Advanced Survival Analysis Using the Generalized Logistic Cox Model and Comparative Analysis across Diverse Medical Datasets

This article proposes the Generalized Logistic-based Cox (GL-Cox) model as a unique approach to survival analysis, founded on the Generalized Logistic distribution with the objective of having greater flexibility in modeling survival data in the clinical scenario. The mathematical formulation of the model is intended to provide a fit to a wide range of hazard shapes often encountered in clinical data sets. For performance comparison, the GL-Cox model is compared to the conventional survival models, such as a number of Accelerated Failure Time AFT models and the Generalized Gamma model, on two real medical datasets of breast and lung cancer patients. The empirical findings indicate that the GL-Cox model achieves the highest concordance index and the lowest Akaike Information Criterion and Bayesian Information Criterion values consistently These results highlight the model's strength and versatility, demonstrating its potential for prognostic modeling and for informing data-driven decisions in medical research and clinical practice. The parametric model form also allows for more stable and interpretable inference, especially in data sets where complicated hazard behaviors are difficult for regular methods to pick up.