Systematic assessment of Cox proportional hazards, exponential, log-normal survival models in time to event using breast cancer data.

Abstract

This study systematically evaluates the performance of Cox proportional hazards, exponential, and Log-normal survival models using a dataset of 230 breast cancer patients. Descriptive statistics reveal a predominance of female patients (96%) and various cancer stages, with the majority at Stage II (41%). The Kaplan-Meier curve illustrates a gradual decline in overall survival probability over 35 months, dropping to approximately 50% by 20 months. Significant differences in survival probabilities are observed based on smoking status (p = 0.006) and occupation (p = 0.001), while no significant differences are detected across cancer stages (p = 0.5) or treatment types (p = 0.1). The Cox model indicates that smoking status and specific occupations significantly affect hazard ratios, while immunotherapy shows a significant reduction in hazard (HR = 0.609, p = 0.018). The proportional hazards assumption remains largely intact across the covariates in the Cox model. The comparison of survival models using AIC and BIC values shows that the Log-Normal model performs best, with the lowest AIC (1255.282) and BIC (1302.461), indicating a better fit while accounting for model complexity. The Cox Proportional Hazards model ranks second with an AIC of 1385.218 and a BIC of 1424.698. The Exponential model, with the highest AIC (1402.989) and BIC (1464.875), fits the data least effectively. Overall, the Log-Normal model provides the best balance between accuracy and simplicity in this analysis.