Sample reuse simulation in optimal design for Tmax in pharmacokinetic experiments

T max and Cmax are important pharmacokinetic parameters in drug development processes. Often a nonparametric procedure is needed to estimate them when model independence is required. This paper proposes a simulation‐based optimal design procedure for finding optimal sampling times for nonparametric estimates of Tmax and Cmax for each subject, assuming that the drug concentration follows a non‐linear mixed model. The main difficulty of using standard optimal design procedures is that the property of the nonparametric estimate is very complicated. This procedure uses a sample reuse simulation to calculate the design criterion, which is an integral of multiple dimension, so that effective optimization procedures such as Newton‐type procedures can be used directly to find optimal designs. This procedure is used to construct optimal designs for an open one‐compartment model. An approximation based on the Taylor expansion is also derived and showed results that were consistent with those based on the sample reuse simulation.