Integrative Bayesian models using Post-selective Inference: a case study in Radiogenomics
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Identifying direct links between gene pathways and clinical endpoints for highly fatal diseases such as cancer is a formidable task. Integrative analyses play a crucial role in modeling these links by relying upon associations between a wealth of intermediary variables and genomic measurements. Motivated to harness phenotypic information about tumors towards a molecular characterization of low-grade gliomas, we develop a data driven Bayesian framework to define sharp models, and calibrate accurately and efficiently uncertainties associated with the promising biological findings. The Bayesian methods we propose in the article (i) are amenable to a flexible class of adaptive models, determined via a complex interplay between signals sifted from variable selection algorithms and domain specific knowledge; (ii) have the advantage of computationally efficient high dimensional inference due to a focus on sharp models with fewer parameters, when compared to their non-adaptive counterparts; (iii) exhibit a significantly better reconciliation between model adaptivity and inferential power than state-of-art approaches, when constrained by the curse of dimensionality. Our main workforce involves a carefully constructed conditional likelihood and utilizes a reparameterization map to obtain compact formulae for a selection-corrected posterior. Deploying our methods to investigate radiogenomic characteristics for diffuse low-grade gliomas, we successfully uncover associations between several biologically important gene pathways and patient survival times.
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