Bayesian Inference for High Dimensional Cox Models with Gaussian and Diffused-Gamma Priors: A Case Study of Mortality in COVID-19 Patients Admitted to the ICU.

Bayesian approaches have been utilized to address the challenge of variable selection and statistical inference in high-dimensional survival analysis. However, the discontinuity of the -norm prior, including the useful spike-and-slab prior, may lead to computational and implementation challenges, potentially limiting the widespread use of Bayesian methods. The Gaussian and diffused-gamma (GD) prior has emerged as a promising alternative due to its continuous-and-differentiable -norm approximation and computational efficiency in generalized linear models. In this paper, we extend the GD prior to semi-parametric Cox models by proposing a rank-based Bayesian inference procedure with the Cox partial likelihood. We develop a computationally efficient algorithm based on the iterative conditional mode (ICM) and Markov chain Monte Carlo methods for posterior inference. Our simulations demonstrate the effectiveness of the proposed method, and we apply it to an electronic health record dataset to identify risk factors associated with COVID-19 mortality in ICU patients at a regional medical center.