  Large-scale {\it 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 multi-omics
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 allow
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
(IPF) with tree-guided group lasso, we create the IPF-tree-lasso method. 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 (EPSGO) algorithm can be used to optimize
multiple penalty parameters efficiently. Simulation studies show that
IPF-tree-lasso can improve the prediction performance compared to other
lasso-type methods, in particular for heterogenous data sources. Finally, we
employ the new methods to analyse data from the Genomics of Drug Sensitivity in
Cancer project.
