Illicit drug use and concomitant problems such as high incarceration rates pose tremendous challenges to those directly involved and to society as a whole. In recent years, many medical, public health, and social science researchers have conducted studies to characterize the nature of these problems and look for potential solutions. These studies often record events such as subjects relapsing into drug use following periods of abstinence, and interest centers on finding or assessing the impact of risk factors for event occurrence. While analyses of these studies have often employed advanced statistical techniques borrowed from the social science literature, there have been few applications of modern Bayesian techniques or advanced event time models. In this dissertation, we develop a general Bayesian event history model with supporting computing tools, and we apply this work in a substance abuse context.

Because the field of survival and event history analysis is so broad, we first provide an extensive review of concepts and literature relevant to our subsequent methodological work. We then describe in detail our general Bayesian event history model. This model combines a number of features which are frequently omitted from analyses because available event time analysis software does not allow their simultaneous use. These features include simultaneous semiparametric incorporation of multiple continuous time-varying covariates, multiple event types or competing risks, and recurrent at-risk episodes. We provide novel Markov chain Monte Carlo (MCMC) algorithms for obtaining posterior inferences from this model, evaluate their performance, and apply them to data on recurrent episodes of cocaine use in a population of illicit drug users.

Next, we extend our general Bayesian event history model to a full multistate model for histories in which subjects pass in between discrete states. In these histories, the state transitions are the events of interest, and the numbers and types of covariates and possible transition events depend on the subject's current state. We apply this multistate model to lifetime histories of cocaine use and incarceration following first use of cocaine. Finally, we conclude the dissertation with a description of our software implementation of our models and a discussion of future projects.