Isobolographic characterization of drug interactions incorporating biological variability

Isobolograms have been widely used to characterize the nature of the interaction between combinations of drugs or chemicals. Some authors have applied this technique without accounting for the variability in the data or without adjusting for multiple comparisons to the line of additivity. This paper develops a graphical procedure which takes into account the variability of the data and which maintains favorable statistical properties. The isobolographic procedure utilized is illustrated by using three classical pharmacological drug combinations in female ICR mice. An additive relationship is illustrated with the loss of righting reflex after combinations of doses of sodium hexobarbital with itself. An antagonistic relationship is illustrated with the protection by mecamylamine of nicotine-induced lethality. A synergistic relationship is illustrated with the loss of righting reflex after combinations of ethanol and chloral hydrate. The procedure's statistical properties (level of significance and power) were determined using a simulation study. The isobolographic procedures developed here are applicable for quantal, continuous and count data. These procedures are applicable for identifying beneficial drug combinations, or conversely, identifying hazards resulting from exposure to multiple toxicants.