  We introduce and analyze a waiting time model for the accumulation of genetic
changes. The continuous time conjunctive Bayesian network is defined by a
partially ordered set of mutations and by the rate of fixation of each
mutation. The partial order encodes constraints on the order in which mutations
can fixate in the population, shedding light on the mutational pathways
underlying the evolutionary process. We study a censored version of the model
and derive equations for an EM algorithm to perform maximum likelihood
estimation of the model parameters. We also show how to select the maximum
likelihood poset. The model is applied to genetic data from different cancers
and from drug resistant HIV samples, indicating implications for diagnosis and
treatment.
