Breast cancer patients may experience relapse or death after surgery during the follow-up period, leading to dependent censoring of relapse. This phenomenon, known as semi-competing risk, imposes challenges in analyzing treatment effects on breast cancer and necessitates advanced statistical tools for unbiased analysis. Despite progress in estimation and inference within semi-competing risks regression, its application to causal inference is still in its early stages. This article aims to propose a frequentist and semi-parametric framework based on copula models that can facilitate valid causal inference, net quantity estimation and interpretation, and sensitivity analysis for unmeasured factors under right-censored semi-competing risks data. We also propose novel procedures to enhance parameter estimation and its applicability in real practice. After that, we apply the proposed framework to a breast cancer study and detect the time-varying causal effects of hormone- and radio-treatments on patients' relapse-free survival and overall survival. Moreover, extensive numerical evaluations demonstrate the method's feasibility, highlighting minimal estimation bias and reliable statistical inference.

翻译：乳腺癌患者在术后随访期间可能经历复发或死亡，这导致复发时间存在相依删失。这种现象被称为半竞争风险，为分析治疗对乳腺癌的影响带来了挑战，并需要先进的统计工具进行无偏分析。尽管半竞争风险回归的估计与推断已取得进展，但其在因果推断中的应用仍处于早期阶段。本文旨在提出一个基于Copula模型的频率学派半参数框架，该框架能够在右删失半竞争风险数据下，促进有效的因果推断、净量估计与解释，以及对未测量因素进行敏感性分析。我们还提出了新颖的程序以增强参数估计及其在实际应用中的适用性。随后，我们将所提框架应用于一项乳腺癌研究，检测了激素治疗与放疗对患者无复发生存期和总生存期的时变因果效应。此外，广泛的数值评估证明了该方法的可行性，突显了其估计偏差极小且统计推断可靠的特点。