The Bliss independence model is widely used to analyze drug combination data when screening for candidate drug combinations. The method compares the observed combination response (Y_O) with the predicted combination response (Y_P), which was obtained based on the assumption that there is no effect from drug-drug interactions. Typically, the combination effect is declared synergistic if Y_O is greater than Y_P. However, this method lacks statistical rigor because it does not take into account the variability of the response measures and can frequently cause false-positive claims. In this article, we introduce a two-stage response surface model to describe the drug interaction across all dose combinations tested. This new method enables robust statistical testing for synergism at any dose combination, thus reducing the risk of false positives. The use of the method is illustrated through an application describing statistically significant “synergy regions” for candidate drug combinations targeting epidermal growth factor receptor and the insulin-like growth factor 1 receptor.