Two-level Bayesian interaction analysis for survival data incorporating pathway information

Genetic interactions play an important role in the progression of complex diseases, providing explanation of variations in disease phenotype missed by main genetic effects. Comparatively, there are fewer investigations on prognostic survival time, given its challenging characteristics such as censoring. In recent biomedical research, two-level analysis of both genes and their involved pathways has received much attention and been demonstrated to be more effective than single-level analysis, however such analysis is limited to main effects. Pathways are not isolated and their interactions have also been suggested to have important contributions to the prognosis of complex diseases. In this article, we develop a novel two-level Bayesian interaction analysis approach for survival data. This approach is the first to conduct the analysis of lower-level gene-gene interactions and higher-level pathway-pathway interactions simultaneously. Significantly advancing from existing Bayesian studies based on the Markov Chain Monte Carlo (MCMC) technique, we propose a variational inference framework based on the accelerated failure time model with favourable priors to account for two-level selection as well as censoring. The computational efficiency is much desirable for high dimensional interaction analysis. We examine performance of the proposed approach using extensive simulation. Application to TCGA melanoma and lung adenocarcinoma data leads to biologically sensible findings with satisfactory prediction accuracy and selection stability.