Efficient trial design for eliciting a pharmacokinetic-pharmacodynamic model-based response surface describing the...

The authors published a pharmacokinetic- pharmacodynamic model for two drugs based on response surface methodology. Because of the complexity of the model, they performed a simulation study to answer two questions about use of the model: (1) which study design would be most satisfactory; and (2) how many patients would need to be studied to adequately describe an entire response surface.

Data were simulated using realistic variability for two hypothetical intravenous anesthetic drugs that interact synergistically and that could be given by computer-controlled infusion. Three trial designs were simulated, one that made a series of parallel slices of the response surface, one that crisscrossed the response surface, and one that made a series of radial slices across the surface. Series of 5, 10, 20, and 40 "subjects" were simulated. A pooled data approach was used to assess the ability of the various trial designs and numbers of subjects to adequately identify the interaction response surface and estimate the original response surface.

The crisscross design was shown to be the most robust in terms of its ability to both discriminate the correct order of the interaction term and to discriminate the original response surface using the least number of patients. Twenty subjects would be required to adequately define a surface using the crisscross study design, and 40 subjects would be required using the other trial designs.

The results showed that a number of trial designs would be viable, but a design that crossed the surface in a crisscross fashion would give the most robust result with the least patients.