Diagnostics for confounding in PK/PD models for oxcarbazepine

One type of pharmacokinetic/pharmacodynamic (PK/PD) relationship that is used to characterize the therapeutic action of a drug is the relationship between some univariate summary of the plasma-concentration-versus-time profile and the drug effect on a response outcome. Operationally, such a relationship may be observed in a large clinical trial where randomly sampled patients are randomized to different values of the concentration summary. If, under such conditions, the relationship between concentration and effect does not depend on the dose needed to attain the target concentration, such a relationship will be called a true PK/PD relationship. When the true PK/PD relationship is assessed as an object of estimation in a dose-controlled clinical trial (i.e. when dose is randomized), observed drug concentration is an outcome variable. The estimated PK/PD relationship between observed outcome and observed concentration, which we then refer to as the conventional PK/PD relationship, may be biased for the true PK/PD relationship. Because of this bias, the conventional relationship is called confounded for the true one. We show that diagnostics for confounding can be devised under reasonable assumptions. We then apply these diagnostics to PK/PD assessments of adults and children on oxcarbazepine adjunctive therapy. It was necessary to demonstrate the similarity of the true PK/PD relationships of adults and children on adjunctive therapy in order to support the approval of oxcarbazepine monotherapy in children by a bridging argument.