Waiting times in a branching process model of colorectal cancer initiation

We consider a multi-type branching process model for the initiation of colorectal cancer, which progresses through a complex sequence of driver mutations. The model incorporates the relative fitness advantages conferred by driver mutations, which leads us to consider non-dividing sub-populations, and the effects of neutral and advantageous mutations. We analyze large-time limits to approximate the population sizes of sub-clones founded by neutral or advantageous mutations, and use the results to compute the waiting time distributions for the incidence of novel mutations in colorectal cancer initiation. Analytic waiting time distributions, including the distribution of waiting time to malignancy, are in good agreement with results from Monte Carlo simulations of the model. The approach presented here can be extended to other multi-type branching process models where population growth rates of consecutive types are non-decreasing.