A generalized response surface model with varying relative potency for assessing drug interaction

When multiple drugs are administered simultaneously, investigators are often interested in assessing whether the drug combinations are synergistic, additive, or antagonistic. Based on the Loewe additivity reference model, many existing response surface models require constant relative potency and some of them use a single parameter to capture synergy, additivity, or antagonism. However, the assumption of constant relative potency is too restrictive, and these models using a single parameter to capture drug interaction are inadequate to describe the phenomenon when synergy, additivity, and antagonism are interspersed in different regions of drug combinations. We propose a generalized response surface model with a function of doses instead of one single parameter to identify and quantify departure from additivity. The proposed model can incorporate varying relative potencies among multiple drugs as well. Examples and simulations are given to demonstrate that the proposed model is effective in capturing different patterns of drug interaction.