Application of the Cox Proportional Hazards Model to Analyze Survival Times in Women with Breast Cancer

Abstract

Breast cancer is still claimed to be one of the most number causes of cancer-related mortality all round the world, highlighting the importance of identifying factors that influence patient survival time. Variations in clinical outcomes among patients indicate the need for appropriate statistical methods to evaluate prognostic factors. This studi aims to analyze factors affecting the survival time by applying the Cox Propotional Hazard (Cox PH) model. The data consist of breast cancer patient record with several predictor variabel, including age at diagnosis, type of breast surgery, chemotherapy, hormone therapy, Nottingham Prognostic Index, and tumor size. The analysis procedure includes testingthe propotional hazards assumption and assessing parameter significance using the likelihood ratio test for simultaneous affect and also the test of wald for partial effect. The resuls show that the propotional hazards assumption is satisfied, indicating that the Cox PH model is appropriate for the data. Simultaneous testing reveals that at least one predictor significanly affect survuval time, while partial testing identifies type of surgery, chemotherapy as significant factors. The hazard ratio estimates indicate that patients undergoing mastectomy have a lower risk of death compared to those receiving breast-conserving surgery. Conversely, chemotherapy and hormone theraoy are associated with a higher risk of death, wich may reflect the more severe clinical conditions of patients receiving these treatments. In conclusion, the Cox PH model provides a reliable approach for identifying key factors influetncing breast cancer survival and offers important implications for clinical decision-making and treatment planning.