Optimal experimental designs for estimating the drug combination index in toxicology

When studying combination treatments made up of different substances, the interaction of these treatments is of primary research interest. One way to express the interaction is through a combination index τ based on Loewe additivity. Regarding the statistical optimal design of trials to estimate τ, the problem generally corresponds to a c-optimality design problem. Unfortunately, c-optimal designs have several practical problems, commonly including an inability to also estimate the underlying dose-response parameters in the same trial. It is demonstrated how optimal designs for combination indices can be generated as well as how these designs can be adapted to guarantee that at least a satisfactory degree of precision can be maintained for all parameter estimates. This is achieved by introducing secondary constraints on efficiency regarding the D-criterion, and optimizing within these constraints only. All of the proposals are demonstrated using a practical toxicological example. Furthermore, it is also investigated how the performance of the proposed designs is affected by misspecifications regarding the a priori parameter assumptions used to generate the designs.