Method to Assess Interactivity of Drugs with Nonparallel Concentration Effect Relationships

Background: Commonly used methods for analyzing interactivity between drugs (e.g. synergy, antagonism) such as isobologram, combination index, and curve shift are based on the Loewe Additivity principle of dose equivalence and the inherent assumption of similar concentration- effect (C-E) including parallel curves and equal maximum effects (E-max), and therefore are not suitable for drugs with dissimilar C-E. This study describes a new method that is without this limitation and has the additional advantage of enabling statistical analysis. Methods and Results: The method comprises two steps. First, based on the dose equivalence principle, the experimentally obtained C-E of one drug was used to calculate the equally effective C-E of the other drug at no interactivity; the resulting two zero-interactivity C-E formed the upper and lower boundaries of Additivity Envelope. Next, 95% confidence intervals calculated from experimental data were added to Additivity Envelope to obtain Uncertainty Envelope (UE). Experimentally observed effects of drug combinations (C-E-comb,E- observed) located within UE indicate additivity whereas C-E-comb,E- observed located above or below UE indicate statistically significant (p<0.05) synergy or antagonism, respectively. Additional in silico studies demonstrated the shape and size of Additivity Envelope, which determines the ability to detect drug interactivity, depended on the Drug A-to-B concentration ratios and the ratios of their C-E curve shape parameter. Analyses of experimental results of combinations of drugs with nonparallel C-E and/or unequal E-max indicated UE as more versatile and provided more information, compared to earlier methods. Conclusion: UE is a broadly applicable method for analysis, including statistical significance assessment, of drug interactivity.