A large number of cancer drugs have been developed to target particular genes/pathways that are crucial for cancer growth. Drugs that share a molecular target may also have some common predictive omic features, e.g., somatic mutations or gene expression. Therefore, it is desirable to analyze these drugs as a group to identify the associated omic features, which may provide biological insights into the underlying drug response. Furthermore, these omic features may be robust predictors for any drug sharing the same target. The high dimensionality and the strong correlations among the omic features are the main challenges of this task. Motivated by this problem, we develop a new method for high-dimensional bilevel feature selection using a group of response variables that may share a common set of predictors in addition to their individual predictors. Simulation results show that our method has a substantially higher sensitivity and specificity than existing methods. We apply our method to two large-scale drug sensitivity studies in cancer cell lines. Both within-study and between-study validation demonstrate the good efficacy of our method
