A Bayesian model for detecting acute change in nonlinear profiles

We propose a model for longitudinal data with random effects that includes model-based smoothing of measurements over time. This research is motivated by experiments evaluating the hemodynamic effects of various agents in tumor-bearing rats. In one set of experiments, the rats breathed room air, followed by carbogen (a mixture of pure oxygen and carbon dioxide). The experimental responses are longitudinal measurements of oxygen pressure measured in tissue, tumor blood flow, and mean arterial pressure. The nature of the recorded responses does not allow any meaningful parametric form to model these profiles over time. Additionally, response patterns differ widely across individuals. Therefore, we propose a nonparametric regression to model the profile data over time. We propose a dynamic state-space model to smooth the data at the profile level. Using the state parameters, we formally define "change" in the measured responses. A hierarchical extension allows inference to include a regression on covariates. The proposed approach provides a modeling framework for any longitudinal data, where no parsimonious parametric model is available at the level of the repeated measurements and a hierarchical modeling of some feature of a smooth fit for these profiles data is desired. The proposed MCMC algorithm for inference on the hierarchical extension is appropriate in any hierarchical model in which posterior simulation for the submodels is significantly easier.