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Integrative analyses based on statistically relevant associations betweengenomics and a wealth of intermediary phenotypes (such as imaging) providevital insights into their clinical relevance in terms of the diseasemechanisms. Estimates for uncertainty in the resulting integrative models arehowever unreliable unless inference accounts for the selection of theseassociations with accuracy. In this article, we develop selection-awareBayesian methods which: (i) counteract the impact of model selection biasthrough a "selection-aware posterior" in a flexible class of integrativeBayesian models post a selection of promising variables via$\ell_1$-regularized algorithms; (ii) strike an inevitable tradeoff between thequality of model selection and inferential power when the same dataset is usedfor both selection and uncertainty estimation. Central to our methodologicaldevelopment, a carefully constructed conditional likelihood function deployedwith a reparameterization mapping provides notably tractable updates whengradient-based MCMC sampling is used for estimating uncertainties from theselection-aware posterior. Applying our methods to a radiogenomic analysis, wesuccessfully recover several important gene pathways and estimate uncertaintiesfor their associations with patient survival times.

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