Testing for synergism over a range of fixed ratio drug combinations: replacing the isobologram

An isobologram is a Cartesian plot of pairs of doses that, in combination, yield a specified level of effect. It is a convenient and presently popular way of graphically displaying results of drug-combination and similar studies, because paired values of experimental points that fall below or above the line connecting the axial points (usually ED50 values) denote supra- and sub-additive combinations, respectively. However, an isobologram does not fulfill the criteria for standard least squares regression analysis. It is thus less useful for addressing questions related to the range of combination ratios over which synergy occurs. We describe herein a substitute for the isobologram in which log(total-dose) is plotted against the proportion of a component in a combination. One advantage is that a nonlinear curve-fitting procedure and determination of the confidence interval of a single parameter allow the determination of departure from additivity over a range of fixed proportion mixtures. An example is given of the combination of two analgesics (acetaminophen and tramadol hydrochloride). Another advantage of the new method is the reduction of animal use.