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Summary  Large‐scale  in vitro  drug sensitivity screens are an important tool in personalized oncology to predict the effectiveness of potential cancer drugs. The prediction of the sensitivity of cancer cell lines to a panel of drugs is a multivariate regression problem with high dimensional heterogeneous multiomics data as input data and with potentially strong correlations between the outcome variables which represent the sensitivity to the different drugs. We propose a joint penalized regression approach with structured penalty terms which enable us to utilize the correlation structure between drugs with group‐lasso‐type penalties and at the same time address the heterogeneity between ‘omics’ data sources by introducing data‐source‐specific penalty factors to penalize different data sources differently. By combining integrative penalty factors (IPFs) with the tree‐guided group lasso, we create a method called ‘IPF‐tree‐lasso’. We present a unified framework to transform more general IPF‐type methods to the original penalized method. Because the structured penalty terms have multiple parameters, we demonstrate how the interval search ‘Efficient parameter selection via global optimization’ algorithm can be used to optimize multiple penalty parameters efficiently. Simulation studies show that IPF‐tree‐lasso can improve the prediction performance compared with other lasso‐type methods, in particular for heterogeneous sources of data. Finally, we employ the new methods to analyse data from the ‘Genomics of drug sensitivity in cancer’ project.

Structured penalized regression for drug sensitivity prediction