Semiparametric mixed-effects analysis of PK/PD models using differential equations

Motivated by the use of semiparametric nonlinear mixed-effects modeling on longitudinal data, we develop a new semiparametric modeling approach to address potential structural model misspecification for population pharmacokinetic/ pharmacodynamic (PK/PD) analysis. Specifically, we use a set of ordinary differential equations (ODEs) with form dx/dt = A(t)x + B(t) where B(t) is a nonparametric function that is estimated using penalized splines. The inclusion of a nonparametric function in the ODEs makes identification of structural model misspecification feasible by quantifying the model uncertainty and provides flexibility for accommodating possible structural model deficiencies. The resulting model will be implemented in a nonlinear mixed-effects modeling setup for population analysis. We illustrate the method with an application to cefamandole data and evaluate its performance through simulations.