Confidence Intervals of Interaction Index for Assessing Multiple Drug Interaction

Studies of interactions among biologically active agents have become increasingly important in many branches of biomedical research. We consider that the Loewe additivity model is one of the best general reference models for defining drug interactions. Based on the Loewe additivity model, synergy occurs when the interaction index is less than one, and antagonism occurs when interaction index is greater than one. Starting from the Loewe additivity model and the marginal dose-effect curve for each drug involved in a combination, we first present a procedure to estimate the interaction index and its associated confidence interval at a combination dose with observed effects. Following Chou and Talalay's method for assessing drug interaction based on the plot of interaction indices versus effects for combination doses at a fixed ray, we then construct a pointwise (1-alpha) x 100% confidence bound for the curve of interaction indices versus effects. We found that these methods work better on the logarithm transformed scale than on the untransformed scale of the interaction index. We provide simulations and case studies to illustrate the performances of these two procedures, and present their pros and cons. We also provide S-Plus/R code to facilitate the implementation of these two procedures.