Mathematical formulation of additivity for antimicrobial agents

The ability to describe and quantify pharmacodynamic interaction objectively is of paramount importance in the study of combination chemotherapy. Current methods based on Loewe additivity and Bliss independence are associated with implicit assumptions of the interacting system. We reviewed the hyperplane theorem that used a generalized equation for defining the isobols (surfaces of equal effect) for 2 noninteracting drugs. We showed that under certain conditions, the original equation might lead to nonintuitive results, which were inconsistent with the definition of additivity. To circumvent these limitations, an alternative model for defining additivity based on effect summation is proposed. This alternative definition for isobols deviates from the Loewe additivity, the null interaction criterion used as the foundation for Berenbaum's isobol equation. However, its results are simple, easily interpreted, and may be more applicable to a wide variety of clinical and experimental circumstances.