Using Stochastic Differential Equations for PK/PD Model Development

A method for PK/PD model development based on stochastic differential equation models is proposed. The new method has a number of advantages compared to conventional methods. In particular, the new method avoids the exhaustive trial-and-error based search often conducted to determine the most appropriate model structure, because it allows information about the appropriate model structure to be extracted directly from data. This is accomplished through quantification of the uncertainty of the individual parts of an initial model, by means of which tools for performing model diagnostics can be constructed and guidelines for model improvement provided. Furthermore, the new method allows time-variations in key parameters to be tracked and visualized graphically, which allows important functional relationships to be revealed. Using simulated data, the performance of the new method is demonstrated by means of two examples. The first example shows how, starting from a simple assumption of linear PK, the method can be used to determine the correct nonlinear model for describing the PK of a drug following an oral dose. The second example shows how, starting from a simple assumption of no drug effect, the method can be used to determine the correct model for the nonlinear effect of a drug with known PK in an indirect response model.