High-dimensional data have attracted considerable interest from researchers, especially in the area 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. Moreover, 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 and PSBC-GL) to incorporate the grouping structure of the covariates (genes) and optimally perform variable selection. The proposed methods assign a beta process prior to the cumulative baseline hazard function (PSBC-EN-B and PSBC-GL-B), instead of the gamma process prior 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.

In recent years, the growing availability of large-scale data across a wide range of disciplines has created new opportunities for developing models that improve the predictive accuracy of statistical models. Although techniques such as regularization and Bayesian hierarchical methods are commonly used for building predictive models, substantial challenges remain, particularly when dealing with high-dimensional datasets that contain considerable noise. In this study, we propose a Bayesian hierarchical model that employs a spike-and-slab hierarchical elastic net prior that regularizes the Cox Proportional Hazards (Cox-PH) model. The method combines Bayesian modeling with the regularized partial log-likelihood of the Cox-PH framework, incorporating an Elastic Net penalty to estimate the joint posterior distribution under a hierarchical elastic net prior. We compute this posterior using an Expectation–Maximization Cyclic Coordinate Descent Algorithm (EM-CCDA), which streamlines feature selection and enhances overall predictive performance. We evaluate the algorithm’s performance through Monte Carlo simulations and apply it to three real-world datasets, comparing the results with those from established classical and Bayesian survival analysis approaches. The findings demonstrate notable gains in both feature selection and predictive accuracy, highlighting the model’s strong ability to predict patient survival and identify relevant genes in real biological datasets.

High-dimensional survival data, such as microarray datasets, present significant challenges in variable selection and model performance due to their complexity and dimensionality. Identifying important genes and understanding how these genes influence the survival of patients with cancer are of great interest and a major challenge to biomedical scientists, healthcare practitioners, and oncologists. Therefore, this study combined the strengths of two complementary feature selection methodologies: a filtering (correlation-based) approach and a wrapper method based on Iterative Bayesian Model Averaging (IBMA). This new approach, termed Correlation-Based IBMA, offers a highly efficient and effective means of selecting the most important and influential genes for predicting the survival of patients with cancer. The efficiency and consistency of the method were demonstrated using diffuse large B-cell lymphoma cancer data. The results revealed that the 15 most important genes out of 3835 gene features were consistently selected at a threshold p-value of 0.001, with genes with posterior probabilities below 1% being removed. The influence of these 15 genes on patient survival was assessed using the Cox Proportional Hazards (Cox-PH) Model. The results further revealed that eight genes were highly associated with patient survival at a 0.05 level of significance. Finally, these findings underscore the importance of integrating feature selection with robust modeling approaches to enhance accuracy and interpretability in high-dimensional survival data analysis.

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.