Drug interaction: focusing on response surface models

Anesthesiologists have been aware of the importance of optimal drug combination long ago and performed many investigations about the combined use of anesthetic agents. There are 3 classes of drug interaction: additive, synergistic, and antagonistic. These definitions of drug interaction suggest that a zero interaction model should exist to be used as a reference in classifying the interaction of drug combinations. The Loewe additivity has been used as a universal reference model for classifying drug interaction. Most anesthetic drugs follow the sigmoid E(max) model (Hill equation); this model will be used for modeling response surface. Among lots of models for drug interaction in the anesthetic area, the Greco model, Machado model, Plummer model, Carter model, Minto model, Fidler model, and Kong model are adequate to be applied to the data of anesthetic drug interaction. A model with a single interaction parameter does not accept an inconsistency in the classes of drug interactions. To solve this problem, some researchers proposed parametric models which have a polynomial interaction function to capture synergy, additivity, and antagonism scattered all over the surface of drug combinations. Inference about truth must be based on an optimal approximating model. Akaike information criterion (AIC) is the most popular approach to choosing the best model among the aforementioned models. Whatever the good qualities of a chosen model, it is uncertain whether the chosen model is the best model. A more robust inference can be extracted from averaging several models that are considered relevant.