In cancer, mutually exclusive or co-occurring somatic alterations across genes can suggest functional interactions. Existing tests for such patterns make the unrealistic assumption of identical gene alteration probabilities across tumors. We present Discrete Independence Statistic Controlling for Observations with Varying Event Rates (DISCOVER), a novel test that is more sensitive than other methods and controls its false positive rate. A pan-cancer analysis using DISCOVER finds no evidence for widespread co-occurrence, and most co-occurrences previously detected do not exceed expectation by chance. Many mutual exclusivities are identified involving well-known genes related to cell cycle and growth factor signaling, as well as lesser known regulators of Hedgehog signaling.@en