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Application of the Cox Proportional Hazards Model to Analyze Survival Times in Women with Breast Cancer Rahmadani; Vinna Sulvia; Fathina Nafisa; Septrina Kiki Arisandi; Tessy Octavia Mukhti
UNP Journal of Statistics and Data Science Vol. 4 No. 2 (2026): UNP Journal of Statistics and Data Science
Publisher : Departemen Statistika Universitas Negeri Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/ujsds/vol4-iss2/485

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.
Comparison of Kernel and Spline Nonparametric Regression (Case Study: Food Security Index of Jambi Province 2023) Rosa Salsabila Azarine; Septrina Kiki Arisandi; Fadhilah Fitri; Yenni Kurniawati
UNP Journal of Statistics and Data Science Vol. 3 No. 3 (2025): UNP Journal of Statistics and Data Science
Publisher : Departemen Statistika Universitas Negeri Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/ujsds/vol3-iss3/397

Abstract

Food security is one of the issues that plays an important role in national development, especially in regions with varying levels of economic welfare such as Jambi Province. One of the main factors affecting food security is food expenditure, which reflects the economic capacity of households to access food. The complex and non-linear relationship between Food Security Index (FSI) and Food Expenditure requires a flexible modeling approach in the analysis. This study aims to compare the performance of nonparametric regression Kernel ans Spline regression methods, namely the Nadaraya-Watson Estimator (NWE) and Local Polynomial Estimator (LPE) for Kernel Regression as well as Smoothing Spline and B-Spline for Spline Regression. The analysis was conducted using secondary data obtained from the Food Security and Vulnerability Map (FSVA) of 2023, with a total of 141 subdistricts in Jambi Province. The response variable is the Food Security Index (FSI), while the predictor variable is Food Expenditure. Model evaluation was conducted using the Mean Squared Error (MSE) and the coefficient of determination (R²). The results showed that the NWE method had the best performance with the smallest MSE value of 24.47690 and the highest R² value of 0.3332, meaning that approximately 33.32% of the variation in FSI could be explained by Food Expenditure. The LPE method showed nearly comparable performance, while Smoothing Spline and B-Spline exhibited higher prediction error rates. Therefore, the NWE method can be recommended as an effective nonparametric regression approach for modeling the relationship between food expenditure and food security.