Abstract Computational drug sensitivity models have the potential to improve therapeutic outcomes by identifying targeted drugs components that are tailored to the transcriptomic profile of a given primary tumor. The SMILES representation of molecules that is used by state-of-the-art drug-sensitivity models is not conducive for neural networks to generalize to new drugs, in part because the distance between atoms does not generally correspond to the distance between their representation in the SMILES strings. Graph-attention networks, on the other hand, are high-capacity models that require large training-data volumes which are not available for drug-sensitivity estimation. We develop a modular drug-sensitivity graph-attentional neural network. The modular architecture allows us to separately pre-train the graph encoder and graph-attentional pooling layer on related tasks for which more data are available. We observe that this model outperforms reference models for the use cases of precision oncology and drug discovery; in particular, it is better able to predict the specific interaction between drug and cell line that is not explained by the general cytotoxicity of the drug and the overall survivability of the cell line. The complete source code is available at https://zenodo.org/doi/10.5281/zenodo.8020945. All experiments are based on the publicly available GDSC data.