Statistical analysis of drug-drug and site-site interactions with isobolograms

The use of more than one drug to achieve a desired effect has been a common practice in pharmacologic testing and in clinical practice. For example, combinations of analgesics are frequently prescribed with a view to enhancing pain relief and reducing adverse effects. It is also well established that administration of more than one drug may give effects that are greater than, or less than, the additive effect of each drug given individually. A non-mechanistic method of characterizing the effect resulting from the administration of two compounds is the isobologram. It is relatively simple to draw and interpret isobolograms. However, this graphical technique, which employs equieffective concentrations of individual drugs and combinations of these, obtains the concentrations as random variables from concentration-effect data, usually transformed to a parallel line assay. Thus, statistical confidence limits from such assays, as well as from non-parallel designs, must be expressed on the isobologram if this diagram is to establish superadditive, subadditive, or merely additive effects. We now present a detailed statistical analysis of the isobolographic method illustrated with examples of the statistical procedures, a rational basis for selecting proportions of each drug in the combination, and a relatively novel application of the isobolographic concept, i.e., interactions involving different anatomical sites.