  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.

Methodology