Flexible yet Sparse Bayesian Survival Models with Time-Varying Coefficients and Unobserved Heterogeneity

Survival analysis is an important area of medical research, yet existing models often struggle to balance simplicity with flexibility. Simple models require minimal adjustments but come with strong assumptions, while more flexible models require significant input and tuning from researchers. We present a survival model using a Bayesian hierarchical shrinkage method that automatically determines whether each covariate should be treated as static, time-varying, or excluded altogether. This approach strikes a balance between simplicity and flexibility, minimizes the need for tuning, and naturally quantifies uncertainty. The method is supported by an efficient Markov chain Monte Carlo sampler, implemented in the R package shrinkDSM. Comprehensive simulation studies and an application to a clinical dataset involving patients with adenocarcinoma of the gastroesophageal junction showcase the advantages of our approach compared to existing models.