Kayla Argya Puruhita
Department of Statistics, Universitas Sebelas Maret

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Application of Proportional Hazard and Additive Models in the Survival Analysis of Breast Cancer Patients Muhammad Bayu Nirwana; Tiara Fitri Adani; Kayla Argya Puruhita; Andreas Rony Wijaya; Hasih Pratiwi; Silvina Rosita Yulianti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 3 (2026): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i3.37028

Abstract

Breast cancer is the most common type of cancer among women and one of the highest causes of death among other types of cancer. This study aims to evaluate the methodological advantages of additive hazard models over the multiplicative Cox model in identifying temporal risk factors for breast cancer survival. Using secondary data from 1458 patients and 10 covariates, applying three methods, Cox proportional hazards model, Lin-Ying additive hazard model, and Aalen additive hazard model. The proportional hazard assumption test indicated that Cox regression model did not fully satisfy the assumption; therefore, the Lin–Ying and Aalen additive models were applied. In the Lin–Ying models, hormonal therapy, radiotherapy, the Nottingham Prognostic Index (NPI), and tumor size were identified as significant predictors of survival, whereas in the Aalen model, significant factors also included age and chemotherapy in addition to those four covariates. These findings highlight that while the Cox model provides efficient estimation and interpretable hazard ratios, the Lin–Ying and Aalen models offer more robust alternatives when the proportional hazard assumption is violated. The Aalen model was selected based on the results of the Aalen plot. Overall, risk control efforts in breast cancer patients should focus on managing NPI scores and tumor size as well as ensuring appropriate therapies, particularly hormonal therapy and radiotherapy, which have been demonstrated to provide protective effects.