Modelling the survival rate of breast cancer patients: Non-parametric and semi-parametric approach
Ayinla, Faruq Ayomide
Department of Statistics, Faculty of Physical Sciences, University of Ilorin, Nigeria.
https://orcid.org/0009-0001-2768-1040
Adejumo, Adebowale Olusola
Department of Statistics, Faculty of Physical Sciences, University of Ilorin, Nigeria.
https://orcid.org/0000-0002-3127-1685
DOI: https://doi.org/10.20448/iras.v11i1.7770
Keywords: Breast cancer, Cox proportional hazard, Kaplan-Meier, Survival rate, Stratification, Hazard Ratio, Early diagnosis.
Abstract
The comparison of survival among patients with breast cancer was analyzed using the Cox proportional hazards model and the Kaplan-Meier estimator to model the survival outcomes. A sample of 563 patients was selected to evaluate the impact of risk factors such as age, tumor stage, type of surgery, chemotherapy, radiotherapy, and hormone therapy. The log-rank test results indicated that radiotherapy (p = 0.8) and age (p = 0.08) did not significantly affect survival distribution. Conversely, tumor stage (p < 0.0001), surgical type (p = 0.0004), chemotherapy (p = 0.04), and hormone therapy (p = 0.0004) showed significant differences in survival outcomes. Cox regression analysis identified tumor stage as the most influential factor, with patients at Stage 2, 3, and 4 exhibiting 1.85 to 3.98 times higher risks of mortality compared to those at Stage 1. Additionally, patients undergoing mastectomy had a 1.32 times higher risk than those receiving breast-conserving surgery (p = 0.0288). The assumptions of proportional hazards were violated for chemotherapy and hormone therapy (p = 0.015 and p = 0.018, respectively), which contributed to the overall significance of the model (p = 0.048). Stratification of these variables confirmed the robustness of the model, with tumor stage and surgical option remaining key factors. These findings underscore the importance of early diagnosis in improving survival outcomes for breast cancer patients.