Optimal experimental designs for detecting departures from additivity in drug/chemical mixtures

There are many situations for which the detection and characterization of the nature of the interaction between mixtures/combinations of drugs or chemicals is important. Thus, there is a need for methodology to detect interactions among the drugs or chemicals. Also of importance is the consideration of experimental design when studying mixtures/combinations of drugs/chemicals. The traditional approach to estimate and test for interactions among multiple drugs/chemicals in a statistical model involves response surface methodology (RSM), often supported by factorial designs. Although such an approach permits the investigation of both the effects of individual chemicals and their interactions, the number of design points needed to study the chemical mixtures becomes prohibitive when the number of compounds increases. Fixed ratio ray designs have been developed to reduce the amount of experimental effort when interest can be restricted to a specific ray. We focus on the design and analysis issues involved in studying mixtures/combinations of compounds along a fixed ratio ray of the drug/chemical. To obtain the inference regarding the interactions among the drugs/chemicals, it is shown that the only data required are those along the fixed ratio ray.