Combinations of common drugs may, when taken together, have unexpected effects on diseases like cancer. It is not feasible to test for all combination drug effects in clinical trials, but in the real world, drugs are frequently taken in combination. Then, there may be undiscovered effects protecting users of drug combinations from cancer--or increasing their risk. By analyzing health claims data containing numerous people exposed to drug combinations, we have an opportunity to evaluate the association of drug combinations with cancer risk. Discovering these effects can not only contribute to prevention of cancer, but also suggest new clinical uses for drug combinations to prevent or treat cancer. Here we describe new methods for discovery of drug combination effects on cancer. Our approach emulates a randomized trial where one arm would have been assigned to take a drug alone, while the other arm takes the drug together with a second drug. Because discovery of associations from observational data is prone to spurious results due to confounding, we develop a number of strategies to distinguish confounding from biomedically relevant findings.