  Significant advances in biotechnology have allowed for simultaneous
measurement of molecular data points across multiple genomic and transcriptomic
levels from a single tumor/cancer sample. This has motivated systematic
approaches to integrate multi-dimensional structured datasets since cancer
development and progression is driven by numerous co-ordinated molecular
alterations and the interactions between them. We propose a novel two-step
Bayesian approach that combines a variable selection framework with integrative
structure learning between multiple sources of data. The structure learning in
the first step is accomplished through novel joint graphical models for
heterogeneous (mixed scale) data allowing for flexible incorporation of prior
knowledge. This structure learning subsequently informs the variable selection
in the second step to identify groups of molecular features within and across
platforms associated with outcomes of cancer progression. The variable
selection strategy adjusts for collinearity and multiplicity, and also has
theoretical justifications. We evaluate our methods through simulations and
apply them to a motivating genomic (DNA copy number and methylation) and
transcriptomic (mRNA expression) data for assessing important markers
associated with Glioblastoma progression.
