Integrative Bayesian models using Post-selective Inference: a case study in Radiogenomics

Identifying direct links between genomic pathways and clinical endpoints for highly fatal diseases such as cancer is a formidable task. By selecting statistically relevant associations between a wealth of intermediary variables such as imaging and genomic measurements, integrative analyses can potentially result in sharper clinical models with interpretable parameters, in terms of their mechanisms. Estimates of uncertainty in the resulting models are however unreliable unless inference accounts for the preceding steps of selection. In this article, we develop selection-aware Bayesian methods which are: (i) amenable to a flexible class of integrative Bayesian models post a selection of promising variables via $\ell_1$-regularized algorithms; (ii) enjoy computational efficiency due to a focus on sharp models with meaning; (iii) strike a crucial tradeoff between the quality of model selection and inferential power. Central to our selection-aware workflow, a conditional likelihood constructed with a reparameterization map is deployed for obtaining uncertainty estimates in integrative models. Investigating the potential of our methods in a radiogenomic analysis, we successfully recover several important gene pathways and calibrate uncertainties for their associations with patient survival times.