| This dissertation develops mixed-effects state space models for longitudinal data that consist of a series of observations over each individual involved in a study. Variation within each subject is described by a state-space model, which contains parameters specific to an individual. Variation between subjects is described by differences between these parameters.; For parameters in mixed-effects state space models, we propose three estimation methods. The global two stage (GTS) method estimates individual parameters in the first stage, and population parameters in the second stage. For the maximum likelihood estimation we adopt an EM algorithm in which the Markov Chain Monte Carlo (MCMC) method is used to approximate the conditional expectations of sufficient statistics in the E-step. Bayesian methods are considered for both univariate cases and multivariate cases. The full conditional distributions of parameters given certain priors are derived, and a Gibbs sampler is constructed to explore the posterior distributions of parameters.; Simulation results indicate that these estimation methods perform well when the number of observations per subject is at least 20. When data are sparse, the Bayesian method shows the best results. We apply mixed-effects state space models to data from an AIDS clinical trial. Two models are considered for this data set. The first model assumes that the viral clearance features one phase, and the second model assumes two phases. We show that the second model provides better forecasts. |
