Graphical Methods for Analysing Combination Effects in Dose-Response Experiments

An organbath experiment with bovine tracheal muscle strips with cumulative increases in concentrations of a substance A in the absence and presence of a fixed concentration of a second substance B is considered as an example for demonstrating graphical methods to analyse drug combination effects. The response of each strip is individually described and estimated by a nonlinear dose response curve. From the curves of the combined action theoretical curves of substance A are derived, which were expected if the combination effect was simple similar or independent, respectively. The first graphical method consists in comparing the derived curves for substance A with the curves for substance A directly fitted. It is cheeked by eye if the group of derived curves can clearly be distinguished from the group of directly fitted curves. The second graphical method differs from the first method in so far, as not the curves are visualized but the parameter vectors corresponding to them. In contrast to widely used analytical methods the proposed graphical methods allow to treat individual instead of averaged dose response relationships. The methods can help to decide if the combination effect may be considered as independent, simple similar or none of both.