Bayesian Survival Models with Latent Variables Modeled by the Zero-Modified Power Series Distribution

The project explores Bayesian methodologies to analyze survival data with latent variables, utilizing INLA and Stan frameworks. A key innovation lies in modeling the latent variables with the **Zero-Modified Power Series distribution**, enabling flexible handling of overdispersion and structural zeros. This approach is particularly suited for survival models with complex data structures, such as those arising in medical and epidemiological studies. The research specifically focuses on applications in lung cancer and melanoma, where survival analysis plays a crucial role in understanding disease progression and treatment efficacy. By integrating prior knowledge and computational efficiency, the project aims to estimate model parameters, assess covariate effects, and provide robust uncertainty quantification. The findings are expected to advance Bayesian methods for survival analysis and offer practical tools for applied researchers in oncology and beyond.