Accommodating uncertainty in a tree set for function estimation

Multiple branching trees have been used to model the acquisition of HIV drug resistance mutations, and several different algorithms have been developed to construct the tree set that best describes the data. These algorithms have mainly focused on the structure of the tree set. The focal point of this paper is estimation of functions of the tree set parameters that incorporate uncertainty in the tree set. The functions of interest are the state probabilities, the co-occurrence of mutations and the order of acquisition. Such functions are of interest because they help characterize the genetic pathways that lead to multi-drug resistance. We propose a bootstrap technique to account for the additional variability in estimates due to uncertainty in the tree set. The methods are applied to genetic sequences of patients from a database compiled by the Forum for Collaborative HIV Research in an effort to characterize genetic pathways to resistance to drugs from the nucleoside reverse transcriptase inhibitor (NRTI) class. The main results were that patients with a 211K mutation in the RT region of the viral genome were more likely to have a 215Y mutation and less likely to have a 70R mutation compared to patients without a 211K mutation.