Optimal Sampling Times in Bioequivalence Studies Using a Simulated Annealing Algorithm

In pharmacokinetic (PK) studies, blood samples are taken over time on subjects after the administration of a drug to measure the time-course of the plasma drug concentrations. In bioequivalence studies, the trapezoidal rule on the sampled time points is often used to estimate the area under the plasma concentration-time curve, a quantity of principle interest. This manuscript investigates the choice of sampling time points to estimate the area under the curve. In particular, we explore the relative merits of several objective functions, those functions which are minimized with respect to the sampling times to obtain an optimal study design. We propose an objective function which overcomes some of the deficits of existing choices. We also present a simulated annealing algorithm to perform the minimization. The main benefits of the simulated annealing algorithm are the ease in which it can handle constraints on the sampling schedules and its ability to accommodate a variety of models and objective functions. The manuscript presents optimal sampling times for some key examples of true underlying models.