Abstract Objectives: To investigate the proportional hazards' assumption in breast cancer survival analysis. Also to build a more flexible version of the Cox regression model that brings in time-dependent covariates, aiming for sharper hazard estimates. Method: A retrospective analysis was conducted using a publicly available dataset comprising 272 breast cancer patients with long-term follow-up. Descriptive statistics, Kaplan-Meier estimation, and multivariable Cox proportional hazards modeling were applied. The proportional hazards assumption was examined through time-dependent covariate interactions. An extended Cox model was subsequently formulated, and model performance was assessed using -2 log-likelihood, Akaike Information Criterion, and likelihood ratio statistics. Findings: Out of all patients, 77 (28.3%) events were observed during the study period. Tumor grade was identified as a significant predictor of survival (HR = 2.382; 95% CI 1.653-3.433). The proportional hazards assumption was violated for age (pNovelty: This study presents an integrated modeling approach that combines proportional hazards assessment with a time-dependent Cox regression model. By addressing violations of model assumptions while preserving interpretability, the proposed framework provides a practical and methodologically robust alternative to conventional survival models. Keywords: Breast cancer, Survival analysis, Cox proportional hazards, Time-dependent covariates, Non-proportional hazards, Hazard modeling
Vetrivel et al. (Tue,) studied this question.