The analysis of alterations that may occur in nature when segments of chromosomes are copied (known as copy number alterations) has been a focus of research to identify genetic markers of cancer. One high-throughput technique recently adopted is the use of molecular inversion probes (MIPs) to measure probe copy number changes. The resulting data consist of high-dimensional copy number profiles that can be used to ascertain probe-specific copy number alterations in correlative studies with patient outcomes to guide risk stratification and future treatment. We propose a novel Bayesian variable selection method, the hierarchical structured variable selection (HSVS) method, which accounts for the natural gene and probe-within-gene architecture to identify important genes and probes associated with clinically relevant outcomes. We propose the HSVS model for grouped variable selection, where simultaneous selection of both groups and within-group variables is of interest. The HSVS model utilizes a discrete mixture prior distribution for group selection and group-specific Bayesian lasso hierarchies for variable selection within groups. We provide methods for accounting for serial correlations within groups that incorporate Bayesian fused lasso methods for within-group selection. Through simulations we establish that our method results in lower model errors than other methods when a natural grouping structure exists. We apply our method to an MIP study of breast cancer and show that it identifies genes and probes that are significantly associated with clinically relevant subtypes of breast cancer.