Genomic biomarkers have greatly impacted the field of cancer therapeutics, where tumor heterogeneity can necessitate the introduction of subgroup-specific interventions, thus opening the door to personalized medicine. We shall use a combination of individual-level demographic factors (age, sex) and genomic biomarkers to predict patient sensitivity in clinical trials. To tackle the challenge of the curse of high dimensions brought about by the high number of potentially important genomic signatures, we shall be building on well-known shrinkage methods like the LASSO, and the Bayesian LASSO. This will ensure efficient variable selection and will adaptively allocate future subgroups of patients into appropriate treatment arms, using MCMC simulation and posterior predictive probabilities. It will be flexible enough to allow posterior results to be even integrated into the cross-validated adaptive signature design along with the ability to handle binary, ordinal and time-to-event outcomes, as well as multimodal genomic signatures. We shall validate the performance of our method through extensive simulation studies, compare with existing methods, and apply to some cancer genomics data.