| In many biomedical studies, the observed data may violate the assumptions of standard parametric methods. In these situations, Bayesian methods are appealing since nonparametric priors, such as the Dirichlet process (DP), can incorporate a priori knowledge regarding the shape or location of an unknown distribution and exact inferences are available using Markov chain Monte Carlo methods. Despite the promise of Bayesian nonparametric methods, computation can be difficult under large sample sizes. In addition, there is a paucity of methods for multiple event time data and for testing across multiple groups.; In this dissertation, we propose three methods which address important computational, modelling, and testing issues in Bayesian nonparametrics. Our first method is a computationally simple approach to fitting Bayesian semiparametric random effects models to large longitudinal data sets. Our approach involves fitting a model to a smaller set of pseudo-data, which is constructed using expert opinion. The research was motivated by data from the Collaborative Perinatal Project, which was a prospective epidemiology study consisting of over 30,000 children.; We next develop a dynamic frailty model which accounts for age-dependent changes in susceptibility to a repeated health event, such as the occurrence of new tumors. Our model generalizes the traditional shared frailty model for multiple event time data to accommodate smooth, time dependent trends in the frailty, baseline hazard, and covariate effects. We also relax our assumptions on the frailty using DP priors.; Lastly, we present a Bayesian nonparametric method for testing for changes in a response distribution with an ordinal predictor. The research was motivated by data from toxicology studies, in which dose may affect both the shape and location of the response distribution. Using a generalization of the dynamic mixture of DPs (Dunson, 2006, Biostatistics, to appear), we test for equivalence in the unknown distribution across dose groups and estimate threshold doses. Our method accommodates multivariate responses without complication. |
