The Cox Proportional Hazards Approach in Survival Analysis of an Ovarian Cancer Dataset with Stratification and an Extended Model

Abstract

This analysis uses the Ovarian dataset available on the R Pubs platform to evaluate the factors influencing the risk of an event occurring. This dataset is one of the most commonly used survival datasets for analyzing treatment effectiveness or risk factors in medical research. The aim of this analysis is to evaluate the Cox Proportional Hazards model in analyzing the factors influencing the risk of an event occurring, while accounting for interactions between variables. The two model approaches tested are the Stratified Cox and Extended Cox models, both with and without interactions. The evaluation was conducted using four primary methods: the Concordance Index, Dynamic-AUC, Brier Score, and Integrated Square Error. The likelihood ratio test results indicate that the inclusion of interactions does not significantly improve model fit, as evidenced by p-values > 0.05 for both model approaches. Therefore, the Stratified Cox model without interactions was selected as the best model. This model is considered simpler yet still capable of providing an accurate interpretation of the relationship between the studied variables and the risk of an event. The selection of this model is expected to make a significant contribution to the development of survival analysis, particularly in applications involving complex data with stratification factors. The analysis results indicate that patient age is significantly associated with the risk of death; each additional year of age increases the risk of death by approximately 2.4%. Treatment type and the presence of residual disease are not significantly associated with the risk of death; however, the analysis results show that patients receiving experimental treatment have a 28.4% lower risk of death, and patients with residual disease have a 38.9% higher risk of death compared to patients without residual disease.