  In this study, we develop consistent estimators for key parameters that
govern the dynamics of tumor cell populations when subjected to pharmacological
treatments. While these treatments often lead to an initial reduction in the
abundance of drug-sensitive cells, a population of drug-resistant cells
frequently emerges over time, resulting in cancer recurrence. Samples from
recurrent tumors present as an invaluable data source that can offer crucial
insights into the ability of cancer cells to adapt and withstand treatment
interventions. To effectively utilize the data obtained from recurrent tumors,
we derive several large number limit theorems, specifically focusing on the
metrics that quantify the clonal diversity of cancer cell populations at the
time of cancer recurrence. These theorems then serve as the foundation for
constructing our estimators. A distinguishing feature of our approach is that
our estimators only require a single time-point sequencing data from a single
tumor, thereby enhancing the practicality of our approach and enabling the
understanding of cancer recurrence at the individual level.
