Survival Analysis of Prostate Cancer Patients Using Cox Regression Model and Log-Logistic Model

Survival time analysis focuses on the time until an event occurs and is used to identify risks in survival data. This study employs Non-Parametric (Kaplan-Meier) methods to assess median survival time, Log-rank tests to compare hazard and survivor functions, Semi-Parametric (Cox Proportional Hazards), and Parametric approaches to determine the best-fitting distribution. Prostate Cancer (PC) is the second most common malignancy in men worldwide, with 1,276,106 new cases and 358,989 deaths in 2018 (Rawla, 2019). The incidence and mortality of prostate cancer increase with age, with the average diagnosis age being 66 years. African-American men have higher incidence rates (158.3 new cases per 100,000 men) and nearly double the mortality rate compared to White men (Capece et al., 2020). This study found that both the age of patients and the year of admission were consistently significant factors. The Log-logistic model was identified as the bestfitting model with an AIC value of 302.7047, compared to the Cox Regression model's AIC value of 434.0985.