  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.
