Semiparametric Bayesian kernel survival model for evaluating pathway effects

Massive amounts of high-dimensional data have been accumulated over the past two decades, which has cultured increasing interests in identifying gene pathways related to certain biological processes. In particular, since pathway-based analysis has the ability to detect subtle changes of differentially expressed genes that could be missed when using gene-based analysis, detecting the gene pathways that regulate certain diseases can provide new strategies for medical procedures and new targets for drug discovery. Limited work has been carried out, primarily in regression settings, to study the effects of pathways on survival outcomes. Motivated by a breast cancer gene-pathway data set, which exhibits the "small n, large p" characteristics, we propose a semiparametric Bayesian kernel survival model (s-BKSurv) to study the effects of both clinical covariates and gene expression levels within a pathway on survival time. We model the unknown high-dimensional functions of pathways via Gaussian kernel machine to consider the possibility that genes within the same pathway interact with each other. To address the multiple comparisons problem under a full Bayesian setting, we propose a similarity-dependent procedure based on Bayes factor to control the family-wise error rate. We demonstrate the outperformance of our approach under various simulation settings and pathways data.