Precision oncology seeks to predict the best therapeutic option for individual patients based on the molecular characteristics of their tumors. To assess the preclinical feasibility of drug sensitivity prediction, several studies have measured drug responses for cytotoxic and targeted therapies across large collections of genomically and transcriptomically characterized cancer cell lines and trained predictive models using standard methods like elastic net regression. Here we use existing drug response data sets to demonstrate that multitask learning across drugs strongly improves the accuracy and interpretability of drug prediction models. Our method uses trace norm regularization with a highly efficient ADMM (alternating direction method of multipliers) optimization algorithm that readily scales to large data sets. We anticipate that our approach will enhance efforts to exploit growing drug response compendia in order to advance personalized therapy.