Despite the abundance of large-scale molecular and drug-response data, the insights gained about the mechanisms underlying treatment efficacy in cancer has been in general limited. Machine learning algorithms applied to those datasets most often are used to provide predictions without interpretation, or reveal single drug-gene association and fail to derive robust insights. We propose to use Macau, a bayesian multitask multi-relational algorithm to generalize from individual drugs and genes and explore the interactions between the drug targets and signaling pathways' activation. A typical insight would be: "Activation of pathway Y will confer sensitivity to any drug targeting protein X". We applied our methodology to the Genomics of Drug Sensitivity in Cancer (GDSC) screening, using gene expression of 990 cancer cell lines, activity scores of 11 signaling pathways derived from the tool PROGENy as cell line input and 228 nominal targets for 265 drugs as drug input. These interactions can guide a tissue-specific combination treatment strategy, for example suggesting to modulate a certain pathway to maximize the drug response for a given tissue. We confirmed in literature drug combination strategies derived from our result for brain, skin and stomach tissues. Such an analysis of interactions across tissues might help target discovery, drug repurposing and patient stratification strategies.