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ABSTRACT 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 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 and overall survival. Moreover, extensive numerical evaluations demonstrate the method's feasibility, highlighting minimal estimation bias and reliable statistical inference.