Exploring causal effects of hormone- and radio-treatments in an observational study of breast cancer using copula-based semi-competing risks models

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.