Exploring Complex Survival Data through Frailty Modeling and Regularization

This study addresses the analysis of complex multivariate survival data, where each individual may experience multiple events and a wide range of relevant covariates are available. We propose an advanced modeling approach that extends the classical shared frailty framework to account for within-subject dependence. Our model incorporates a flexible frailty distribution, encompassing well-known distributions, such as gamma, log-normal, and inverse Gaussian. To ensure accurate estimation and effective model selection, we utilize innovative regularization techniques. The proposed methodology exhibits desirable theoretical properties and has been validated through comprehensive simulation studies. Additionally, we apply the approach to real-world data from the Medical Information Mart for Intensive Care (MIMIC-III) dataset, demonstrating its practical utility in analyzing complex survival data structures.