Studying and understanding the joint effect of combined treatments is important in pharmacology and in the development of combination therapies. The Loewe additivity model is one of the best general reference models for evaluating drug interactions. Based on this model, synergy occurs when the interaction index is less than one, while antagonism occurs when interaction index is greater than one. We expanded the meaning of the interaction index, and propose a procedure to calculate the interaction index and its associated confidence interval under the assumption that the dose-effect curve for a single agent follows Chou and Talalay's median effect equation. In addition, we review four response surface models based on the Loewe additivity model using a single parameter to determine drug interactions. We describe each of these models in the context of Loewe additivity model and discuss their relative advantages and disadvantages. We also provide S-PLUS/R code for each approach to facilitate the implementation of these commonly used methods.