Cox proportional hazards model with Bayesian neural network for survival prediction.

Survival analysis plays a crucial aspect in medical research and other domains where understanding the time-to-events is paramount. In this study, we present a novel approach for estimating survival outcomes that combines Bayesian neural networks with Cox proportional hazards modeling. Our results highlight the capability of Bayesian neural networks to comprehend intricate relationships within survival data. The fusion of Bayesian methodologies with traditional survival analysis techniques presents a promising pathway for propelling the field forward addressing real-world challenges in predicting time-to-event outcomes. Bayesian neural networks are utilized to estimate the non-parametric component of the hazard function. In the simulation study, we evaluated the results under two distinct cases, considering different distributions for the covariates and the different non-parametric functions. Our methodology demonstrates its effectiveness in practical settings by successfully applying it to the renowned Worcester Heart Attack Study dataset and SEER breast cancer dataset, thereby affirming its potential for real-world utility and significance. Furthermore, we perform a comparative analysis between the Bayesian Deep Partially Linear Cox Model (BDPLCM) model and the Partially Linear Additive Cox Model (PLACM) and Deep Partially Linear Cox Model (DPLCM) models to evaluate and highlight the improvements in predictive performance achieved by our approach.