Mathematical models of cancer progression

Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is associated with the occurrence of genetic alterations and their fixation in the population. We describe the accumulation of mutations using conjunctive Bayesian networks, an exponential family of waiting time models in which the occurrence of mutations is constrained by a partial order. Two opposing limit cases arise if mutations either follow a linear order or occur independently. We derive analytical expressions for the waiting time until a specific number of mutations have accumulated and show how the waiting time relates to the dependency structure among mutations.