Targeted anticancer medicine holds much promise, but determining the optimal treatment for a given patient is often difficult. In order to improve treatment selection, research has focused on the identification of genomic markers of drug sensitivity, often guided by statistical methods that identify relations between characteristics of a tumour's DNA and drug response. However, these statistical methods often result in many spuriously identified relations, which confound the discovery of genomic markers in follow-up experiments. We propose to reduce the amount of spuriously identified relations by using Multi-task Learning, a machine learning technique that identifies relations between DNA and drug response simultaneously for multiple drugs. We show that using Multi-task Learning, the number of identified relations between DNA and drug response can be strongly reduced, while retaining similar prediction performance.