Keywords: dose-response surface, interaction, geometry, curvature
When studying the effect of combination therapy under different dose combinations, Bliss independence and Loewe additivity are the two most widely accepted quantitative methods inferring whether the combined action of multiple drugs or agents exhibits any form of interaction (synergistic or antagonistic) or is purely independent (or additive). Similarities and distinctions between these two concepts have been analyzed thoroughly in previous works. However, the connection of these methods to the geometric properties of the multidimensional dose-response surface has been rarely explored. We will fill in such gap and motivate a curvature-based statistic to define synergism or antagonism. The large-sample properties of such statistic are derived and simulation/real data analysis are performed to demonstrate the utility of the curvature-based statistic.