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.

翻译：本研究针对肿瘤细胞群体在药物治疗作用下的动态变化，建立了关键参数的一致估计量。尽管此类治疗常能有效减少药物敏感细胞的丰度，但耐药细胞群体会随时间逐渐出现，最终导致癌症复发。复发肿瘤的样本作为宝贵的数据源，可为揭示癌细胞适应和抵抗治疗干预的能力提供关键信息。为充分利用复发肿瘤数据，我们推导了若干大数极限定理，重点聚焦于量化癌症复发时肿瘤细胞群体克隆多样性的指标。基于这些定理，我们构建了相应的估计量。该方法的核心优势在于仅需单个肿瘤的单时间点测序数据，由此显著提升了方法的实用性，并实现了在个体层面理解癌症复发机制。