Bayesian methods for fitting mixture models that characterize branching tree processes: An application to development of resistant TB strains

For pathogens that must be treated with combinations of antibiotics and acquire resistance through genetic mutation, knowledge of the order in which drug-resistance mutations occur may be important for determining treatment policies. Diagnostic specimens collected from patients are often available; this makes it possible to determine the presence of individual drug resistance-conferring mutations and combinations of these mutations. In most cases, these specimens are only available from a patient at a single point in time; it is very rare to have access to multiple specimens from a single patient collected over time as resistance accumulates to multiple drugs. Statistical methods that use branching trees have been successfully applied to such cross-sectional data to make inference on the ordering of events that occurred prior to sampling. Here, we propose a Bayesian approach to fitting branching tree models that has several advantages, including the ability to accommodate prior information regarding measurement error or cross resistance and the natural way it permits the characterization of uncertainty. Our methods are applied to a data set for drug-resistant TB in Peru; the goal of the analysis was to determine the order with which patients develop resistance to the drugs commonly used for treating TB in this setting.