For example, Lu et al () assume the dynamic latent trait to follow the Ornstein–Uhlenbeck Gaussian process (Uhlenbeck & Ornstein, ), whose distribution is given by an SDE.…”

“…The continuous‐time models typically assume that the dynamic latent traits follow a stochastic differential equation (SDE; Oud & Jansen, ; Voelkle, Oud, Davidov, & Schmidt, ; Lu, Chow, Sherwood, & Zhu, ). For example, Lu et al () assume the dynamic latent trait to follow the Ornstein–Uhlenbeck Gaussian process (Uhlenbeck & Ornstein, ), whose distribution is given by an SDE.…”