Implications of Age-Based Clustering for Survival and Relapse-Free Analysis in METABRIC Breast Cancer

Azhari, Alif (Departement of Mathematics, Hasanuddin University, Makassar, 90245, Indonesia)
Mauliddin, Mauliddin (Departement of Mathematics, Hasanuddin University, Makassar, 90245, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan

Cox proportional hazards models are widely used for breast cancer survival analysis, but their validity is often limited by violations of the proportional hazard assumption. Machine learning techniques offer potential ways to improve model robustness, yet their combined use remains underexplored. This study aims to compare the proportional hazard assumptions fulfilment and the discriminatory ability of the models before and after age-based clustering. K-medoids was selected for its robustness to outliers. The results demonstrate that clustering significantly improved adherence to the proportional hazards assumption and increased the concordance index, indicating better predictive performance. Number of variables satisfying the assumption increased from 3 in the global model to 5-6 across clusters. Tumor size and positive lymph nodes consistently had a significant effect on all clusters for both survival time and relapse-free time. These findings suggest that age-based clustering can enhance the robustness and predictive performance of Cox models.