Severe adverse drug reactions (ADRs) are the fourth leading cause of fatality in the US with more than 100,000 deaths per year. As up to 30% of all ADRs are believed to be caused by drug-drug interactions (DDIs), typically mediated by cytochrome P450s, possibilities to predict DDIs from existing knowledge are important. We collected data from public sources on 1,485, 2,628, 4,371, 27,966 possible DDIs mediated by four cytochrome P450 isoforms 1A2, 2C9, 2D6, 3A4 for 55, 73, 94, 237 drugs, respectively. For each of these datasets we developed and validated QSAR models for the prediction of DDIs. As a unique feature of our approach, the interacting drug pairs were represented as binary chemical mixtures in a 1:1 ratio. We used two types of chemical descriptors: Neighborhoods of Atoms (QNA) and Simplex descriptors. Radial basis functions with self-consistent regression (RBF-SCR) and Random Forest (RF) were utilized to build QSAR models forecasting the likelihood of DDIs for any pair of drug molecules. Our models showed balanced accuracy of 72%-79% for the external test sets with the coverage of 81.36%-100% when the conservative threshold for model applicability domain was applied. We generated virtually all possible binary combinations of marketed drugs and employed our models to identify drug pairs predicted to be instances of DDI. More than 4,500 of these predicted DDIs that were not found in our training sets were confirmed by data from the DrugBank database.