Experiment design for nonparametric models based on minimizing Bayes Risk: application to voriconazole

An experimental design approach is presented for individualized therapy in the special case where the prior information is specified by a nonparametric (NP) population model. Here, a NP model refers to a discrete probability model characterized by a finite set of support points and their associated weights. An important question arises as to how to best design experiments for this type of model. Many experimental design methods are based on Fisher information or other approaches originally developed for parametric models. While such approaches have been used with some success across various applications, it is interesting to note that they largely fail to address the fundamentally discrete nature of the NP model. Specifically, the problem of identifying an individual from a NP prior is more naturally treated as a problem of classification, i.e., to find a support point that best matches the patient's behavior. This paper studies the discrete nature of the NP experiment design problem from a classification point of view. Several new insights are provided including the use of Bayes Risk as an information measure, and new alternative methods for experiment design. One particular method, denoted as MMopt (multiple-model optimal), will be examined in detail and shown to require minimal computation while having distinct advantages compared to existing approaches. Several simulated examples, including a case study involving oral voriconazole in children, are given to demonstrate the usefulness of MMopt in pharmacokinetics applications.