Spike-and-slab type variable selection in the Cox proportional hazards model for high-dimensional features

Abstract

In this paper, we develop a variable selection framework with the spike-and-slab prior distribution via the hazard function of the Cox model. Specifically, we consider the transformation of the score and information functions for the partial likelihood function evaluated at the given data from the parameter space into the space generated by the logarithm of the hazard ratio. Thereby, we reduce the nonlinear complexity of the estimation equation for the Cox model and allow the utilization of a wider variety of stable variable selection methods. Then, we use a stochastic variable search Gibbs sampling approach via the spike-and-slab prior distribution to obtain the sparsity structure of the covariates associated with the survival outcome. Additionally, we conduct numerical simulations to evaluate the finite-sample performance of our proposed method. Finally, we apply this novel framework on lung adenocarcinoma data to find important genes associated with decreased survival in subjects with the disease.

Keywords:

• Bayesian modeling
• latent indicator
• Markov chain Monte Carlo
• score function
• stochastic variable search
• lung adenocarcinoma

2010 Mathematics Subject Classifications:

• 62J05
• 62N02

Acknowledgments

We thank the Associate Editor and two reviewers for their insightful comments and constructive suggestions to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

Wu and Ahn were supported by National Institute of General Medical Sciences of the National Institutes of Health (NIH/NIGMS) under grant number P20 GM103650. Ahn was also supported by the Simons Foundation Award ID 714241. Yang was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) (No. NRF2021R1C1C1007023).