Exploring the Flexible Penalization of Bayesian Survival Analysis Using Beta Process Prior for Baseline Hazard

High-dimensional data has significantly captured the interest of many researchers, particularly in the context of variable selection. However, when dealing with time-to-event data in survival analysis, where censoring is a key consideration, progress in addressing this complex problem has remained somewhat limited. More-over, in microarray research, it is common to identify groupings of genes involved in the same biological pathways. These gene groupings frequently collaborate and operate as a unified entity. Therefore, this study is motivated to adopt the idea of a Penalized semi-parametric Bayesian Cox (PSBC) model through elastic-net and group lasso penalty functions (PSBC-EN-G and PSBC-GL-G) to incorporate the grouping structure of the covariates (genes) and optimally perform variable selection. The proposed methods assign a beta prior process to the cumulative baseline hazard function (PSBC-EN-B and PSBC-GL-B), instead of the gamma prior process used in existing methods (PSBC-EN-G and PSBC-GL-G). Three real-life datasets and simulation scenarios were considered to compare and validate the efficiency of the modified methods with existing techniques, using Bayesian Information Criteria (BIC). The results of the simulated studies provided empirical evidence that the proposed methods performed better than the existing methods across a wide range of data scenarios. Similarly, the results of the real-life study showed that the proposed methods revealed a substantial improvement over the existing techniques in terms of feature selection and grouping behavior.