Modeling a non-homogeneous Markov process via time transformation

Longitudinal studies are a powerful tool used to characterize the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time-homogeneity, that is, that the transition rates are constant over time. This assumption may not be satisfied in many disease processes. However, limited statistical tools are available for dealing with non-homogeneity.; We propose a novel model in which the timescale of a non-homogeneous Markov process is transformed to an operational timescale on which the process is homogeneous. We develop methods for jointly estimating the time transformation and the transition intensity matrix for the time-transformed homogeneous process. Specifically, we propose Bayesian and maximum likelihood estimation. We assess these estimation procedures using simulation studies.; We extend this model to allow for between subject variation in the rate of evolution of the disease process via fixed and random effects models for the time transformation parameters and via covariate adjustment of the time transformation function.; Finally, we develop a joint model that provides a link between the non-homogeneous disease processes and health outcomes. Our model allows for prediction of longitudinal health outcomes trajectories conditional upon both current disease state and the rate of progression of disease over time.; We apply our methodology to a study of delirium progression in a cohort of stem cell transplant recipients and to a study of self-rated health in a population based cohort study of older adults. In both applications we identified non-homogeneity of the disease process. We found no association between functional status in delirium patients and either delirium state or the likelihood of being non-delirious in one day. Our joint model indicated that diminished cognitive function in older adults is associated with both current health status and increased hazard of death.