Clonal Diversity at Cancer Recurrence

Despite initial success, many cancer therapies eventually fail due to mutation driven drug resistance. In this work we are interested in the status of the tumor at the time of cancer recurrence. In particular we investigate clonal diversity at the time of cancer recurrence, an important factor to consider when treating recurrent cancers. To model cancer dynamics involving drug-sensitive and drug-resistant cells, we employ a two-type branching process. During treatment, drug-resistant cells develop from drug-sensitive cells. We investigate the clonal diversity of drug-resistant cells at the time of cancer recurrence, defined as the first time the population size of drug-resistant cells exceeds a specified proportion of the initial population of drug-sensitive cells. We examine two clonal diversity indices: the number of clones and the Simpson's Index. We obtain the expectation of these two indices with and without conditioning on early recurrence. We demonstrate that the recurrence time is a useful indicator of clonal diversity, providing valuable insight into treating recurrent cancers. Finally, we use our recurrence measures to develop statistics that estimate model parameters based on tumor diversity data at recurrence.