Mathematical models of complex dose-response relationships: implications for experimental design in psychopharmacologic research.

We develop a mathematical model to account for the complex relationship between drug dose and clinical response in psychopharmacologic research. The model specifies relationships among drug dose, drug bioavailability, pharmacokinetic factors, course moderators, clinical response and the heterogeneity of the disorder, and allows for the derivation of results that have implications for experimental design in psychopharmacologic research. These results form the basis for computer simulations which indicate that random assignment to two fixed doses is more powerful and less sensitive to heterogeneity than assignment to clinically determined doses. Fixed dose designs, however, tend to overestimate the magnitude of drug bioavailability-clinical response relationships. Clinically determined dose designs are useful in some experimental situations; their effectiveness is enhanced by systematically reducing the clinically determined dose. Larger dose reductions improve the ability to detect bioavailability-clinical response relationships.