Bayesian Methods for Modeling Branching Tree Processes with Application to Drug Resistant Tuberculosis

Branching trees are a restricted family of Bayesian networks that aim to sequence a set of binary events that occur in some unknown order. Considerable work has been done to develop single and multiple branching tree models in the application of oncology and HIV. This dissertation aims to extend these methods by employing a Bayesian approach which can easily accommodates additional complexities and apply these methods for the first time to modeling the development of resistant tuberculosis (TB) strains. The first chapter explores Bayesian methods to identify tree structures and to estimate the parameters that characterize these structure. The second chapter extends these methods by accommodating nonuniform false negatives and false positive observations. Uncertainty in the measurement error can be easily integrated under the Bayesian approach. Methods from chapters 1 and 2 are applied to model the sequence of phenotypic drug resistance in tuberculosis from a data set comprised of samples from patients in Peru who have a prior TB treatment history. The third chapter investigates estimating mixture models in which aspects are pre-specified. This method is used to classifying drug resistant TB in previously treated patients using data from the Anti-Tuberculosis Drug Resistance in the World, Fourth Global Report sponsored by the WHO/IUATLD.