Model selection for mixtures of mutagenetic trees

The evolution of drug resistance in HIV is characterized by the accumulation of resistance-associated mutations in the HIV genome. Mutagenetic trees, a family of restricted Bayesian tree models, have been applied to infer the order and rate of occurrence of these mutations. Understanding and predicting this evolutionary process is an important prerequisite for the rational design of antiretroviral therapies. In practice, mixtures models of K mutagenetic trees provide more flexibility and are often more appropriate for modelling observed mutational patterns. Here, we investigate the model selection problem for K-mutagenetic trees mixture models. We evaluate several classical model selection criteria including cross-validation, the Bayesian Information Criterion (BIC), and the Akaike Information Criterion. We also use the empirical Bayes method by constructing a prior probability distribution for the parameters of a mutagenetic trees mixture model and deriving the posterior probability of the model. In addition to the model dimension, we consider the redundancy of a mixture model, which is measured by comparing the topologies of trees within a mixture model. Based on the redundancy, we propose a new model selection criterion, which is a modification of the BIC. Experimental results on simulated and on real HIV data show that the classical criteria tend to select models with far too many tree components. Only cross-validation and the modified BIC recover the correct number of trees and the tree topologies most of the time. At the same optimal performance, the runtime of the new BIC modification is about one order of magnitude lower. Thus, this model selection criterion can also be used for large data sets for which cross-validation becomes computationally infeasible.